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Diffstat (limited to 'hacks/glx/polytopes.c')
| -rw-r--r-- | hacks/glx/polytopes.c | 3189 |
1 files changed, 3189 insertions, 0 deletions
diff --git a/hacks/glx/polytopes.c b/hacks/glx/polytopes.c new file mode 100644 index 0000000..76c1287 --- /dev/null +++ b/hacks/glx/polytopes.c @@ -0,0 +1,3189 @@ +/* polytopes --- Shows one of the six regular polytopes rotating in 4d */ + +#if 0 +static const char sccsid[] = "@(#)polytopes.c 1.2 05/09/28 xlockmore"; +#endif + +/* Copyright (c) 2003-2009 Carsten Steger <carsten@mirsanmir.org>. */ + +/* + * Permission to use, copy, modify, and distribute this software and its + * documentation for any purpose and without fee is hereby granted, + * provided that the above copyright notice appear in all copies and that + * both that copyright notice and this permission notice appear in + * supporting documentation. + * + * This file is provided AS IS with no warranties of any kind. The author + * shall have no liability with respect to the infringement of copyrights, + * trade secrets or any patents by this file or any part thereof. In no + * event will the author be liable for any lost revenue or profits or + * other special, indirect and consequential damages. + * + * REVISION HISTORY: + * C. Steger - 03/08/10: Initial version + * C. Steger - 05/09/28: Added trackball support + * C. Steger - 07/01/23: Improved 4d trackball support + * C. Steger - 09/08/23: Removed check-config.pl warnings + */ + +/* + * This program shows one of the six regular 4D polytopes rotating in 4D. + * Written by Carsten Steger, inspired by H.S.M Coxeter's book "Regular + * Polytopes", 3rd Edition, Dover Publications, Inc., 1973, and Thomas + * Banchoff's book "Beyond the Third Dimension: Geometry, Computer + * Graphics, and Higher Dimensions", Scientific American Library, 1990. + */ + +#ifndef M_PI +#define M_PI 3.14159265358979323846 +#endif + +#define SQRT15OVER4 1.93649167310370844259 /* sqrt(15/4) */ +#define SQRT10OVER3 1.82574185835055371152 /* sqrt(10/3) */ +#define SQRT5OVER2 1.58113883008418966600 /* sqrt(5/2) */ +#define SQRT5OVER6 0.91287092917527685576 /* sqrt(5/6) */ +#define SQRT5OVER12 0.64549722436790281420 /* sqrt(5/12) */ +#define SQRT2 1.41421356237309504880 /* sqrt(2) */ +#define GOLDEN 1.61803398874989484820 /* (sqrt(5)+1)/2 */ +#define GOLDENINV 0.61803398874989484820 /* (sqrt(5)-1)/2 */ +#define SQRT2INV 0.70710678118654752440 /* sqrt(1/2) */ +#define GOLDEN2 1.14412280563536859520 /* ((sqrt(5)+1)/2)/sqrt(2) */ +#define GOLDENINV2 0.43701602444882107080 /* ((sqrt(5)-1)/2)/sqrt(2) */ +#define GOLDEN22 1.85122958682191611960 /* (((sqrt(5)+1)/2)^2)/sqrt(2) */ +#define GOLDENINV22 0.27009075673772645360 /* (((sqrt(5)-1)/2)^2)/sqrt(2) */ + +#define DISP_WIREFRAME 0 +#define DISP_SURFACE 1 +#define DISP_TRANSPARENT 2 + +#define POLYTOPE_RANDOM -1 +#define POLYTOPE_5_CELL 0 +#define POLYTOPE_8_CELL 1 +#define POLYTOPE_16_CELL 2 +#define POLYTOPE_24_CELL 3 +#define POLYTOPE_120_CELL 4 +#define POLYTOPE_600_CELL 5 +#define POLYTOPE_LAST_CELL POLYTOPE_600_CELL + +#define COLORS_SINGLE 0 +#define COLORS_DEPTH 1 + +#define DISP_3D_PERSPECTIVE 0 +#define DISP_3D_ORTHOGRAPHIC 1 + +#define DISP_4D_PERSPECTIVE 0 +#define DISP_4D_PERSPECTIVE_STR "0" +#define DISP_4D_ORTHOGRAPHIC 1 +#define DISP_4D_ORTHOGRAPHIC_STR "1" + +#define DEF_DISPLAY_MODE "transparent" +#define DEF_POLYTOPE "random" +#define DEF_COLORS "depth" +#define DEF_PROJECTION_3D "perspective" +#define DEF_PROJECTION_4D "perspective" +#define DEF_SPEEDWX "1.1" +#define DEF_SPEEDWY "1.3" +#define DEF_SPEEDWZ "1.5" +#define DEF_SPEEDXY "1.7" +#define DEF_SPEEDXZ "1.9" +#define DEF_SPEEDYZ "2.1" + +#ifdef STANDALONE +# define DEFAULTS "*delay: 25000 \n" \ + "*showFPS: False \n" \ + "*suppressRotationAnimation: True\n" \ + +# define free_polytopes 0 +# define release_polytopes 0 +# include "xlockmore.h" /* from the xscreensaver distribution */ +#else /* !STANDALONE */ +# include "xlock.h" /* from the xlockmore distribution */ +#endif /* !STANDALONE */ + +#ifdef USE_GL + +#ifndef HAVE_JWXYZ +# include <X11/keysym.h> +#endif +#include "gltrackball.h" + + +#ifdef USE_MODULES +ModStruct polytopes_description = +{"polytopes", "init_polytopes", "draw_polytopes", NULL, + "draw_polytopes", "change_polytopes", NULL, &polytopes_opts, + 25000, 1, 1, 1, 1.0, 4, "", + "Shows one of the six regular 4d polytopes rotating in 4d", 0, NULL}; + +#endif + + +static char *mode; +static int display_mode; +static char *poly_str; +static int polytope; +static char *color_str; +static int color_mode; +static char *proj_3d; +static int projection_3d; +static char *proj_4d; +static int projection_4d; +static float speed_wx; +static float speed_wy; +static float speed_wz; +static float speed_xy; +static float speed_xz; +static float speed_yz; + +static const float offset4d[4] = { 0.0, 0.0, 0.0, 3.0 }; +static const float offset3d[4] = { 0.0, 0.0, -2.0, 0.0 }; + + +static XrmOptionDescRec opts[] = +{ + {"-mode", ".displayMode", XrmoptionSepArg, 0 }, + {"-wireframe", ".displayMode", XrmoptionNoArg, "wireframe" }, + {"-surface", ".displayMode", XrmoptionNoArg, "surface" }, + {"-transparent", ".displayMode", XrmoptionNoArg, "transparent" }, + {"-polytope", ".polytope", XrmoptionSepArg, 0 }, + {"-random", ".polytope", XrmoptionNoArg, "random" }, + {"-5-cell", ".polytope", XrmoptionNoArg, "5-cell" }, + {"-8-cell", ".polytope", XrmoptionNoArg, "8-cell" }, + {"-16-cell", ".polytope", XrmoptionNoArg, "16-cell" }, + {"-24-cell", ".polytope", XrmoptionNoArg, "24-cell" }, + {"-120-cell", ".polytope", XrmoptionNoArg, "120-cell" }, + {"-600-cell", ".polytope", XrmoptionNoArg, "600-cell" }, + {"-single-color", ".colors", XrmoptionNoArg, "single" }, + {"-depth-colors", ".colors", XrmoptionNoArg, "depth" }, + {"-perspective-3d", ".projection3d", XrmoptionNoArg, "perspective" }, + {"-orthographic-3d", ".projection3d", XrmoptionNoArg, "orthographic" }, + {"-perspective-4d", ".projection4d", XrmoptionNoArg, "perspective" }, + {"-orthographic-4d", ".projection4d", XrmoptionNoArg, "orthographic" }, + {"-speed-wx", ".speedwx", XrmoptionSepArg, 0 }, + {"-speed-wy", ".speedwy", XrmoptionSepArg, 0 }, + {"-speed-wz", ".speedwz", XrmoptionSepArg, 0 }, + {"-speed-xy", ".speedxy", XrmoptionSepArg, 0 }, + {"-speed-xz", ".speedxz", XrmoptionSepArg, 0 }, + {"-speed-yz", ".speedyz", XrmoptionSepArg, 0 } +}; + +static argtype vars[] = +{ + { &mode, "displayMode", "DisplayMode", DEF_DISPLAY_MODE, t_String }, + { &poly_str, "polytope", "Polytope", DEF_POLYTOPE, t_String }, + { &color_str, "colors", "Colors", DEF_COLORS, t_String }, + { &proj_3d, "projection3d", "Projection3d",DEF_PROJECTION_3D, t_String }, + { &proj_4d, "projection4d", "Projection4d",DEF_PROJECTION_4D, t_String }, + { &speed_wx, "speedwx", "Speedwx", DEF_SPEEDWX, t_Float}, + { &speed_wy, "speedwy", "Speedwy", DEF_SPEEDWY, t_Float}, + { &speed_wz, "speedwz", "Speedwz", DEF_SPEEDWZ, t_Float}, + { &speed_xy, "speedxy", "Speedxy", DEF_SPEEDXY, t_Float}, + { &speed_xz, "speedxz", "Speedxz", DEF_SPEEDXZ, t_Float}, + { &speed_yz, "speedyz", "Speedyz", DEF_SPEEDYZ, t_Float} +}; + +static OptionStruct desc[] = +{ + { "-wireframe", "display the polytope as a wireframe mesh" }, + { "-surface", "display the polytope as a solid surface" }, + { "-transparent", "display the polytope as a transparent surface" }, + { "-solid", "display the polytope as a solid object" }, + { "-bands", "display the polytope as see-through bands" }, + { "-twosided", "display the polytope with two colors" }, + { "-colorwheel", "display the polytope with a smooth color wheel" }, + { "-perspective-3d", "project the polytope perspectively from 3d to 2d" }, + { "-orthographic-3d", "project the polytope orthographically from 3d to 2d"}, + { "-perspective-4d", "project the polytope perspectively from 4d to 3d" }, + { "-orthographic-4d", "project the polytope orthographically from 4d to 3d"}, + { "-speed-wx <arg>", "rotation speed around the wx plane" }, + { "-speed-wy <arg>", "rotation speed around the wy plane" }, + { "-speed-wz <arg>", "rotation speed around the wz plane" }, + { "-speed-xy <arg>", "rotation speed around the xy plane" }, + { "-speed-xz <arg>", "rotation speed around the xz plane" }, + { "-speed-yz <arg>", "rotation speed around the yz plane" } +}; + +ENTRYPOINT ModeSpecOpt polytopes_opts = +{sizeof opts / sizeof opts[0], opts, sizeof vars / sizeof vars[0], vars, desc}; + + +/* 5-cell {3,3,3} */ +#define NUM_VERT_5 5 +#define NUM_EDGE_5 10 +#define NUM_FACE_5 10 +#define VERT_PER_FACE_5 3 + +#define MIN_EDGE_DEPTH_5 (-0.5) +#define MAX_EDGE_DEPTH_5 0.75 +#define MIN_FACE_DEPTH_5 (-0.5) +#define MAX_FACE_DEPTH_5 (1.0/3.0) + + +/* 8-cell {4,3,3} */ +#define NUM_VERT_8 16 +#define NUM_EDGE_8 32 +#define NUM_FACE_8 24 +#define VERT_PER_FACE_8 4 + +#define MIN_EDGE_DEPTH_8 (-1.0) +#define MAX_EDGE_DEPTH_8 1.0 +#define MIN_FACE_DEPTH_8 (-1.0) +#define MAX_FACE_DEPTH_8 1.0 + +/* 16-cell {3,3,4} */ +#define NUM_VERT_16 8 +#define NUM_EDGE_16 24 +#define NUM_FACE_16 32 +#define VERT_PER_FACE_16 3 + +#define MIN_EDGE_DEPTH_16 (-1.0) +#define MAX_EDGE_DEPTH_16 1.0 +#define MIN_FACE_DEPTH_16 (-2.0/3.0) +#define MAX_FACE_DEPTH_16 (2.0/3.0) + + +/* 24-cell {3,4,3} */ +#define NUM_VERT_24 24 +#define NUM_EDGE_24 96 +#define NUM_FACE_24 96 +#define VERT_PER_FACE_24 3 + +#define MIN_EDGE_DEPTH_24 (-SQRT2) +#define MAX_EDGE_DEPTH_24 SQRT2 +#define MIN_FACE_DEPTH_24 (-SQRT2) +#define MAX_FACE_DEPTH_24 SQRT2 + + +/* 120-cell {5,3,3} */ +#define NUM_VERT_120 600 +#define NUM_EDGE_120 1200 +#define NUM_FACE_120 720 +#define VERT_PER_FACE_120 5 + +#define MIN_EDGE_DEPTH_120 (-GOLDEN22) +#define MAX_EDGE_DEPTH_120 GOLDEN22 +#define MIN_FACE_DEPTH_120 (-GOLDEN22) +#define MAX_FACE_DEPTH_120 GOLDEN22 + + +/* 600-cell {3,3,5} */ +#define NUM_VERT_600 120 +#define NUM_EDGE_600 720 +#define NUM_FACE_600 1200 +#define VERT_PER_FACE_600 3 + +#define MIN_EDGE_DEPTH_600 (-GOLDEN/2.0-1) +#define MAX_EDGE_DEPTH_600 (GOLDEN/2.0+1) +#define MIN_FACE_DEPTH_600 ((-2*GOLDEN-2)/3.0) +#define MAX_FACE_DEPTH_600 ((2*GOLDEN+2)/3.0) + + +typedef struct { + GLint WindH, WindW; + GLXContext *glx_context; + /* 4D rotation angles */ + float alpha, beta, delta, zeta, eta, theta; + /* Aspect ratio of the current window */ + float aspect; + /* Counter */ + int tick, poly; + /* Trackball states */ + trackball_state *trackballs[2]; + int current_trackball; + Bool button_pressed; + + float edge_color_5[NUM_EDGE_5][4]; + float face_color_5[NUM_FACE_5][4]; + float face_color_trans_5[NUM_FACE_5][4]; + + float edge_color_8[NUM_EDGE_8][4]; + float face_color_8[NUM_FACE_8][4]; + float face_color_trans_8[NUM_FACE_8][4]; + + float edge_color_16[NUM_EDGE_16][4]; + float face_color_16[NUM_FACE_16][4]; + float face_color_trans_16[NUM_FACE_16][4]; + + float edge_color_24[NUM_EDGE_24][4]; + float face_color_24[NUM_FACE_24][4]; + float face_color_trans_24[NUM_FACE_24][4]; + + float edge_color_120[NUM_EDGE_120][4]; + float face_color_120[NUM_FACE_120][4]; + float face_color_trans_120[NUM_FACE_120][4]; + + float edge_color_600[NUM_EDGE_600][4]; + float face_color_600[NUM_FACE_600][4]; + float face_color_trans_600[NUM_FACE_600][4]; + + float speed_scale; + +} polytopesstruct; + +static polytopesstruct *poly = (polytopesstruct *) NULL; + + +/* Vertex, edge, and face data for the six regular polytopes. All the + polytopes are constructed with coordinates chosen such that their 4d + circumsphere has a radius of 2. */ + +static const float vert_5[NUM_VERT_5][4] = { + { -SQRT5OVER2, -SQRT5OVER6, -SQRT5OVER12, -0.5 }, + { SQRT5OVER2, -SQRT5OVER6, -SQRT5OVER12, -0.5 }, + { 0.0, SQRT10OVER3, -SQRT5OVER12, -0.5 }, + { 0.0, 0.0, SQRT15OVER4, -0.5 }, + { 0.0, 0.0, 0.0, 2.0 } +}; + +static const int edge_5[NUM_EDGE_5][2] = { + { 0, 1 }, { 0, 2 }, { 0, 3 }, { 0, 4 }, { 1, 2 }, { 1, 3 }, { 1, 4 }, + { 2, 3 }, { 2, 4 }, { 3, 4 } +}; + +static const int face_5[NUM_FACE_5][VERT_PER_FACE_5] = { + { 0, 1, 2 }, { 0, 1, 3 }, { 0, 1, 4 }, { 0, 2, 3 }, { 0, 2, 4 }, { 0, 3, 4 }, + { 1, 2, 3 }, { 1, 2, 4 }, { 1, 3, 4 }, { 2, 3, 4 } +}; + + +static const float vert_8[NUM_VERT_8][4] = { + { -1.0, -1.0, -1.0, -1.0 }, { 1.0, -1.0, -1.0, -1.0 }, + { -1.0, 1.0, -1.0, -1.0 }, { 1.0, 1.0, -1.0, -1.0 }, + { -1.0, -1.0, 1.0, -1.0 }, { 1.0, -1.0, 1.0, -1.0 }, + { -1.0, 1.0, 1.0, -1.0 }, { 1.0, 1.0, 1.0, -1.0 }, + { -1.0, -1.0, -1.0, 1.0 }, { 1.0, -1.0, -1.0, 1.0 }, + { -1.0, 1.0, -1.0, 1.0 }, { 1.0, 1.0, -1.0, 1.0 }, + { -1.0, -1.0, 1.0, 1.0 }, { 1.0, -1.0, 1.0, 1.0 }, + { -1.0, 1.0, 1.0, 1.0 }, { 1.0, 1.0, 1.0, 1.0 } +}; + +static const int edge_8[NUM_EDGE_8][2] = { + { 0, 1 }, { 0, 2 }, { 0, 4 }, { 0, 8 }, { 1, 3 }, { 1, 5 }, + { 1, 9 }, { 2, 3 }, { 2, 6 }, { 2, 10 }, { 3, 7 }, { 3, 11 }, + { 4, 5 }, { 4, 6 }, { 4, 12 }, { 5, 7 }, { 5, 13 }, { 6, 7 }, + { 6, 14 }, { 7, 15 }, { 8, 9 }, { 8, 10 }, { 8, 12 }, { 9, 11 }, + { 9, 13 }, { 10, 11 }, { 10, 14 }, { 11, 15 }, { 12, 13 }, { 12, 14 }, + { 13, 15 }, { 14, 15 } +}; + +static const int face_8[NUM_FACE_8][VERT_PER_FACE_8] = { + { 0, 1, 3, 2 }, { 0, 1, 5, 4 }, { 0, 1, 9, 8 }, + { 0, 2, 6, 4 }, { 0, 2, 10, 8 }, { 0, 4, 12, 8 }, + { 1, 3, 7, 5 }, { 1, 3, 11, 9 }, { 1, 5, 13, 9 }, + { 2, 3, 7, 6 }, { 2, 3, 11, 10 }, { 2, 6, 14, 10 }, + { 3, 7, 15, 11 }, { 4, 5, 7, 6 }, { 4, 5, 13, 12 }, + { 4, 6, 14, 12 }, { 5, 7, 15, 13 }, { 6, 7, 15, 14 }, + { 8, 9, 11, 10 }, { 8, 9, 13, 12 }, { 8, 10, 14, 12 }, + { 9, 11, 15, 13 }, { 10, 11, 15, 14 }, { 12, 13, 15, 14 } +}; + + + +static const float vert_16[NUM_VERT_16][4] = { + { 0.0, 0.0, 0.0, -2.0 }, { 0.0, 0.0, -2.0, 0.0 }, + { 0.0, -2.0, 0.0, 0.0 }, { -2.0, 0.0, 0.0, 0.0 }, + { 2.0, 0.0, 0.0, 0.0 }, { 0.0, 2.0, 0.0, 0.0 }, + { 0.0, 0.0, 2.0, 0.0 }, { 0.0, 0.0, 0.0, 2.0 } +}; + +static const int edge_16[NUM_EDGE_16][2] = { + { 0, 1 }, { 0, 2 }, { 0, 3 }, { 0, 4 }, { 0, 5 }, { 0, 6 }, { 1, 2 }, + { 1, 3 }, { 1, 4 }, { 1, 5 }, { 1, 7 }, { 2, 3 }, { 2, 4 }, { 2, 6 }, + { 2, 7 }, { 3, 5 }, { 3, 6 }, { 3, 7 }, { 4, 5 }, { 4, 6 }, { 4, 7 }, + { 5, 6 }, { 5, 7 }, { 6, 7 } +}; + +static const int face_16[NUM_FACE_16][VERT_PER_FACE_16] = { + { 0, 1, 2 }, { 0, 1, 3 }, { 0, 1, 4 }, { 0, 1, 5 }, { 0, 2, 3 }, { 0, 2, 4 }, + { 0, 2, 6 }, { 0, 3, 5 }, { 0, 3, 6 }, { 0, 4, 5 }, { 0, 4, 6 }, { 0, 5, 6 }, + { 1, 2, 3 }, { 1, 2, 4 }, { 1, 2, 7 }, { 1, 3, 5 }, { 1, 3, 7 }, { 1, 4, 5 }, + { 1, 4, 7 }, { 1, 5, 7 }, { 2, 3, 6 }, { 2, 3, 7 }, { 2, 4, 6 }, { 2, 4, 7 }, + { 2, 6, 7 }, { 3, 5, 6 }, { 3, 5, 7 }, { 3, 6, 7 }, { 4, 5, 6 }, { 4, 5, 7 }, + { 4, 6, 7 }, { 5, 6, 7 } +}; + + + +static const float vert_24[NUM_VERT_24][4] = { + { 0.0, 0.0, -SQRT2, -SQRT2 }, { 0.0, -SQRT2, 0.0, -SQRT2 }, + { -SQRT2, 0.0, 0.0, -SQRT2 }, { SQRT2, 0.0, 0.0, -SQRT2 }, + { 0.0, SQRT2, 0.0, -SQRT2 }, { 0.0, 0.0, SQRT2, -SQRT2 }, + { 0.0, -SQRT2, -SQRT2, 0.0 }, { -SQRT2, 0.0, -SQRT2, 0.0 }, + { SQRT2, 0.0, -SQRT2, 0.0 }, { 0.0, SQRT2, -SQRT2, 0.0 }, + { -SQRT2, -SQRT2, 0.0, 0.0 }, { SQRT2, -SQRT2, 0.0, 0.0 }, + { -SQRT2, SQRT2, 0.0, 0.0 }, { SQRT2, SQRT2, 0.0, 0.0 }, + { 0.0, -SQRT2, SQRT2, 0.0 }, { -SQRT2, 0.0, SQRT2, 0.0 }, + { SQRT2, 0.0, SQRT2, 0.0 }, { 0.0, SQRT2, SQRT2, 0.0 }, + { 0.0, 0.0, -SQRT2, SQRT2 }, { 0.0, -SQRT2, 0.0, SQRT2 }, + { -SQRT2, 0.0, 0.0, SQRT2 }, { SQRT2, 0.0, 0.0, SQRT2 }, + { 0.0, SQRT2, 0.0, SQRT2 }, { 0.0, 0.0, SQRT2, SQRT2 } +}; + +static const int edge_24[NUM_EDGE_24][2] = { + { 0, 1 }, { 0, 2 }, { 0, 3 }, { 0, 4 }, { 0, 6 }, { 0, 7 }, + { 0, 8 }, { 0, 9 }, { 1, 2 }, { 1, 3 }, { 1, 5 }, { 1, 6 }, + { 1, 10 }, { 1, 11 }, { 1, 14 }, { 2, 4 }, { 2, 5 }, { 2, 7 }, + { 2, 10 }, { 2, 12 }, { 2, 15 }, { 3, 4 }, { 3, 5 }, { 3, 8 }, + { 3, 11 }, { 3, 13 }, { 3, 16 }, { 4, 5 }, { 4, 9 }, { 4, 12 }, + { 4, 13 }, { 4, 17 }, { 5, 14 }, { 5, 15 }, { 5, 16 }, { 5, 17 }, + { 6, 7 }, { 6, 8 }, { 6, 10 }, { 6, 11 }, { 6, 18 }, { 6, 19 }, + { 7, 9 }, { 7, 10 }, { 7, 12 }, { 7, 18 }, { 7, 20 }, { 8, 9 }, + { 8, 11 }, { 8, 13 }, { 8, 18 }, { 8, 21 }, { 9, 12 }, { 9, 13 }, + { 9, 18 }, { 9, 22 }, { 10, 14 }, { 10, 15 }, { 10, 19 }, { 10, 20 }, + { 11, 14 }, { 11, 16 }, { 11, 19 }, { 11, 21 }, { 12, 15 }, { 12, 17 }, + { 12, 20 }, { 12, 22 }, { 13, 16 }, { 13, 17 }, { 13, 21 }, { 13, 22 }, + { 14, 15 }, { 14, 16 }, { 14, 19 }, { 14, 23 }, { 15, 17 }, { 15, 20 }, + { 15, 23 }, { 16, 17 }, { 16, 21 }, { 16, 23 }, { 17, 22 }, { 17, 23 }, + { 18, 19 }, { 18, 20 }, { 18, 21 }, { 18, 22 }, { 19, 20 }, { 19, 21 }, + { 19, 23 }, { 20, 22 }, { 20, 23 }, { 21, 22 }, { 21, 23 }, { 22, 23 } +}; + +static const int face_24[NUM_FACE_24][VERT_PER_FACE_24] = { + { 0, 1, 2 }, { 0, 1, 3 }, { 0, 1, 6 }, { 0, 2, 4 }, + { 0, 2, 7 }, { 0, 3, 4 }, { 0, 3, 8 }, { 0, 4, 9 }, + { 0, 6, 7 }, { 0, 6, 8 }, { 0, 7, 9 }, { 0, 8, 9 }, + { 1, 2, 5 }, { 1, 2, 10 }, { 1, 3, 5 }, { 1, 3, 11 }, + { 1, 5, 14 }, { 1, 6, 10 }, { 1, 6, 11 }, { 1, 10, 14 }, + { 1, 11, 14 }, { 2, 4, 5 }, { 2, 4, 12 }, { 2, 5, 15 }, + { 2, 7, 10 }, { 2, 7, 12 }, { 2, 10, 15 }, { 2, 12, 15 }, + { 3, 4, 5 }, { 3, 4, 13 }, { 3, 5, 16 }, { 3, 8, 11 }, + { 3, 8, 13 }, { 3, 11, 16 }, { 3, 13, 16 }, { 4, 5, 17 }, + { 4, 9, 12 }, { 4, 9, 13 }, { 4, 12, 17 }, { 4, 13, 17 }, + { 5, 14, 15 }, { 5, 14, 16 }, { 5, 15, 17 }, { 5, 16, 17 }, + { 6, 7, 10 }, { 6, 7, 18 }, { 6, 8, 11 }, { 6, 8, 18 }, + { 6, 10, 19 }, { 6, 11, 19 }, { 6, 18, 19 }, { 7, 9, 12 }, + { 7, 9, 18 }, { 7, 10, 20 }, { 7, 12, 20 }, { 7, 18, 20 }, + { 8, 9, 13 }, { 8, 9, 18 }, { 8, 11, 21 }, { 8, 13, 21 }, + { 8, 18, 21 }, { 9, 12, 22 }, { 9, 13, 22 }, { 9, 18, 22 }, + { 10, 14, 15 }, { 10, 14, 19 }, { 10, 15, 20 }, { 10, 19, 20 }, + { 11, 14, 16 }, { 11, 14, 19 }, { 11, 16, 21 }, { 11, 19, 21 }, + { 12, 15, 17 }, { 12, 15, 20 }, { 12, 17, 22 }, { 12, 20, 22 }, + { 13, 16, 17 }, { 13, 16, 21 }, { 13, 17, 22 }, { 13, 21, 22 }, + { 14, 15, 23 }, { 14, 16, 23 }, { 14, 19, 23 }, { 15, 17, 23 }, + { 15, 20, 23 }, { 16, 17, 23 }, { 16, 21, 23 }, { 17, 22, 23 }, + { 18, 19, 20 }, { 18, 19, 21 }, { 18, 20, 22 }, { 18, 21, 22 }, + { 19, 20, 23 }, { 19, 21, 23 }, { 20, 22, 23 }, { 21, 22, 23 } +}; + + + + +static const float vert_120[NUM_VERT_120][4] = { + { -GOLDENINV22, 0.0, -SQRT2INV, -GOLDEN22 }, + { GOLDENINV22, 0.0, -SQRT2INV, -GOLDEN22 }, + { -GOLDENINV2, -GOLDENINV2, -GOLDENINV2, -GOLDEN22 }, + { GOLDENINV2, -GOLDENINV2, -GOLDENINV2, -GOLDEN22 }, + { -GOLDENINV2, GOLDENINV2, -GOLDENINV2, -GOLDEN22 }, + { GOLDENINV2, GOLDENINV2, -GOLDENINV2, -GOLDEN22 }, + { 0.0, -SQRT2INV, -GOLDENINV22, -GOLDEN22 }, + { 0.0, SQRT2INV, -GOLDENINV22, -GOLDEN22 }, + { -SQRT2INV, -GOLDENINV22, 0.0, -GOLDEN22 }, + { SQRT2INV, -GOLDENINV22, 0.0, -GOLDEN22 }, + { -SQRT2INV, GOLDENINV22, 0.0, -GOLDEN22 }, + { SQRT2INV, GOLDENINV22, 0.0, -GOLDEN22 }, + { 0.0, -SQRT2INV, GOLDENINV22, -GOLDEN22 }, + { 0.0, SQRT2INV, GOLDENINV22, -GOLDEN22 }, + { -GOLDENINV2, -GOLDENINV2, GOLDENINV2, -GOLDEN22 }, + { GOLDENINV2, -GOLDENINV2, GOLDENINV2, -GOLDEN22 }, + { -GOLDENINV2, GOLDENINV2, GOLDENINV2, -GOLDEN22 }, + { GOLDENINV2, GOLDENINV2, GOLDENINV2, -GOLDEN22 }, + { -GOLDENINV22, 0.0, SQRT2INV, -GOLDEN22 }, + { GOLDENINV22, 0.0, SQRT2INV, -GOLDEN22 }, + { -GOLDENINV2, 0.0, -GOLDEN2, -SQRT5OVER2 }, + { GOLDENINV2, 0.0, -GOLDEN2, -SQRT5OVER2 }, + { -SQRT2INV, -SQRT2INV, -SQRT2INV, -SQRT5OVER2 }, + { SQRT2INV, -SQRT2INV, -SQRT2INV, -SQRT5OVER2 }, + { -SQRT2INV, SQRT2INV, -SQRT2INV, -SQRT5OVER2 }, + { SQRT2INV, SQRT2INV, -SQRT2INV, -SQRT5OVER2 }, + { 0.0, -GOLDEN2, -GOLDENINV2, -SQRT5OVER2 }, + { 0.0, GOLDEN2, -GOLDENINV2, -SQRT5OVER2 }, + { -GOLDEN2, -GOLDENINV2, 0.0, -SQRT5OVER2 }, + { GOLDEN2, -GOLDENINV2, 0.0, -SQRT5OVER2 }, + { -GOLDEN2, GOLDENINV2, 0.0, -SQRT5OVER2 }, + { GOLDEN2, GOLDENINV2, 0.0, -SQRT5OVER2 }, + { 0.0, -GOLDEN2, GOLDENINV2, -SQRT5OVER2 }, + { 0.0, GOLDEN2, GOLDENINV2, -SQRT5OVER2 }, + { -SQRT2INV, -SQRT2INV, SQRT2INV, -SQRT5OVER2 }, + { SQRT2INV, -SQRT2INV, SQRT2INV, -SQRT5OVER2 }, + { -SQRT2INV, SQRT2INV, SQRT2INV, -SQRT5OVER2 }, + { SQRT2INV, SQRT2INV, SQRT2INV, -SQRT5OVER2 }, + { -GOLDENINV2, 0.0, GOLDEN2, -SQRT5OVER2 }, + { GOLDENINV2, 0.0, GOLDEN2, -SQRT5OVER2 }, + { 0.0, 0.0, -SQRT2, -SQRT2 }, + { -SQRT2INV, -GOLDENINV2, -GOLDEN2, -SQRT2 }, + { SQRT2INV, -GOLDENINV2, -GOLDEN2, -SQRT2 }, + { -SQRT2INV, GOLDENINV2, -GOLDEN2, -SQRT2 }, + { SQRT2INV, GOLDENINV2, -GOLDEN2, -SQRT2 }, + { -GOLDENINV2, -GOLDEN2, -SQRT2INV, -SQRT2 }, + { GOLDENINV2, -GOLDEN2, -SQRT2INV, -SQRT2 }, + { -GOLDENINV2, GOLDEN2, -SQRT2INV, -SQRT2 }, + { GOLDENINV2, GOLDEN2, -SQRT2INV, -SQRT2 }, + { -GOLDEN2, -SQRT2INV, -GOLDENINV2, -SQRT2 }, + { GOLDEN2, -SQRT2INV, -GOLDENINV2, -SQRT2 }, + { -GOLDEN2, SQRT2INV, -GOLDENINV2, -SQRT2 }, + { GOLDEN2, SQRT2INV, -GOLDENINV2, -SQRT2 }, + { 0.0, -SQRT2, 0.0, -SQRT2 }, + { -SQRT2, 0.0, 0.0, -SQRT2 }, + { SQRT2, 0.0, 0.0, -SQRT2 }, + { 0.0, SQRT2, 0.0, -SQRT2 }, + { -GOLDEN2, -SQRT2INV, GOLDENINV2, -SQRT2 }, + { GOLDEN2, -SQRT2INV, GOLDENINV2, -SQRT2 }, + { -GOLDEN2, SQRT2INV, GOLDENINV2, -SQRT2 }, + { GOLDEN2, SQRT2INV, GOLDENINV2, -SQRT2 }, + { -GOLDENINV2, -GOLDEN2, SQRT2INV, -SQRT2 }, + { GOLDENINV2, -GOLDEN2, SQRT2INV, -SQRT2 }, + { -GOLDENINV2, GOLDEN2, SQRT2INV, -SQRT2 }, + { GOLDENINV2, GOLDEN2, SQRT2INV, -SQRT2 }, + { -SQRT2INV, -GOLDENINV2, GOLDEN2, -SQRT2 }, + { SQRT2INV, -GOLDENINV2, GOLDEN2, -SQRT2 }, + { -SQRT2INV, GOLDENINV2, GOLDEN2, -SQRT2 }, + { SQRT2INV, GOLDENINV2, GOLDEN2, -SQRT2 }, + { 0.0, 0.0, SQRT2, -SQRT2 }, + { 0.0, -GOLDENINV2, -SQRT5OVER2, -GOLDEN2 }, + { 0.0, GOLDENINV2, -SQRT5OVER2, -GOLDEN2 }, + { -GOLDENINV2, -SQRT2INV, -SQRT2, -GOLDEN2 }, + { GOLDENINV2, -SQRT2INV, -SQRT2, -GOLDEN2 }, + { -GOLDENINV2, SQRT2INV, -SQRT2, -GOLDEN2 }, + { GOLDENINV2, SQRT2INV, -SQRT2, -GOLDEN2 }, + { -GOLDENINV22, -GOLDEN2, -GOLDEN2, -GOLDEN2 }, + { GOLDENINV22, -GOLDEN2, -GOLDEN2, -GOLDEN2 }, + { -GOLDEN2, -GOLDENINV22, -GOLDEN2, -GOLDEN2 }, + { GOLDEN2, -GOLDENINV22, -GOLDEN2, -GOLDEN2 }, + { -GOLDEN2, GOLDENINV22, -GOLDEN2, -GOLDEN2 }, + { GOLDEN2, GOLDENINV22, -GOLDEN2, -GOLDEN2 }, + { -GOLDENINV22, GOLDEN2, -GOLDEN2, -GOLDEN2 }, + { GOLDENINV22, GOLDEN2, -GOLDEN2, -GOLDEN2 }, + { -SQRT2, -GOLDENINV2, -SQRT2INV, -GOLDEN2 }, + { SQRT2, -GOLDENINV2, -SQRT2INV, -GOLDEN2 }, + { -SQRT2, GOLDENINV2, -SQRT2INV, -GOLDEN2 }, + { SQRT2, GOLDENINV2, -SQRT2INV, -GOLDEN2 }, + { -SQRT2INV, -SQRT2, -GOLDENINV2, -GOLDEN2 }, + { SQRT2INV, -SQRT2, -GOLDENINV2, -GOLDEN2 }, + { -SQRT5OVER2, 0.0, -GOLDENINV2, -GOLDEN2 }, + { SQRT5OVER2, 0.0, -GOLDENINV2, -GOLDEN2 }, + { -SQRT2INV, SQRT2, -GOLDENINV2, -GOLDEN2 }, + { SQRT2INV, SQRT2, -GOLDENINV2, -GOLDEN2 }, + { -GOLDEN2, -GOLDEN2, -GOLDENINV22, -GOLDEN2 }, + { GOLDEN2, -GOLDEN2, -GOLDENINV22, -GOLDEN2 }, + { -GOLDEN2, GOLDEN2, -GOLDENINV22, -GOLDEN2 }, + { GOLDEN2, GOLDEN2, -GOLDENINV22, -GOLDEN2 }, + { -GOLDENINV2, -SQRT5OVER2, 0.0, -GOLDEN2 }, + { GOLDENINV2, -SQRT5OVER2, 0.0, -GOLDEN2 }, + { -GOLDENINV2, SQRT5OVER2, 0.0, -GOLDEN2 }, + { GOLDENINV2, SQRT5OVER2, 0.0, -GOLDEN2 }, + { -GOLDEN2, -GOLDEN2, GOLDENINV22, -GOLDEN2 }, + { GOLDEN2, -GOLDEN2, GOLDENINV22, -GOLDEN2 }, + { -GOLDEN2, GOLDEN2, GOLDENINV22, -GOLDEN2 }, + { GOLDEN2, GOLDEN2, GOLDENINV22, -GOLDEN2 }, + { -SQRT2INV, -SQRT2, GOLDENINV2, -GOLDEN2 }, + { SQRT2INV, -SQRT2, GOLDENINV2, -GOLDEN2 }, + { -SQRT5OVER2, 0.0, GOLDENINV2, -GOLDEN2 }, + { SQRT5OVER2, 0.0, GOLDENINV2, -GOLDEN2 }, + { -SQRT2INV, SQRT2, GOLDENINV2, -GOLDEN2 }, + { SQRT2INV, SQRT2, GOLDENINV2, -GOLDEN2 }, + { -SQRT2, -GOLDENINV2, SQRT2INV, -GOLDEN2 }, + { SQRT2, -GOLDENINV2, SQRT2INV, -GOLDEN2 }, + { -SQRT2, GOLDENINV2, SQRT2INV, -GOLDEN2 }, + { SQRT2, GOLDENINV2, SQRT2INV, -GOLDEN2 }, + { -GOLDENINV22, -GOLDEN2, GOLDEN2, -GOLDEN2 }, + { GOLDENINV22, -GOLDEN2, GOLDEN2, -GOLDEN2 }, + { -GOLDEN2, -GOLDENINV22, GOLDEN2, -GOLDEN2 }, + { GOLDEN2, -GOLDENINV22, GOLDEN2, -GOLDEN2 }, + { -GOLDEN2, GOLDENINV22, GOLDEN2, -GOLDEN2 }, + { GOLDEN2, GOLDENINV22, GOLDEN2, -GOLDEN2 }, + { -GOLDENINV22, GOLDEN2, GOLDEN2, -GOLDEN2 }, + { GOLDENINV22, GOLDEN2, GOLDEN2, -GOLDEN2 }, + { -GOLDENINV2, -SQRT2INV, SQRT2, -GOLDEN2 }, + { GOLDENINV2, -SQRT2INV, SQRT2, -GOLDEN2 }, + { -GOLDENINV2, SQRT2INV, SQRT2, -GOLDEN2 }, + { GOLDENINV2, SQRT2INV, SQRT2, -GOLDEN2 }, + { 0.0, -GOLDENINV2, SQRT5OVER2, -GOLDEN2 }, + { 0.0, GOLDENINV2, SQRT5OVER2, -GOLDEN2 }, + { 0.0, -GOLDENINV22, -GOLDEN22, -SQRT2INV }, + { 0.0, GOLDENINV22, -GOLDEN22, -SQRT2INV }, + { -SQRT2INV, -SQRT2INV, -SQRT5OVER2, -SQRT2INV }, + { SQRT2INV, -SQRT2INV, -SQRT5OVER2, -SQRT2INV }, + { -SQRT2INV, SQRT2INV, -SQRT5OVER2, -SQRT2INV }, + { SQRT2INV, SQRT2INV, -SQRT5OVER2, -SQRT2INV }, + { -GOLDEN2, -GOLDENINV2, -SQRT2, -SQRT2INV }, + { GOLDEN2, -GOLDENINV2, -SQRT2, -SQRT2INV }, + { -GOLDEN2, GOLDENINV2, -SQRT2, -SQRT2INV }, + { GOLDEN2, GOLDENINV2, -SQRT2, -SQRT2INV }, + { -GOLDENINV2, -SQRT2, -GOLDEN2, -SQRT2INV }, + { GOLDENINV2, -SQRT2, -GOLDEN2, -SQRT2INV }, + { -GOLDENINV2, SQRT2, -GOLDEN2, -SQRT2INV }, + { GOLDENINV2, SQRT2, -GOLDEN2, -SQRT2INV }, + { -SQRT2INV, -SQRT5OVER2, -SQRT2INV, -SQRT2INV }, + { SQRT2INV, -SQRT5OVER2, -SQRT2INV, -SQRT2INV }, + { -SQRT5OVER2, -SQRT2INV, -SQRT2INV, -SQRT2INV }, + { SQRT5OVER2, -SQRT2INV, -SQRT2INV, -SQRT2INV }, + { -SQRT5OVER2, SQRT2INV, -SQRT2INV, -SQRT2INV }, + { SQRT5OVER2, SQRT2INV, -SQRT2INV, -SQRT2INV }, + { -SQRT2INV, SQRT5OVER2, -SQRT2INV, -SQRT2INV }, + { SQRT2INV, SQRT5OVER2, -SQRT2INV, -SQRT2INV }, + { -SQRT2, -GOLDEN2, -GOLDENINV2, -SQRT2INV }, + { SQRT2, -GOLDEN2, -GOLDENINV2, -SQRT2INV }, + { -SQRT2, GOLDEN2, -GOLDENINV2, -SQRT2INV }, + { SQRT2, GOLDEN2, -GOLDENINV2, -SQRT2INV }, + { -GOLDEN22, 0.0, -GOLDENINV22, -SQRT2INV }, + { GOLDEN22, 0.0, -GOLDENINV22, -SQRT2INV }, + { -GOLDENINV22, -GOLDEN22, 0.0, -SQRT2INV }, + { GOLDENINV22, -GOLDEN22, 0.0, -SQRT2INV }, + { -GOLDENINV22, GOLDEN22, 0.0, -SQRT2INV }, + { GOLDENINV22, GOLDEN22, 0.0, -SQRT2INV }, + { -GOLDEN22, 0.0, GOLDENINV22, -SQRT2INV }, + { GOLDEN22, 0.0, GOLDENINV22, -SQRT2INV }, + { -SQRT2, -GOLDEN2, GOLDENINV2, -SQRT2INV }, + { SQRT2, -GOLDEN2, GOLDENINV2, -SQRT2INV }, + { -SQRT2, GOLDEN2, GOLDENINV2, -SQRT2INV }, + { SQRT2, GOLDEN2, GOLDENINV2, -SQRT2INV }, + { -SQRT2INV, -SQRT5OVER2, SQRT2INV, -SQRT2INV }, + { SQRT2INV, -SQRT5OVER2, SQRT2INV, -SQRT2INV }, + { -SQRT5OVER2, -SQRT2INV, SQRT2INV, -SQRT2INV }, + { SQRT5OVER2, -SQRT2INV, SQRT2INV, -SQRT2INV }, + { -SQRT5OVER2, SQRT2INV, SQRT2INV, -SQRT2INV }, + { SQRT5OVER2, SQRT2INV, SQRT2INV, -SQRT2INV }, + { -SQRT2INV, SQRT5OVER2, SQRT2INV, -SQRT2INV }, + { SQRT2INV, SQRT5OVER2, SQRT2INV, -SQRT2INV }, + { -GOLDENINV2, -SQRT2, GOLDEN2, -SQRT2INV }, + { GOLDENINV2, -SQRT2, GOLDEN2, -SQRT2INV }, + { -GOLDENINV2, SQRT2, GOLDEN2, -SQRT2INV }, + { GOLDENINV2, SQRT2, GOLDEN2, -SQRT2INV }, + { -GOLDEN2, -GOLDENINV2, SQRT2, -SQRT2INV }, + { GOLDEN2, -GOLDENINV2, SQRT2, -SQRT2INV }, + { -GOLDEN2, GOLDENINV2, SQRT2, -SQRT2INV }, + { GOLDEN2, GOLDENINV2, SQRT2, -SQRT2INV }, + { -SQRT2INV, -SQRT2INV, SQRT5OVER2, -SQRT2INV }, + { SQRT2INV, -SQRT2INV, SQRT5OVER2, -SQRT2INV }, + { -SQRT2INV, SQRT2INV, SQRT5OVER2, -SQRT2INV }, + { SQRT2INV, SQRT2INV, SQRT5OVER2, -SQRT2INV }, + { 0.0, -GOLDENINV22, GOLDEN22, -SQRT2INV }, + { 0.0, GOLDENINV22, GOLDEN22, -SQRT2INV }, + { -GOLDENINV2, -GOLDENINV2, -GOLDEN22, -GOLDENINV2 }, + { GOLDENINV2, -GOLDENINV2, -GOLDEN22, -GOLDENINV2 }, + { -GOLDENINV2, GOLDENINV2, -GOLDEN22, -GOLDENINV2 }, + { GOLDENINV2, GOLDENINV2, -GOLDEN22, -GOLDENINV2 }, + { -GOLDEN2, 0.0, -SQRT5OVER2, -GOLDENINV2 }, + { GOLDEN2, 0.0, -SQRT5OVER2, -GOLDENINV2 }, + { -SQRT2INV, -GOLDEN2, -SQRT2, -GOLDENINV2 }, + { SQRT2INV, -GOLDEN2, -SQRT2, -GOLDENINV2 }, + { -SQRT2INV, GOLDEN2, -SQRT2, -GOLDENINV2 }, + { SQRT2INV, GOLDEN2, -SQRT2, -GOLDENINV2 }, + { 0.0, -SQRT5OVER2, -GOLDEN2, -GOLDENINV2 }, + { -SQRT2, -SQRT2INV, -GOLDEN2, -GOLDENINV2 }, + { SQRT2, -SQRT2INV, -GOLDEN2, -GOLDENINV2 }, + { -SQRT2, SQRT2INV, -GOLDEN2, -GOLDENINV2 }, + { SQRT2, SQRT2INV, -GOLDEN2, -GOLDENINV2 }, + { 0.0, SQRT5OVER2, -GOLDEN2, -GOLDENINV2 }, + { -GOLDEN2, -SQRT2, -SQRT2INV, -GOLDENINV2 }, + { GOLDEN2, -SQRT2, -SQRT2INV, -GOLDENINV2 }, + { -GOLDEN2, SQRT2, -SQRT2INV, -GOLDENINV2 }, + { GOLDEN2, SQRT2, -SQRT2INV, -GOLDENINV2 }, + { -GOLDENINV2, -GOLDEN22, -GOLDENINV2, -GOLDENINV2 }, + { GOLDENINV2, -GOLDEN22, -GOLDENINV2, -GOLDENINV2 }, + { -GOLDEN22, -GOLDENINV2, -GOLDENINV2, -GOLDENINV2 }, + { GOLDEN22, -GOLDENINV2, -GOLDENINV2, -GOLDENINV2 }, + { -GOLDEN22, GOLDENINV2, -GOLDENINV2, -GOLDENINV2 }, + { GOLDEN22, GOLDENINV2, -GOLDENINV2, -GOLDENINV2 }, + { -GOLDENINV2, GOLDEN22, -GOLDENINV2, -GOLDENINV2 }, + { GOLDENINV2, GOLDEN22, -GOLDENINV2, -GOLDENINV2 }, + { -SQRT5OVER2, -GOLDEN2, 0.0, -GOLDENINV2 }, + { SQRT5OVER2, -GOLDEN2, 0.0, -GOLDENINV2 }, + { -SQRT5OVER2, GOLDEN2, 0.0, -GOLDENINV2 }, + { SQRT5OVER2, GOLDEN2, 0.0, -GOLDENINV2 }, + { -GOLDENINV2, -GOLDEN22, GOLDENINV2, -GOLDENINV2 }, + { GOLDENINV2, -GOLDEN22, GOLDENINV2, -GOLDENINV2 }, + { -GOLDEN22, -GOLDENINV2, GOLDENINV2, -GOLDENINV2 }, + { GOLDEN22, -GOLDENINV2, GOLDENINV2, -GOLDENINV2 }, + { -GOLDEN22, GOLDENINV2, GOLDENINV2, -GOLDENINV2 }, + { GOLDEN22, GOLDENINV2, GOLDENINV2, -GOLDENINV2 }, + { -GOLDENINV2, GOLDEN22, GOLDENINV2, -GOLDENINV2 }, + { GOLDENINV2, GOLDEN22, GOLDENINV2, -GOLDENINV2 }, + { -GOLDEN2, -SQRT2, SQRT2INV, -GOLDENINV2 }, + { GOLDEN2, -SQRT2, SQRT2INV, -GOLDENINV2 }, + { -GOLDEN2, SQRT2, SQRT2INV, -GOLDENINV2 }, + { GOLDEN2, SQRT2, SQRT2INV, -GOLDENINV2 }, + { 0.0, -SQRT5OVER2, GOLDEN2, -GOLDENINV2 }, + { -SQRT2, -SQRT2INV, GOLDEN2, -GOLDENINV2 }, + { SQRT2, -SQRT2INV, GOLDEN2, -GOLDENINV2 }, + { -SQRT2, SQRT2INV, GOLDEN2, -GOLDENINV2 }, + { SQRT2, SQRT2INV, GOLDEN2, -GOLDENINV2 }, + { 0.0, SQRT5OVER2, GOLDEN2, -GOLDENINV2 }, + { -SQRT2INV, -GOLDEN2, SQRT2, -GOLDENINV2 }, + { SQRT2INV, -GOLDEN2, SQRT2, -GOLDENINV2 }, + { -SQRT2INV, GOLDEN2, SQRT2, -GOLDENINV2 }, + { SQRT2INV, GOLDEN2, SQRT2, -GOLDENINV2 }, + { -GOLDEN2, 0.0, SQRT5OVER2, -GOLDENINV2 }, + { GOLDEN2, 0.0, SQRT5OVER2, -GOLDENINV2 }, + { -GOLDENINV2, -GOLDENINV2, GOLDEN22, -GOLDENINV2 }, + { GOLDENINV2, -GOLDENINV2, GOLDEN22, -GOLDENINV2 }, + { -GOLDENINV2, GOLDENINV2, GOLDEN22, -GOLDENINV2 }, + { GOLDENINV2, GOLDENINV2, GOLDEN22, -GOLDENINV2 }, + { -SQRT2INV, 0.0, -GOLDEN22, -GOLDENINV22 }, + { SQRT2INV, 0.0, -GOLDEN22, -GOLDENINV22 }, + { -GOLDEN2, -GOLDEN2, -GOLDEN2, -GOLDENINV22 }, + { GOLDEN2, -GOLDEN2, -GOLDEN2, -GOLDENINV22 }, + { -GOLDEN2, GOLDEN2, -GOLDEN2, -GOLDENINV22 }, + { GOLDEN2, GOLDEN2, -GOLDEN2, -GOLDENINV22 }, + { 0.0, -GOLDEN22, -SQRT2INV, -GOLDENINV22 }, + { 0.0, 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GOLDEN2 }, + { -GOLDENINV2, SQRT2INV, -SQRT2, GOLDEN2 }, + { GOLDENINV2, SQRT2INV, -SQRT2, GOLDEN2 }, + { -GOLDENINV22, -GOLDEN2, -GOLDEN2, GOLDEN2 }, + { GOLDENINV22, -GOLDEN2, -GOLDEN2, GOLDEN2 }, + { -GOLDEN2, -GOLDENINV22, -GOLDEN2, GOLDEN2 }, + { GOLDEN2, -GOLDENINV22, -GOLDEN2, GOLDEN2 }, + { -GOLDEN2, GOLDENINV22, -GOLDEN2, GOLDEN2 }, + { GOLDEN2, GOLDENINV22, -GOLDEN2, GOLDEN2 }, + { -GOLDENINV22, GOLDEN2, -GOLDEN2, GOLDEN2 }, + { GOLDENINV22, GOLDEN2, -GOLDEN2, GOLDEN2 }, + { -SQRT2, -GOLDENINV2, -SQRT2INV, GOLDEN2 }, + { SQRT2, -GOLDENINV2, -SQRT2INV, GOLDEN2 }, + { -SQRT2, GOLDENINV2, -SQRT2INV, GOLDEN2 }, + { SQRT2, GOLDENINV2, -SQRT2INV, GOLDEN2 }, + { -SQRT2INV, -SQRT2, -GOLDENINV2, GOLDEN2 }, + { SQRT2INV, -SQRT2, -GOLDENINV2, GOLDEN2 }, + { -SQRT5OVER2, 0.0, -GOLDENINV2, GOLDEN2 }, + { SQRT5OVER2, 0.0, -GOLDENINV2, GOLDEN2 }, + { -SQRT2INV, SQRT2, -GOLDENINV2, GOLDEN2 }, + { SQRT2INV, SQRT2, -GOLDENINV2, GOLDEN2 }, + { -GOLDEN2, -GOLDEN2, -GOLDENINV22, GOLDEN2 }, + { GOLDEN2, -GOLDEN2, -GOLDENINV22, GOLDEN2 }, + { -GOLDEN2, GOLDEN2, -GOLDENINV22, GOLDEN2 }, + { GOLDEN2, GOLDEN2, -GOLDENINV22, GOLDEN2 }, + { -GOLDENINV2, -SQRT5OVER2, 0.0, GOLDEN2 }, + { GOLDENINV2, -SQRT5OVER2, 0.0, GOLDEN2 }, + { -GOLDENINV2, SQRT5OVER2, 0.0, GOLDEN2 }, + { GOLDENINV2, SQRT5OVER2, 0.0, GOLDEN2 }, + { -GOLDEN2, -GOLDEN2, GOLDENINV22, GOLDEN2 }, + { GOLDEN2, -GOLDEN2, GOLDENINV22, GOLDEN2 }, + { -GOLDEN2, GOLDEN2, GOLDENINV22, GOLDEN2 }, + { GOLDEN2, GOLDEN2, GOLDENINV22, GOLDEN2 }, + { -SQRT2INV, -SQRT2, GOLDENINV2, GOLDEN2 }, + { SQRT2INV, -SQRT2, GOLDENINV2, GOLDEN2 }, + { -SQRT5OVER2, 0.0, GOLDENINV2, GOLDEN2 }, + { SQRT5OVER2, 0.0, GOLDENINV2, GOLDEN2 }, + { -SQRT2INV, SQRT2, GOLDENINV2, GOLDEN2 }, + { SQRT2INV, SQRT2, GOLDENINV2, GOLDEN2 }, + { -SQRT2, -GOLDENINV2, SQRT2INV, GOLDEN2 }, + { SQRT2, -GOLDENINV2, SQRT2INV, GOLDEN2 }, + { -SQRT2, GOLDENINV2, SQRT2INV, GOLDEN2 }, + { SQRT2, GOLDENINV2, SQRT2INV, GOLDEN2 }, + { -GOLDENINV22, -GOLDEN2, GOLDEN2, GOLDEN2 }, + { GOLDENINV22, -GOLDEN2, GOLDEN2, GOLDEN2 }, + { -GOLDEN2, -GOLDENINV22, GOLDEN2, GOLDEN2 }, + { GOLDEN2, -GOLDENINV22, GOLDEN2, GOLDEN2 }, + { -GOLDEN2, GOLDENINV22, GOLDEN2, GOLDEN2 }, + { GOLDEN2, GOLDENINV22, GOLDEN2, GOLDEN2 }, + { -GOLDENINV22, GOLDEN2, GOLDEN2, GOLDEN2 }, + { GOLDENINV22, GOLDEN2, GOLDEN2, GOLDEN2 }, + { -GOLDENINV2, -SQRT2INV, SQRT2, GOLDEN2 }, + { GOLDENINV2, -SQRT2INV, SQRT2, GOLDEN2 }, + { -GOLDENINV2, SQRT2INV, SQRT2, GOLDEN2 }, + { GOLDENINV2, SQRT2INV, SQRT2, GOLDEN2 }, + { 0.0, -GOLDENINV2, SQRT5OVER2, GOLDEN2 }, + { 0.0, GOLDENINV2, SQRT5OVER2, GOLDEN2 }, + { 0.0, 0.0, -SQRT2, SQRT2 }, + { -SQRT2INV, -GOLDENINV2, -GOLDEN2, SQRT2 }, + { SQRT2INV, -GOLDENINV2, -GOLDEN2, SQRT2 }, + { -SQRT2INV, GOLDENINV2, -GOLDEN2, SQRT2 }, + { SQRT2INV, GOLDENINV2, -GOLDEN2, SQRT2 }, + { -GOLDENINV2, -GOLDEN2, -SQRT2INV, SQRT2 }, + { GOLDENINV2, -GOLDEN2, -SQRT2INV, SQRT2 }, + { -GOLDENINV2, GOLDEN2, -SQRT2INV, SQRT2 }, + { GOLDENINV2, GOLDEN2, -SQRT2INV, SQRT2 }, + { -GOLDEN2, -SQRT2INV, -GOLDENINV2, SQRT2 }, + { GOLDEN2, -SQRT2INV, -GOLDENINV2, SQRT2 }, + { -GOLDEN2, SQRT2INV, -GOLDENINV2, SQRT2 }, + { GOLDEN2, SQRT2INV, -GOLDENINV2, SQRT2 }, + { 0.0, -SQRT2, 0.0, SQRT2 }, + { -SQRT2, 0.0, 0.0, SQRT2 }, + { SQRT2, 0.0, 0.0, SQRT2 }, + { 0.0, SQRT2, 0.0, SQRT2 }, + { -GOLDEN2, -SQRT2INV, GOLDENINV2, SQRT2 }, + { GOLDEN2, -SQRT2INV, GOLDENINV2, SQRT2 }, + { -GOLDEN2, SQRT2INV, GOLDENINV2, SQRT2 }, + { GOLDEN2, SQRT2INV, GOLDENINV2, SQRT2 }, + { -GOLDENINV2, -GOLDEN2, SQRT2INV, SQRT2 }, + { GOLDENINV2, -GOLDEN2, SQRT2INV, SQRT2 }, + { -GOLDENINV2, GOLDEN2, SQRT2INV, SQRT2 }, + { GOLDENINV2, GOLDEN2, SQRT2INV, SQRT2 }, + { -SQRT2INV, -GOLDENINV2, GOLDEN2, SQRT2 }, + { SQRT2INV, -GOLDENINV2, GOLDEN2, SQRT2 }, + { -SQRT2INV, GOLDENINV2, GOLDEN2, SQRT2 }, + { SQRT2INV, GOLDENINV2, GOLDEN2, SQRT2 }, + { 0.0, 0.0, SQRT2, SQRT2 }, + { -GOLDENINV2, 0.0, -GOLDEN2, SQRT5OVER2 }, + { GOLDENINV2, 0.0, -GOLDEN2, SQRT5OVER2 }, + { -SQRT2INV, -SQRT2INV, -SQRT2INV, SQRT5OVER2 }, + { SQRT2INV, -SQRT2INV, -SQRT2INV, SQRT5OVER2 }, + { -SQRT2INV, SQRT2INV, -SQRT2INV, SQRT5OVER2 }, + { SQRT2INV, SQRT2INV, -SQRT2INV, SQRT5OVER2 }, + { 0.0, -GOLDEN2, -GOLDENINV2, SQRT5OVER2 }, + { 0.0, GOLDEN2, -GOLDENINV2, SQRT5OVER2 }, + { -GOLDEN2, -GOLDENINV2, 0.0, SQRT5OVER2 }, + { GOLDEN2, -GOLDENINV2, 0.0, SQRT5OVER2 }, + { -GOLDEN2, GOLDENINV2, 0.0, SQRT5OVER2 }, + { GOLDEN2, GOLDENINV2, 0.0, SQRT5OVER2 }, + { 0.0, -GOLDEN2, GOLDENINV2, SQRT5OVER2 }, + { 0.0, GOLDEN2, GOLDENINV2, SQRT5OVER2 }, + { -SQRT2INV, -SQRT2INV, SQRT2INV, SQRT5OVER2 }, + { SQRT2INV, -SQRT2INV, SQRT2INV, SQRT5OVER2 }, + { -SQRT2INV, SQRT2INV, SQRT2INV, SQRT5OVER2 }, + { SQRT2INV, SQRT2INV, SQRT2INV, SQRT5OVER2 }, + { -GOLDENINV2, 0.0, GOLDEN2, SQRT5OVER2 }, + { GOLDENINV2, 0.0, GOLDEN2, SQRT5OVER2 }, + { -GOLDENINV22, 0.0, -SQRT2INV, GOLDEN22 }, + { GOLDENINV22, 0.0, -SQRT2INV, GOLDEN22 }, + { -GOLDENINV2, -GOLDENINV2, -GOLDENINV2, GOLDEN22 }, + { GOLDENINV2, -GOLDENINV2, -GOLDENINV2, GOLDEN22 }, + { -GOLDENINV2, GOLDENINV2, -GOLDENINV2, GOLDEN22 }, + { GOLDENINV2, GOLDENINV2, -GOLDENINV2, GOLDEN22 }, + { 0.0, -SQRT2INV, -GOLDENINV22, GOLDEN22 }, + { 0.0, SQRT2INV, -GOLDENINV22, GOLDEN22 }, + { -SQRT2INV, -GOLDENINV22, 0.0, GOLDEN22 }, + { SQRT2INV, -GOLDENINV22, 0.0, GOLDEN22 }, + { -SQRT2INV, GOLDENINV22, 0.0, GOLDEN22 }, + { SQRT2INV, GOLDENINV22, 0.0, GOLDEN22 }, + { 0.0, -SQRT2INV, GOLDENINV22, GOLDEN22 }, + { 0.0, SQRT2INV, GOLDENINV22, GOLDEN22 }, + { -GOLDENINV2, -GOLDENINV2, GOLDENINV2, GOLDEN22 }, + { GOLDENINV2, -GOLDENINV2, GOLDENINV2, GOLDEN22 }, + { -GOLDENINV2, GOLDENINV2, GOLDENINV2, GOLDEN22 }, + { GOLDENINV2, GOLDENINV2, GOLDENINV2, GOLDEN22 }, + { -GOLDENINV22, 0.0, SQRT2INV, GOLDEN22 }, + { GOLDENINV22, 0.0, SQRT2INV, GOLDEN22 } +}; + +static const int edge_120[NUM_EDGE_120][2] = { + { 0, 1 }, { 0, 2 }, { 0, 4 }, { 0, 20 }, { 1, 3 }, + { 1, 5 }, { 1, 21 }, { 2, 6 }, { 2, 8 }, { 2, 22 }, + { 3, 6 }, { 3, 9 }, { 3, 23 }, { 4, 7 }, { 4, 10 }, + { 4, 24 }, { 5, 7 }, { 5, 11 }, { 5, 25 }, { 6, 12 }, + { 6, 26 }, { 7, 13 }, { 7, 27 }, { 8, 10 }, { 8, 14 }, + { 8, 28 }, { 9, 11 }, { 9, 15 }, { 9, 29 }, { 10, 16 }, + { 10, 30 }, { 11, 17 }, { 11, 31 }, { 12, 14 }, { 12, 15 }, + { 12, 32 }, { 13, 16 }, { 13, 17 }, { 13, 33 }, { 14, 18 }, + { 14, 34 }, { 15, 19 }, { 15, 35 }, { 16, 18 }, { 16, 36 }, + { 17, 19 }, { 17, 37 }, { 18, 19 }, { 18, 38 }, { 19, 39 }, + { 20, 40 }, { 20, 41 }, { 20, 43 }, { 21, 40 }, { 21, 42 }, + { 21, 44 }, { 22, 41 }, { 22, 45 }, { 22, 49 }, { 23, 42 }, + { 23, 46 }, { 23, 50 }, { 24, 43 }, { 24, 47 }, { 24, 51 }, + { 25, 44 }, { 25, 48 }, { 25, 52 }, { 26, 45 }, { 26, 46 }, + { 26, 53 }, { 27, 47 }, { 27, 48 }, { 27, 56 }, { 28, 49 }, + { 28, 54 }, { 28, 57 }, { 29, 50 }, { 29, 55 }, { 29, 58 }, + { 30, 51 }, { 30, 54 }, { 30, 59 }, { 31, 52 }, { 31, 55 }, + { 31, 60 }, { 32, 53 }, { 32, 61 }, { 32, 62 }, { 33, 56 }, + { 33, 63 }, { 33, 64 }, { 34, 57 }, { 34, 61 }, { 34, 65 }, + { 35, 58 }, { 35, 62 }, { 35, 66 }, { 36, 59 }, { 36, 63 }, + { 36, 67 }, { 37, 60 }, { 37, 64 }, { 37, 68 }, { 38, 65 }, + { 38, 67 }, { 38, 69 }, { 39, 66 }, { 39, 68 }, { 39, 69 }, + { 40, 70 }, { 40, 71 }, { 41, 72 }, { 41, 78 }, { 42, 73 }, + { 42, 79 }, { 43, 74 }, { 43, 80 }, { 44, 75 }, { 44, 81 }, + { 45, 76 }, { 45, 88 }, { 46, 77 }, { 46, 89 }, { 47, 82 }, + { 47, 92 }, { 48, 83 }, { 48, 93 }, { 49, 84 }, { 49, 94 }, + { 50, 85 }, { 50, 95 }, { 51, 86 }, { 51, 96 }, { 52, 87 }, + { 52, 97 }, { 53, 98 }, { 53, 99 }, { 54, 90 }, { 54, 108 }, + { 55, 91 }, { 55, 109 }, { 56, 100 }, { 56, 101 }, { 57, 102 }, + { 57, 112 }, { 58, 103 }, { 58, 113 }, { 59, 104 }, { 59, 114 }, + { 60, 105 }, { 60, 115 }, { 61, 106 }, { 61, 116 }, { 62, 107 }, + { 62, 117 }, { 63, 110 }, { 63, 122 }, { 64, 111 }, { 64, 123 }, + { 65, 118 }, { 65, 124 }, { 66, 119 }, { 66, 125 }, { 67, 120 }, + { 67, 126 }, { 68, 121 }, { 68, 127 }, { 69, 128 }, { 69, 129 }, + { 70, 72 }, { 70, 73 }, { 70, 130 }, { 71, 74 }, { 71, 75 }, + { 71, 131 }, { 72, 76 }, { 72, 132 }, { 73, 77 }, { 73, 133 }, + { 74, 82 }, { 74, 134 }, { 75, 83 }, { 75, 135 }, { 76, 77 }, + { 76, 140 }, { 77, 141 }, { 78, 80 }, { 78, 84 }, { 78, 136 }, + { 79, 81 }, { 79, 85 }, { 79, 137 }, { 80, 86 }, { 80, 138 }, + { 81, 87 }, { 81, 139 }, { 82, 83 }, { 82, 142 }, { 83, 143 }, + { 84, 90 }, { 84, 146 }, { 85, 91 }, { 85, 147 }, { 86, 90 }, + { 86, 148 }, { 87, 91 }, { 87, 149 }, { 88, 94 }, { 88, 98 }, + { 88, 144 }, { 89, 95 }, { 89, 99 }, { 89, 145 }, { 90, 156 }, + { 91, 157 }, { 92, 96 }, { 92, 100 }, { 92, 150 }, { 93, 97 }, + { 93, 101 }, { 93, 151 }, { 94, 102 }, { 94, 152 }, { 95, 103 }, + { 95, 153 }, { 96, 104 }, { 96, 154 }, { 97, 105 }, { 97, 155 }, + { 98, 106 }, { 98, 158 }, { 99, 107 }, { 99, 159 }, { 100, 110 }, + { 100, 160 }, { 101, 111 }, { 101, 161 }, { 102, 106 }, { 102, 164 }, + { 103, 107 }, { 103, 165 }, { 104, 110 }, { 104, 166 }, { 105, 111 }, + { 105, 167 }, { 106, 168 }, { 107, 169 }, { 108, 112 }, { 108, 114 }, + { 108, 162 }, { 109, 113 }, { 109, 115 }, { 109, 163 }, { 110, 174 }, + { 111, 175 }, { 112, 118 }, { 112, 170 }, { 113, 119 }, { 113, 171 }, + { 114, 120 }, { 114, 172 }, { 115, 121 }, { 115, 173 }, { 116, 117 }, + { 116, 124 }, { 116, 176 }, { 117, 125 }, { 117, 177 }, { 118, 120 }, + { 118, 180 }, { 119, 121 }, { 119, 181 }, { 120, 182 }, { 121, 183 }, + { 122, 123 }, { 122, 126 }, { 122, 178 }, { 123, 127 }, { 123, 179 }, + { 124, 128 }, { 124, 184 }, { 125, 128 }, { 125, 185 }, { 126, 129 }, + { 126, 186 }, { 127, 129 }, { 127, 187 }, { 128, 188 }, { 129, 189 }, + { 130, 131 }, { 130, 190 }, { 130, 191 }, { 131, 192 }, { 131, 193 }, + { 132, 136 }, { 132, 190 }, { 132, 196 }, { 133, 137 }, { 133, 191 }, + { 133, 197 }, { 134, 138 }, { 134, 192 }, { 134, 198 }, { 135, 139 }, + { 135, 193 }, { 135, 199 }, { 136, 194 }, { 136, 201 }, { 137, 195 }, + { 137, 202 }, { 138, 194 }, { 138, 203 }, { 139, 195 }, { 139, 204 }, + { 140, 144 }, { 140, 196 }, { 140, 200 }, { 141, 145 }, { 141, 197 }, + { 141, 200 }, { 142, 150 }, { 142, 198 }, { 142, 205 }, { 143, 151 }, + { 143, 199 }, { 143, 205 }, { 144, 206 }, { 144, 210 }, { 145, 207 }, + { 145, 211 }, { 146, 152 }, { 146, 201 }, { 146, 212 }, { 147, 153 }, + { 147, 202 }, { 147, 213 }, { 148, 154 }, { 148, 203 }, { 148, 214 }, + { 149, 155 }, { 149, 204 }, { 149, 215 }, { 150, 208 }, { 150, 216 }, + { 151, 209 }, { 151, 217 }, { 152, 206 }, { 152, 218 }, { 153, 207 }, + { 153, 219 }, { 154, 208 }, { 154, 220 }, { 155, 209 }, { 155, 221 }, + { 156, 162 }, { 156, 212 }, { 156, 214 }, { 157, 163 }, { 157, 213 }, + { 157, 215 }, { 158, 159 }, { 158, 210 }, { 158, 222 }, { 159, 211 }, + { 159, 223 }, { 160, 161 }, { 160, 216 }, { 160, 228 }, { 161, 217 }, + { 161, 229 }, { 162, 224 }, { 162, 226 }, { 163, 225 }, { 163, 227 }, + { 164, 170 }, { 164, 218 }, { 164, 230 }, { 165, 171 }, { 165, 219 }, + { 165, 231 }, { 166, 172 }, { 166, 220 }, { 166, 232 }, { 167, 173 }, + { 167, 221 }, { 167, 233 }, { 168, 176 }, { 168, 222 }, { 168, 230 }, + { 169, 177 }, { 169, 223 }, { 169, 231 }, { 170, 224 }, { 170, 235 }, + { 171, 225 }, { 171, 236 }, { 172, 226 }, { 172, 237 }, { 173, 227 }, + { 173, 238 }, { 174, 178 }, { 174, 228 }, { 174, 232 }, { 175, 179 }, + { 175, 229 }, { 175, 233 }, { 176, 234 }, { 176, 240 }, { 177, 234 }, + { 177, 241 }, { 178, 239 }, { 178, 242 }, { 179, 239 }, { 179, 243 }, + { 180, 184 }, { 180, 235 }, { 180, 244 }, { 181, 185 }, { 181, 236 }, + { 181, 245 }, { 182, 186 }, { 182, 237 }, { 182, 244 }, { 183, 187 }, + { 183, 238 }, { 183, 245 }, { 184, 240 }, { 184, 246 }, { 185, 241 }, + { 185, 247 }, { 186, 242 }, { 186, 248 }, { 187, 243 }, { 187, 249 }, + { 188, 189 }, { 188, 246 }, { 188, 247 }, { 189, 248 }, { 189, 249 }, + { 190, 250 }, { 190, 270 }, { 191, 251 }, { 191, 271 }, { 192, 250 }, + { 192, 272 }, { 193, 251 }, { 193, 273 }, { 194, 250 }, { 194, 279 }, + { 195, 251 }, { 195, 280 }, { 196, 252 }, { 196, 274 }, { 197, 253 }, + { 197, 275 }, { 198, 254 }, { 198, 276 }, { 199, 255 }, { 199, 277 }, + { 200, 256 }, { 200, 278 }, { 201, 252 }, { 201, 282 }, { 202, 253 }, + { 202, 283 }, { 203, 254 }, { 203, 284 }, { 204, 255 }, { 204, 285 }, + { 205, 257 }, { 205, 281 }, { 206, 252 }, { 206, 290 }, { 207, 253 }, + { 207, 291 }, { 208, 254 }, { 208, 292 }, { 209, 255 }, { 209, 293 }, + { 210, 256 }, { 210, 294 }, { 211, 256 }, { 211, 295 }, { 212, 258 }, + { 212, 286 }, { 213, 259 }, { 213, 287 }, { 214, 260 }, { 214, 288 }, + { 215, 261 }, { 215, 289 }, { 216, 257 }, { 216, 296 }, { 217, 257 }, + { 217, 297 }, { 218, 258 }, { 218, 298 }, { 219, 259 }, { 219, 299 }, + { 220, 260 }, { 220, 300 }, { 221, 261 }, { 221, 301 }, { 222, 262 }, + { 222, 302 }, { 223, 262 }, { 223, 303 }, { 224, 258 }, { 224, 310 }, + { 225, 259 }, { 225, 311 }, { 226, 260 }, { 226, 312 }, { 227, 261 }, + { 227, 313 }, { 228, 263 }, { 228, 304 }, { 229, 263 }, { 229, 305 }, + { 230, 264 }, { 230, 306 }, { 231, 265 }, { 231, 307 }, { 232, 266 }, + { 232, 308 }, { 233, 267 }, { 233, 309 }, { 234, 262 }, { 234, 318 }, + { 235, 264 }, { 235, 314 }, { 236, 265 }, { 236, 315 }, { 237, 266 }, + { 237, 316 }, { 238, 267 }, { 238, 317 }, { 239, 263 }, { 239, 321 }, + { 240, 264 }, { 240, 322 }, { 241, 265 }, { 241, 323 }, { 242, 266 }, + { 242, 324 }, { 243, 267 }, { 243, 325 }, { 244, 268 }, { 244, 319 }, + { 245, 269 }, { 245, 320 }, { 246, 268 }, { 246, 326 }, { 247, 269 }, + { 247, 327 }, { 248, 268 }, { 248, 328 }, { 249, 269 }, { 249, 329 }, + { 250, 330 }, { 251, 331 }, { 252, 332 }, { 253, 333 }, { 254, 334 }, + { 255, 335 }, { 256, 336 }, { 257, 337 }, { 258, 338 }, { 259, 339 }, + { 260, 340 }, { 261, 341 }, { 262, 342 }, { 263, 343 }, { 264, 344 }, + { 265, 345 }, { 266, 346 }, { 267, 347 }, { 268, 348 }, { 269, 349 }, + { 270, 271 }, { 270, 274 }, { 270, 350 }, { 271, 275 }, { 271, 351 }, + { 272, 273 }, { 272, 276 }, { 272, 352 }, { 273, 277 }, { 273, 353 }, + { 274, 278 }, { 274, 356 }, { 275, 278 }, { 275, 357 }, { 276, 281 }, + { 276, 358 }, { 277, 281 }, { 277, 359 }, { 278, 360 }, { 279, 282 }, + { 279, 284 }, { 279, 354 }, { 280, 283 }, { 280, 285 }, { 280, 355 }, + { 281, 365 }, { 282, 286 }, { 282, 361 }, { 283, 287 }, { 283, 362 }, + { 284, 288 }, { 284, 363 }, { 285, 289 }, { 285, 364 }, { 286, 288 }, + { 286, 372 }, { 287, 289 }, { 287, 373 }, { 288, 374 }, { 289, 375 }, + { 290, 294 }, { 290, 298 }, { 290, 366 }, { 291, 295 }, { 291, 299 }, + { 291, 367 }, { 292, 296 }, { 292, 300 }, { 292, 368 }, { 293, 297 }, + { 293, 301 }, { 293, 369 }, { 294, 302 }, { 294, 370 }, { 295, 303 }, + { 295, 371 }, { 296, 304 }, { 296, 376 }, { 297, 305 }, { 297, 377 }, + { 298, 306 }, { 298, 378 }, { 299, 307 }, { 299, 379 }, { 300, 308 }, + { 300, 380 }, { 301, 309 }, { 301, 381 }, { 302, 306 }, { 302, 382 }, + { 303, 307 }, { 303, 383 }, { 304, 308 }, { 304, 388 }, { 305, 309 }, + { 305, 389 }, { 306, 390 }, { 307, 391 }, { 308, 392 }, { 309, 393 }, + { 310, 312 }, { 310, 314 }, { 310, 384 }, { 311, 313 }, { 311, 315 }, + { 311, 385 }, { 312, 316 }, { 312, 386 }, { 313, 317 }, { 313, 387 }, + { 314, 319 }, { 314, 395 }, { 315, 320 }, { 315, 396 }, { 316, 319 }, + { 316, 397 }, { 317, 320 }, { 317, 398 }, { 318, 322 }, { 318, 323 }, + { 318, 394 }, { 319, 404 }, { 320, 405 }, { 321, 324 }, { 321, 325 }, + { 321, 399 }, { 322, 326 }, { 322, 400 }, { 323, 327 }, { 323, 401 }, + { 324, 328 }, { 324, 402 }, { 325, 329 }, { 325, 403 }, { 326, 327 }, + { 326, 406 }, { 327, 407 }, { 328, 329 }, { 328, 408 }, { 329, 409 }, + { 330, 350 }, { 330, 352 }, { 330, 354 }, { 331, 351 }, { 331, 353 }, + { 331, 355 }, { 332, 356 }, { 332, 361 }, { 332, 366 }, { 333, 357 }, + { 333, 362 }, { 333, 367 }, { 334, 358 }, { 334, 363 }, { 334, 368 }, + { 335, 359 }, { 335, 364 }, { 335, 369 }, { 336, 360 }, { 336, 370 }, + { 336, 371 }, { 337, 365 }, { 337, 376 }, { 337, 377 }, { 338, 372 }, + { 338, 378 }, { 338, 384 }, { 339, 373 }, { 339, 379 }, { 339, 385 }, + { 340, 374 }, { 340, 380 }, { 340, 386 }, { 341, 375 }, { 341, 381 }, + { 341, 387 }, { 342, 382 }, { 342, 383 }, { 342, 394 }, { 343, 388 }, + { 343, 389 }, { 343, 399 }, { 344, 390 }, { 344, 395 }, { 344, 400 }, + { 345, 391 }, { 345, 396 }, { 345, 401 }, { 346, 392 }, { 346, 397 }, + { 346, 402 }, { 347, 393 }, { 347, 398 }, { 347, 403 }, { 348, 404 }, + { 348, 406 }, { 348, 408 }, { 349, 405 }, { 349, 407 }, { 349, 409 }, + { 350, 410 }, { 350, 412 }, { 351, 410 }, { 351, 413 }, { 352, 411 }, + { 352, 414 }, { 353, 411 }, { 353, 415 }, { 354, 416 }, { 354, 418 }, + { 355, 417 }, { 355, 419 }, { 356, 412 }, { 356, 420 }, { 357, 413 }, + { 357, 421 }, { 358, 414 }, { 358, 422 }, { 359, 415 }, { 359, 423 }, + { 360, 420 }, { 360, 421 }, { 361, 416 }, { 361, 426 }, { 362, 417 }, + { 362, 427 }, { 363, 418 }, { 363, 428 }, { 364, 419 }, { 364, 429 }, + { 365, 422 }, { 365, 423 }, { 366, 424 }, { 366, 432 }, { 367, 425 }, + { 367, 433 }, { 368, 430 }, { 368, 434 }, { 369, 431 }, { 369, 435 }, + { 370, 424 }, { 370, 438 }, { 371, 425 }, { 371, 439 }, { 372, 426 }, + { 372, 436 }, { 373, 427 }, { 373, 437 }, { 374, 428 }, { 374, 436 }, + { 375, 429 }, { 375, 437 }, { 376, 430 }, { 376, 440 }, { 377, 431 }, + { 377, 441 }, { 378, 432 }, { 378, 444 }, { 379, 433 }, { 379, 445 }, + { 380, 434 }, { 380, 446 }, { 381, 435 }, { 381, 447 }, { 382, 438 }, + { 382, 448 }, { 383, 439 }, { 383, 449 }, { 384, 442 }, { 384, 450 }, + { 385, 443 }, { 385, 451 }, { 386, 442 }, { 386, 452 }, { 387, 443 }, + { 387, 453 }, { 388, 440 }, { 388, 454 }, { 389, 441 }, { 389, 455 }, + { 390, 444 }, { 390, 448 }, { 391, 445 }, { 391, 449 }, { 392, 446 }, + { 392, 454 }, { 393, 447 }, { 393, 455 }, { 394, 456 }, { 394, 457 }, + { 395, 450 }, { 395, 460 }, { 396, 451 }, { 396, 461 }, { 397, 452 }, + { 397, 462 }, { 398, 453 }, { 398, 463 }, { 399, 458 }, { 399, 459 }, + { 400, 456 }, { 400, 464 }, { 401, 457 }, { 401, 465 }, { 402, 458 }, + { 402, 466 }, { 403, 459 }, { 403, 467 }, { 404, 460 }, { 404, 462 }, + { 405, 461 }, { 405, 463 }, { 406, 464 }, { 406, 468 }, { 407, 465 }, + { 407, 468 }, { 408, 466 }, { 408, 469 }, { 409, 467 }, { 409, 469 }, + { 410, 411 }, { 410, 470 }, { 411, 471 }, { 412, 416 }, { 412, 472 }, + { 413, 417 }, { 413, 473 }, { 414, 418 }, { 414, 474 }, { 415, 419 }, + { 415, 475 }, { 416, 478 }, { 417, 479 }, { 418, 480 }, { 419, 481 }, + { 420, 424 }, { 420, 476 }, { 421, 425 }, { 421, 477 }, { 422, 430 }, + { 422, 482 }, { 423, 431 }, { 423, 483 }, { 424, 488 }, { 425, 489 }, + { 426, 432 }, { 426, 484 }, { 427, 433 }, { 427, 485 }, { 428, 434 }, + { 428, 486 }, { 429, 435 }, { 429, 487 }, { 430, 492 }, { 431, 493 }, + { 432, 494 }, { 433, 495 }, { 434, 496 }, { 435, 497 }, { 436, 442 }, + { 436, 490 }, { 437, 443 }, { 437, 491 }, { 438, 439 }, { 438, 498 }, + { 439, 499 }, { 440, 441 }, { 440, 500 }, { 441, 501 }, { 442, 508 }, + { 443, 509 }, { 444, 450 }, { 444, 502 }, { 445, 451 }, { 445, 503 }, + { 446, 452 }, { 446, 504 }, { 447, 453 }, { 447, 505 }, { 448, 456 }, + { 448, 506 }, { 449, 457 }, { 449, 507 }, { 450, 512 }, { 451, 513 }, + { 452, 514 }, { 453, 515 }, { 454, 458 }, { 454, 510 }, { 455, 459 }, + { 455, 511 }, { 456, 516 }, { 457, 517 }, { 458, 522 }, { 459, 523 }, + { 460, 464 }, { 460, 518 }, { 461, 465 }, { 461, 519 }, { 462, 466 }, + { 462, 520 }, { 463, 467 }, { 463, 521 }, { 464, 524 }, { 465, 525 }, + { 466, 526 }, { 467, 527 }, { 468, 469 }, { 468, 528 }, { 469, 529 }, + { 470, 472 }, { 470, 473 }, { 470, 530 }, { 471, 474 }, { 471, 475 }, + { 471, 530 }, { 472, 476 }, { 472, 531 }, { 473, 477 }, { 473, 532 }, + { 474, 482 }, { 474, 533 }, { 475, 483 }, { 475, 534 }, { 476, 477 }, + { 476, 535 }, { 477, 536 }, { 478, 480 }, { 478, 484 }, { 478, 531 }, + { 479, 481 }, { 479, 485 }, { 479, 532 }, { 480, 486 }, { 480, 533 }, + { 481, 487 }, { 481, 534 }, { 482, 483 }, { 482, 537 }, { 483, 538 }, + { 484, 490 }, { 484, 539 }, { 485, 491 }, { 485, 540 }, { 486, 490 }, + { 486, 541 }, { 487, 491 }, { 487, 542 }, { 488, 494 }, { 488, 498 }, + { 488, 535 }, { 489, 495 }, { 489, 499 }, { 489, 536 }, { 490, 544 }, + { 491, 545 }, { 492, 496 }, { 492, 500 }, { 492, 537 }, { 493, 497 }, + { 493, 501 }, { 493, 538 }, { 494, 502 }, { 494, 539 }, { 495, 503 }, + { 495, 540 }, { 496, 504 }, { 496, 541 }, { 497, 505 }, { 497, 542 }, + { 498, 506 }, { 498, 543 }, { 499, 507 }, { 499, 543 }, { 500, 510 }, + { 500, 546 }, { 501, 511 }, { 501, 546 }, { 502, 506 }, { 502, 547 }, + { 503, 507 }, { 503, 548 }, { 504, 510 }, { 504, 549 }, { 505, 511 }, + { 505, 550 }, { 506, 551 }, { 507, 552 }, { 508, 512 }, { 508, 514 }, + { 508, 544 }, { 509, 513 }, { 509, 515 }, { 509, 545 }, { 510, 553 }, + { 511, 554 }, { 512, 518 }, { 512, 547 }, { 513, 519 }, { 513, 548 }, + { 514, 520 }, { 514, 549 }, { 515, 521 }, { 515, 550 }, { 516, 517 }, + { 516, 524 }, { 516, 551 }, { 517, 525 }, { 517, 552 }, { 518, 520 }, + { 518, 555 }, { 519, 521 }, { 519, 556 }, { 520, 557 }, { 521, 558 }, + { 522, 523 }, { 522, 526 }, { 522, 553 }, { 523, 527 }, { 523, 554 }, + { 524, 528 }, { 524, 555 }, { 525, 528 }, { 525, 556 }, { 526, 529 }, + { 526, 557 }, { 527, 529 }, { 527, 558 }, { 528, 559 }, { 529, 559 }, + { 530, 560 }, { 530, 561 }, { 531, 560 }, { 531, 562 }, { 532, 561 }, + { 532, 563 }, { 533, 560 }, { 533, 564 }, { 534, 561 }, { 534, 565 }, + { 535, 562 }, { 535, 566 }, { 536, 563 }, { 536, 566 }, { 537, 564 }, + { 537, 567 }, { 538, 565 }, { 538, 567 }, { 539, 562 }, { 539, 568 }, + { 540, 563 }, { 540, 569 }, { 541, 564 }, { 541, 570 }, { 542, 565 }, + { 542, 571 }, { 543, 566 }, { 543, 572 }, { 544, 568 }, { 544, 570 }, + { 545, 569 }, { 545, 571 }, { 546, 567 }, { 546, 573 }, { 547, 568 }, + { 547, 574 }, { 548, 569 }, { 548, 575 }, { 549, 570 }, { 549, 576 }, + { 550, 571 }, { 550, 577 }, { 551, 572 }, { 551, 574 }, { 552, 572 }, + { 552, 575 }, { 553, 573 }, { 553, 576 }, { 554, 573 }, { 554, 577 }, + { 555, 574 }, { 555, 578 }, { 556, 575 }, { 556, 579 }, { 557, 576 }, + { 557, 578 }, { 558, 577 }, { 558, 579 }, { 559, 578 }, { 559, 579 }, + { 560, 580 }, { 561, 581 }, { 562, 582 }, { 563, 583 }, { 564, 584 }, + { 565, 585 }, { 566, 586 }, { 567, 587 }, { 568, 588 }, { 569, 589 }, + { 570, 590 }, { 571, 591 }, { 572, 592 }, { 573, 593 }, { 574, 594 }, + { 575, 595 }, { 576, 596 }, { 577, 597 }, { 578, 598 }, { 579, 599 }, + { 580, 581 }, { 580, 582 }, { 580, 584 }, { 581, 583 }, { 581, 585 }, + { 582, 586 }, { 582, 588 }, { 583, 586 }, { 583, 589 }, { 584, 587 }, + { 584, 590 }, { 585, 587 }, { 585, 591 }, { 586, 592 }, { 587, 593 }, + { 588, 590 }, { 588, 594 }, { 589, 591 }, { 589, 595 }, { 590, 596 }, + { 591, 597 }, { 592, 594 }, { 592, 595 }, { 593, 596 }, { 593, 597 }, + { 594, 598 }, { 595, 599 }, { 596, 598 }, { 597, 599 }, { 598, 599 } +}; + +static const int face_120[NUM_FACE_120][VERT_PER_FACE_120] = { + { 0, 1, 3, 6, 2 }, { 0, 1, 5, 7, 4 }, + { 0, 1, 21, 40, 20 }, { 0, 2, 8, 10, 4 }, + { 0, 2, 22, 41, 20 }, { 0, 4, 24, 43, 20 }, + { 1, 3, 9, 11, 5 }, { 1, 3, 23, 42, 21 }, + { 1, 5, 25, 44, 21 }, { 2, 6, 12, 14, 8 }, + { 2, 6, 26, 45, 22 }, { 2, 8, 28, 49, 22 }, + { 3, 6, 12, 15, 9 }, { 3, 6, 26, 46, 23 }, + { 3, 9, 29, 50, 23 }, { 4, 7, 13, 16, 10 }, + { 4, 7, 27, 47, 24 }, { 4, 10, 30, 51, 24 }, + { 5, 7, 13, 17, 11 }, { 5, 7, 27, 48, 25 }, + { 5, 11, 31, 52, 25 }, { 6, 12, 32, 53, 26 }, + { 7, 13, 33, 56, 27 }, { 8, 10, 16, 18, 14 }, + { 8, 10, 30, 54, 28 }, { 8, 14, 34, 57, 28 }, + { 9, 11, 17, 19, 15 }, { 9, 11, 31, 55, 29 }, + { 9, 15, 35, 58, 29 }, { 10, 16, 36, 59, 30 }, + { 11, 17, 37, 60, 31 }, { 12, 14, 18, 19, 15 }, + { 12, 14, 34, 61, 32 }, { 12, 15, 35, 62, 32 }, + { 13, 16, 18, 19, 17 }, { 13, 16, 36, 63, 33 }, + { 13, 17, 37, 64, 33 }, { 14, 18, 38, 65, 34 }, + { 15, 19, 39, 66, 35 }, { 16, 18, 38, 67, 36 }, + { 17, 19, 39, 68, 37 }, { 18, 19, 39, 69, 38 }, + { 20, 40, 70, 72, 41 }, { 20, 40, 71, 74, 43 }, + { 20, 41, 78, 80, 43 }, { 21, 40, 70, 73, 42 }, + { 21, 40, 71, 75, 44 }, { 21, 42, 79, 81, 44 }, + { 22, 41, 72, 76, 45 }, { 22, 41, 78, 84, 49 }, + { 22, 45, 88, 94, 49 }, { 23, 42, 73, 77, 46 }, + { 23, 42, 79, 85, 50 }, { 23, 46, 89, 95, 50 }, + { 24, 43, 74, 82, 47 }, { 24, 43, 80, 86, 51 }, + { 24, 47, 92, 96, 51 }, { 25, 44, 75, 83, 48 }, + { 25, 44, 81, 87, 52 }, { 25, 48, 93, 97, 52 }, + { 26, 45, 76, 77, 46 }, { 26, 45, 88, 98, 53 }, + { 26, 46, 89, 99, 53 }, { 27, 47, 82, 83, 48 }, + { 27, 47, 92, 100, 56 }, { 27, 48, 93, 101, 56 }, + { 28, 49, 84, 90, 54 }, { 28, 49, 94, 102, 57 }, + { 28, 54, 108, 112, 57 }, { 29, 50, 85, 91, 55 }, + { 29, 50, 95, 103, 58 }, { 29, 55, 109, 113, 58 }, + { 30, 51, 86, 90, 54 }, { 30, 51, 96, 104, 59 }, + { 30, 54, 108, 114, 59 }, { 31, 52, 87, 91, 55 }, + { 31, 52, 97, 105, 60 }, { 31, 55, 109, 115, 60 }, + { 32, 53, 98, 106, 61 }, { 32, 53, 99, 107, 62 }, + { 32, 61, 116, 117, 62 }, { 33, 56, 100, 110, 63 }, + { 33, 56, 101, 111, 64 }, { 33, 63, 122, 123, 64 }, + { 34, 57, 102, 106, 61 }, { 34, 57, 112, 118, 65 }, + { 34, 61, 116, 124, 65 }, { 35, 58, 103, 107, 62 }, + { 35, 58, 113, 119, 66 }, { 35, 62, 117, 125, 66 }, + { 36, 59, 104, 110, 63 }, { 36, 59, 114, 120, 67 }, + { 36, 63, 122, 126, 67 }, { 37, 60, 105, 111, 64 }, + { 37, 60, 115, 121, 68 }, { 37, 64, 123, 127, 68 }, + { 38, 65, 118, 120, 67 }, { 38, 65, 124, 128, 69 }, + { 38, 67, 126, 129, 69 }, { 39, 66, 119, 121, 68 }, + { 39, 66, 125, 128, 69 }, { 39, 68, 127, 129, 69 }, + { 40, 70, 130, 131, 71 }, { 41, 72, 132, 136, 78 }, + { 42, 73, 133, 137, 79 }, { 43, 74, 134, 138, 80 }, + { 44, 75, 135, 139, 81 }, { 45, 76, 140, 144, 88 }, + { 46, 77, 141, 145, 89 }, { 47, 82, 142, 150, 92 }, + { 48, 83, 143, 151, 93 }, { 49, 84, 146, 152, 94 }, + { 50, 85, 147, 153, 95 }, { 51, 86, 148, 154, 96 }, + { 52, 87, 149, 155, 97 }, { 53, 98, 158, 159, 99 }, + { 54, 90, 156, 162, 108 }, { 55, 91, 157, 163, 109 }, + { 56, 100, 160, 161, 101 }, { 57, 102, 164, 170, 112 }, + { 58, 103, 165, 171, 113 }, { 59, 104, 166, 172, 114 }, + { 60, 105, 167, 173, 115 }, { 61, 106, 168, 176, 116 }, + { 62, 107, 169, 177, 117 }, { 63, 110, 174, 178, 122 }, + { 64, 111, 175, 179, 123 }, { 65, 118, 180, 184, 124 }, + { 66, 119, 181, 185, 125 }, { 67, 120, 182, 186, 126 }, + { 68, 121, 183, 187, 127 }, { 69, 128, 188, 189, 129 }, + { 70, 72, 76, 77, 73 }, { 70, 72, 132, 190, 130 }, + { 70, 73, 133, 191, 130 }, { 71, 74, 82, 83, 75 }, + { 71, 74, 134, 192, 131 }, { 71, 75, 135, 193, 131 }, + { 72, 76, 140, 196, 132 }, { 73, 77, 141, 197, 133 }, + { 74, 82, 142, 198, 134 }, { 75, 83, 143, 199, 135 }, + { 76, 77, 141, 200, 140 }, { 78, 80, 86, 90, 84 }, + { 78, 80, 138, 194, 136 }, { 78, 84, 146, 201, 136 }, + { 79, 81, 87, 91, 85 }, { 79, 81, 139, 195, 137 }, + { 79, 85, 147, 202, 137 }, { 80, 86, 148, 203, 138 }, + { 81, 87, 149, 204, 139 }, { 82, 83, 143, 205, 142 }, + { 84, 90, 156, 212, 146 }, { 85, 91, 157, 213, 147 }, + { 86, 90, 156, 214, 148 }, { 87, 91, 157, 215, 149 }, + { 88, 94, 102, 106, 98 }, { 88, 94, 152, 206, 144 }, + { 88, 98, 158, 210, 144 }, { 89, 95, 103, 107, 99 }, + { 89, 95, 153, 207, 145 }, { 89, 99, 159, 211, 145 }, + { 92, 96, 104, 110, 100 }, { 92, 96, 154, 208, 150 }, + { 92, 100, 160, 216, 150 }, { 93, 97, 105, 111, 101 }, + { 93, 97, 155, 209, 151 }, { 93, 101, 161, 217, 151 }, + { 94, 102, 164, 218, 152 }, { 95, 103, 165, 219, 153 }, + { 96, 104, 166, 220, 154 }, { 97, 105, 167, 221, 155 }, + { 98, 106, 168, 222, 158 }, { 99, 107, 169, 223, 159 }, + { 100, 110, 174, 228, 160 }, { 101, 111, 175, 229, 161 }, + { 102, 106, 168, 230, 164 }, { 103, 107, 169, 231, 165 }, + { 104, 110, 174, 232, 166 }, { 105, 111, 175, 233, 167 }, + { 108, 112, 118, 120, 114 }, { 108, 112, 170, 224, 162 }, + { 108, 114, 172, 226, 162 }, { 109, 113, 119, 121, 115 }, + { 109, 113, 171, 225, 163 }, { 109, 115, 173, 227, 163 }, + { 112, 118, 180, 235, 170 }, { 113, 119, 181, 236, 171 }, + { 114, 120, 182, 237, 172 }, { 115, 121, 183, 238, 173 }, + { 116, 117, 125, 128, 124 }, { 116, 117, 177, 234, 176 }, + { 116, 124, 184, 240, 176 }, { 117, 125, 185, 241, 177 }, + { 118, 120, 182, 244, 180 }, { 119, 121, 183, 245, 181 }, + { 122, 123, 127, 129, 126 }, { 122, 123, 179, 239, 178 }, + { 122, 126, 186, 242, 178 }, { 123, 127, 187, 243, 179 }, + { 124, 128, 188, 246, 184 }, { 125, 128, 188, 247, 185 }, + { 126, 129, 189, 248, 186 }, { 127, 129, 189, 249, 187 }, + { 130, 131, 192, 250, 190 }, { 130, 131, 193, 251, 191 }, + { 130, 190, 270, 271, 191 }, { 131, 192, 272, 273, 193 }, + { 132, 136, 194, 250, 190 }, { 132, 136, 201, 252, 196 }, + { 132, 190, 270, 274, 196 }, { 133, 137, 195, 251, 191 }, + { 133, 137, 202, 253, 197 }, { 133, 191, 271, 275, 197 }, + { 134, 138, 194, 250, 192 }, { 134, 138, 203, 254, 198 }, + { 134, 192, 272, 276, 198 }, { 135, 139, 195, 251, 193 }, + { 135, 139, 204, 255, 199 }, { 135, 193, 273, 277, 199 }, + { 136, 194, 279, 282, 201 }, { 137, 195, 280, 283, 202 }, + { 138, 194, 279, 284, 203 }, { 139, 195, 280, 285, 204 }, + { 140, 144, 206, 252, 196 }, { 140, 144, 210, 256, 200 }, + { 140, 196, 274, 278, 200 }, { 141, 145, 207, 253, 197 }, + { 141, 145, 211, 256, 200 }, { 141, 197, 275, 278, 200 }, + { 142, 150, 208, 254, 198 }, { 142, 150, 216, 257, 205 }, + { 142, 198, 276, 281, 205 }, { 143, 151, 209, 255, 199 }, + { 143, 151, 217, 257, 205 }, { 143, 199, 277, 281, 205 }, + { 144, 206, 290, 294, 210 }, { 145, 207, 291, 295, 211 }, + { 146, 152, 206, 252, 201 }, { 146, 152, 218, 258, 212 }, + { 146, 201, 282, 286, 212 }, { 147, 153, 207, 253, 202 }, + { 147, 153, 219, 259, 213 }, { 147, 202, 283, 287, 213 }, + { 148, 154, 208, 254, 203 }, { 148, 154, 220, 260, 214 }, + { 148, 203, 284, 288, 214 }, { 149, 155, 209, 255, 204 }, + { 149, 155, 221, 261, 215 }, { 149, 204, 285, 289, 215 }, + { 150, 208, 292, 296, 216 }, { 151, 209, 293, 297, 217 }, + { 152, 206, 290, 298, 218 }, { 153, 207, 291, 299, 219 }, + { 154, 208, 292, 300, 220 }, { 155, 209, 293, 301, 221 }, + { 156, 162, 224, 258, 212 }, { 156, 162, 226, 260, 214 }, + { 156, 212, 286, 288, 214 }, { 157, 163, 225, 259, 213 }, + { 157, 163, 227, 261, 215 }, { 157, 213, 287, 289, 215 }, + { 158, 159, 211, 256, 210 }, { 158, 159, 223, 262, 222 }, + { 158, 210, 294, 302, 222 }, { 159, 211, 295, 303, 223 }, + { 160, 161, 217, 257, 216 }, { 160, 161, 229, 263, 228 }, + { 160, 216, 296, 304, 228 }, { 161, 217, 297, 305, 229 }, + { 162, 224, 310, 312, 226 }, { 163, 225, 311, 313, 227 }, + { 164, 170, 224, 258, 218 }, { 164, 170, 235, 264, 230 }, + { 164, 218, 298, 306, 230 }, { 165, 171, 225, 259, 219 }, + { 165, 171, 236, 265, 231 }, { 165, 219, 299, 307, 231 }, + { 166, 172, 226, 260, 220 }, { 166, 172, 237, 266, 232 }, + { 166, 220, 300, 308, 232 }, { 167, 173, 227, 261, 221 }, + { 167, 173, 238, 267, 233 }, { 167, 221, 301, 309, 233 }, + { 168, 176, 234, 262, 222 }, { 168, 176, 240, 264, 230 }, + { 168, 222, 302, 306, 230 }, { 169, 177, 234, 262, 223 }, + { 169, 177, 241, 265, 231 }, { 169, 223, 303, 307, 231 }, + { 170, 224, 310, 314, 235 }, { 171, 225, 311, 315, 236 }, + { 172, 226, 312, 316, 237 }, { 173, 227, 313, 317, 238 }, + { 174, 178, 239, 263, 228 }, { 174, 178, 242, 266, 232 }, + { 174, 228, 304, 308, 232 }, { 175, 179, 239, 263, 229 }, + { 175, 179, 243, 267, 233 }, { 175, 229, 305, 309, 233 }, + { 176, 234, 318, 322, 240 }, { 177, 234, 318, 323, 241 }, + { 178, 239, 321, 324, 242 }, { 179, 239, 321, 325, 243 }, + { 180, 184, 240, 264, 235 }, { 180, 184, 246, 268, 244 }, + { 180, 235, 314, 319, 244 }, { 181, 185, 241, 265, 236 }, + { 181, 185, 247, 269, 245 }, { 181, 236, 315, 320, 245 }, + { 182, 186, 242, 266, 237 }, { 182, 186, 248, 268, 244 }, + { 182, 237, 316, 319, 244 }, { 183, 187, 243, 267, 238 }, + { 183, 187, 249, 269, 245 }, { 183, 238, 317, 320, 245 }, + { 184, 240, 322, 326, 246 }, { 185, 241, 323, 327, 247 }, + { 186, 242, 324, 328, 248 }, { 187, 243, 325, 329, 249 }, + { 188, 189, 248, 268, 246 }, { 188, 189, 249, 269, 247 }, + { 188, 246, 326, 327, 247 }, { 189, 248, 328, 329, 249 }, + { 190, 250, 330, 350, 270 }, { 191, 251, 331, 351, 271 }, + { 192, 250, 330, 352, 272 }, { 193, 251, 331, 353, 273 }, + { 194, 250, 330, 354, 279 }, { 195, 251, 331, 355, 280 }, + { 196, 252, 332, 356, 274 }, { 197, 253, 333, 357, 275 }, + { 198, 254, 334, 358, 276 }, { 199, 255, 335, 359, 277 }, + { 200, 256, 336, 360, 278 }, { 201, 252, 332, 361, 282 }, + { 202, 253, 333, 362, 283 }, { 203, 254, 334, 363, 284 }, + { 204, 255, 335, 364, 285 }, { 205, 257, 337, 365, 281 }, + { 206, 252, 332, 366, 290 }, { 207, 253, 333, 367, 291 }, + { 208, 254, 334, 368, 292 }, { 209, 255, 335, 369, 293 }, + { 210, 256, 336, 370, 294 }, { 211, 256, 336, 371, 295 }, + { 212, 258, 338, 372, 286 }, { 213, 259, 339, 373, 287 }, + { 214, 260, 340, 374, 288 }, { 215, 261, 341, 375, 289 }, + { 216, 257, 337, 376, 296 }, { 217, 257, 337, 377, 297 }, + { 218, 258, 338, 378, 298 }, { 219, 259, 339, 379, 299 }, + { 220, 260, 340, 380, 300 }, { 221, 261, 341, 381, 301 }, + { 222, 262, 342, 382, 302 }, { 223, 262, 342, 383, 303 }, + { 224, 258, 338, 384, 310 }, { 225, 259, 339, 385, 311 }, + { 226, 260, 340, 386, 312 }, { 227, 261, 341, 387, 313 }, + { 228, 263, 343, 388, 304 }, { 229, 263, 343, 389, 305 }, + { 230, 264, 344, 390, 306 }, { 231, 265, 345, 391, 307 }, + { 232, 266, 346, 392, 308 }, { 233, 267, 347, 393, 309 }, + { 234, 262, 342, 394, 318 }, { 235, 264, 344, 395, 314 }, + { 236, 265, 345, 396, 315 }, { 237, 266, 346, 397, 316 }, + { 238, 267, 347, 398, 317 }, { 239, 263, 343, 399, 321 }, + { 240, 264, 344, 400, 322 }, { 241, 265, 345, 401, 323 }, + { 242, 266, 346, 402, 324 }, { 243, 267, 347, 403, 325 }, + { 244, 268, 348, 404, 319 }, { 245, 269, 349, 405, 320 }, + { 246, 268, 348, 406, 326 }, { 247, 269, 349, 407, 327 }, + { 248, 268, 348, 408, 328 }, { 249, 269, 349, 409, 329 }, + { 270, 271, 275, 278, 274 }, { 270, 271, 351, 410, 350 }, + { 270, 274, 356, 412, 350 }, { 271, 275, 357, 413, 351 }, + { 272, 273, 277, 281, 276 }, { 272, 273, 353, 411, 352 }, + { 272, 276, 358, 414, 352 }, { 273, 277, 359, 415, 353 }, + { 274, 278, 360, 420, 356 }, { 275, 278, 360, 421, 357 }, + { 276, 281, 365, 422, 358 }, { 277, 281, 365, 423, 359 }, + { 279, 282, 286, 288, 284 }, { 279, 282, 361, 416, 354 }, + { 279, 284, 363, 418, 354 }, { 280, 283, 287, 289, 285 }, + { 280, 283, 362, 417, 355 }, { 280, 285, 364, 419, 355 }, + { 282, 286, 372, 426, 361 }, { 283, 287, 373, 427, 362 }, + { 284, 288, 374, 428, 363 }, { 285, 289, 375, 429, 364 }, + { 286, 288, 374, 436, 372 }, { 287, 289, 375, 437, 373 }, + { 290, 294, 302, 306, 298 }, { 290, 294, 370, 424, 366 }, + { 290, 298, 378, 432, 366 }, { 291, 295, 303, 307, 299 }, + { 291, 295, 371, 425, 367 }, { 291, 299, 379, 433, 367 }, + { 292, 296, 304, 308, 300 }, { 292, 296, 376, 430, 368 }, + { 292, 300, 380, 434, 368 }, { 293, 297, 305, 309, 301 }, + { 293, 297, 377, 431, 369 }, { 293, 301, 381, 435, 369 }, + { 294, 302, 382, 438, 370 }, { 295, 303, 383, 439, 371 }, + { 296, 304, 388, 440, 376 }, { 297, 305, 389, 441, 377 }, + { 298, 306, 390, 444, 378 }, { 299, 307, 391, 445, 379 }, + { 300, 308, 392, 446, 380 }, { 301, 309, 393, 447, 381 }, + { 302, 306, 390, 448, 382 }, { 303, 307, 391, 449, 383 }, + { 304, 308, 392, 454, 388 }, { 305, 309, 393, 455, 389 }, + { 310, 312, 316, 319, 314 }, { 310, 312, 386, 442, 384 }, + { 310, 314, 395, 450, 384 }, { 311, 313, 317, 320, 315 }, + { 311, 313, 387, 443, 385 }, { 311, 315, 396, 451, 385 }, + { 312, 316, 397, 452, 386 }, { 313, 317, 398, 453, 387 }, + { 314, 319, 404, 460, 395 }, { 315, 320, 405, 461, 396 }, + { 316, 319, 404, 462, 397 }, { 317, 320, 405, 463, 398 }, + { 318, 322, 326, 327, 323 }, { 318, 322, 400, 456, 394 }, + { 318, 323, 401, 457, 394 }, { 321, 324, 328, 329, 325 }, + { 321, 324, 402, 458, 399 }, { 321, 325, 403, 459, 399 }, + { 322, 326, 406, 464, 400 }, { 323, 327, 407, 465, 401 }, + { 324, 328, 408, 466, 402 }, { 325, 329, 409, 467, 403 }, + { 326, 327, 407, 468, 406 }, { 328, 329, 409, 469, 408 }, + { 330, 350, 410, 411, 352 }, { 330, 350, 412, 416, 354 }, + { 330, 352, 414, 418, 354 }, { 331, 351, 410, 411, 353 }, + { 331, 351, 413, 417, 355 }, { 331, 353, 415, 419, 355 }, + { 332, 356, 412, 416, 361 }, { 332, 356, 420, 424, 366 }, + { 332, 361, 426, 432, 366 }, { 333, 357, 413, 417, 362 }, + { 333, 357, 421, 425, 367 }, { 333, 362, 427, 433, 367 }, + { 334, 358, 414, 418, 363 }, { 334, 358, 422, 430, 368 }, + { 334, 363, 428, 434, 368 }, { 335, 359, 415, 419, 364 }, + { 335, 359, 423, 431, 369 }, { 335, 364, 429, 435, 369 }, + { 336, 360, 420, 424, 370 }, { 336, 360, 421, 425, 371 }, + { 336, 370, 438, 439, 371 }, { 337, 365, 422, 430, 376 }, + { 337, 365, 423, 431, 377 }, { 337, 376, 440, 441, 377 }, + { 338, 372, 426, 432, 378 }, { 338, 372, 436, 442, 384 }, + { 338, 378, 444, 450, 384 }, { 339, 373, 427, 433, 379 }, + { 339, 373, 437, 443, 385 }, { 339, 379, 445, 451, 385 }, + { 340, 374, 428, 434, 380 }, { 340, 374, 436, 442, 386 }, + { 340, 380, 446, 452, 386 }, { 341, 375, 429, 435, 381 }, + { 341, 375, 437, 443, 387 }, { 341, 381, 447, 453, 387 }, + { 342, 382, 438, 439, 383 }, { 342, 382, 448, 456, 394 }, + { 342, 383, 449, 457, 394 }, { 343, 388, 440, 441, 389 }, + { 343, 388, 454, 458, 399 }, { 343, 389, 455, 459, 399 }, + { 344, 390, 444, 450, 395 }, { 344, 390, 448, 456, 400 }, + { 344, 395, 460, 464, 400 }, { 345, 391, 445, 451, 396 }, + { 345, 391, 449, 457, 401 }, { 345, 396, 461, 465, 401 }, + { 346, 392, 446, 452, 397 }, { 346, 392, 454, 458, 402 }, + { 346, 397, 462, 466, 402 }, { 347, 393, 447, 453, 398 }, + { 347, 393, 455, 459, 403 }, { 347, 398, 463, 467, 403 }, + { 348, 404, 460, 464, 406 }, { 348, 404, 462, 466, 408 }, + { 348, 406, 468, 469, 408 }, { 349, 405, 461, 465, 407 }, + { 349, 405, 463, 467, 409 }, { 349, 407, 468, 469, 409 }, + { 350, 410, 470, 472, 412 }, { 351, 410, 470, 473, 413 }, + { 352, 411, 471, 474, 414 }, { 353, 411, 471, 475, 415 }, + { 354, 416, 478, 480, 418 }, { 355, 417, 479, 481, 419 }, + { 356, 412, 472, 476, 420 }, { 357, 413, 473, 477, 421 }, + { 358, 414, 474, 482, 422 }, { 359, 415, 475, 483, 423 }, + { 360, 420, 476, 477, 421 }, { 361, 416, 478, 484, 426 }, + { 362, 417, 479, 485, 427 }, { 363, 418, 480, 486, 428 }, + { 364, 419, 481, 487, 429 }, { 365, 422, 482, 483, 423 }, + { 366, 424, 488, 494, 432 }, { 367, 425, 489, 495, 433 }, + { 368, 430, 492, 496, 434 }, { 369, 431, 493, 497, 435 }, + { 370, 424, 488, 498, 438 }, { 371, 425, 489, 499, 439 }, + { 372, 426, 484, 490, 436 }, { 373, 427, 485, 491, 437 }, + { 374, 428, 486, 490, 436 }, { 375, 429, 487, 491, 437 }, + { 376, 430, 492, 500, 440 }, { 377, 431, 493, 501, 441 }, + { 378, 432, 494, 502, 444 }, { 379, 433, 495, 503, 445 }, + { 380, 434, 496, 504, 446 }, { 381, 435, 497, 505, 447 }, + { 382, 438, 498, 506, 448 }, { 383, 439, 499, 507, 449 }, + { 384, 442, 508, 512, 450 }, { 385, 443, 509, 513, 451 }, + { 386, 442, 508, 514, 452 }, { 387, 443, 509, 515, 453 }, + { 388, 440, 500, 510, 454 }, { 389, 441, 501, 511, 455 }, + { 390, 444, 502, 506, 448 }, { 391, 445, 503, 507, 449 }, + { 392, 446, 504, 510, 454 }, { 393, 447, 505, 511, 455 }, + { 394, 456, 516, 517, 457 }, { 395, 450, 512, 518, 460 }, + { 396, 451, 513, 519, 461 }, { 397, 452, 514, 520, 462 }, + { 398, 453, 515, 521, 463 }, { 399, 458, 522, 523, 459 }, + { 400, 456, 516, 524, 464 }, { 401, 457, 517, 525, 465 }, + { 402, 458, 522, 526, 466 }, { 403, 459, 523, 527, 467 }, + { 404, 460, 518, 520, 462 }, { 405, 461, 519, 521, 463 }, + { 406, 464, 524, 528, 468 }, { 407, 465, 525, 528, 468 }, + { 408, 466, 526, 529, 469 }, { 409, 467, 527, 529, 469 }, + { 410, 411, 471, 530, 470 }, { 412, 416, 478, 531, 472 }, + { 413, 417, 479, 532, 473 }, { 414, 418, 480, 533, 474 }, + { 415, 419, 481, 534, 475 }, { 420, 424, 488, 535, 476 }, + { 421, 425, 489, 536, 477 }, { 422, 430, 492, 537, 482 }, + { 423, 431, 493, 538, 483 }, { 426, 432, 494, 539, 484 }, + { 427, 433, 495, 540, 485 }, { 428, 434, 496, 541, 486 }, + { 429, 435, 497, 542, 487 }, { 436, 442, 508, 544, 490 }, + { 437, 443, 509, 545, 491 }, { 438, 439, 499, 543, 498 }, + { 440, 441, 501, 546, 500 }, { 444, 450, 512, 547, 502 }, + { 445, 451, 513, 548, 503 }, { 446, 452, 514, 549, 504 }, + { 447, 453, 515, 550, 505 }, { 448, 456, 516, 551, 506 }, + { 449, 457, 517, 552, 507 }, { 454, 458, 522, 553, 510 }, + { 455, 459, 523, 554, 511 }, { 460, 464, 524, 555, 518 }, + { 461, 465, 525, 556, 519 }, { 462, 466, 526, 557, 520 }, + { 463, 467, 527, 558, 521 }, { 468, 469, 529, 559, 528 }, + { 470, 472, 476, 477, 473 }, { 470, 472, 531, 560, 530 }, + { 470, 473, 532, 561, 530 }, { 471, 474, 482, 483, 475 }, + { 471, 474, 533, 560, 530 }, { 471, 475, 534, 561, 530 }, + { 472, 476, 535, 562, 531 }, { 473, 477, 536, 563, 532 }, + { 474, 482, 537, 564, 533 }, { 475, 483, 538, 565, 534 }, + { 476, 477, 536, 566, 535 }, { 478, 480, 486, 490, 484 }, + { 478, 480, 533, 560, 531 }, { 478, 484, 539, 562, 531 }, + { 479, 481, 487, 491, 485 }, { 479, 481, 534, 561, 532 }, + { 479, 485, 540, 563, 532 }, { 480, 486, 541, 564, 533 }, + { 481, 487, 542, 565, 534 }, { 482, 483, 538, 567, 537 }, + { 484, 490, 544, 568, 539 }, { 485, 491, 545, 569, 540 }, + { 486, 490, 544, 570, 541 }, { 487, 491, 545, 571, 542 }, + { 488, 494, 502, 506, 498 }, { 488, 494, 539, 562, 535 }, + { 488, 498, 543, 566, 535 }, { 489, 495, 503, 507, 499 }, + { 489, 495, 540, 563, 536 }, { 489, 499, 543, 566, 536 }, + { 492, 496, 504, 510, 500 }, { 492, 496, 541, 564, 537 }, + { 492, 500, 546, 567, 537 }, { 493, 497, 505, 511, 501 }, + { 493, 497, 542, 565, 538 }, { 493, 501, 546, 567, 538 }, + { 494, 502, 547, 568, 539 }, { 495, 503, 548, 569, 540 }, + { 496, 504, 549, 570, 541 }, { 497, 505, 550, 571, 542 }, + { 498, 506, 551, 572, 543 }, { 499, 507, 552, 572, 543 }, + { 500, 510, 553, 573, 546 }, { 501, 511, 554, 573, 546 }, + { 502, 506, 551, 574, 547 }, { 503, 507, 552, 575, 548 }, + { 504, 510, 553, 576, 549 }, { 505, 511, 554, 577, 550 }, + { 508, 512, 518, 520, 514 }, { 508, 512, 547, 568, 544 }, + { 508, 514, 549, 570, 544 }, { 509, 513, 519, 521, 515 }, + { 509, 513, 548, 569, 545 }, { 509, 515, 550, 571, 545 }, + { 512, 518, 555, 574, 547 }, { 513, 519, 556, 575, 548 }, + { 514, 520, 557, 576, 549 }, { 515, 521, 558, 577, 550 }, + { 516, 517, 525, 528, 524 }, { 516, 517, 552, 572, 551 }, + { 516, 524, 555, 574, 551 }, { 517, 525, 556, 575, 552 }, + { 518, 520, 557, 578, 555 }, { 519, 521, 558, 579, 556 }, + { 522, 523, 527, 529, 526 }, { 522, 523, 554, 573, 553 }, + { 522, 526, 557, 576, 553 }, { 523, 527, 558, 577, 554 }, + { 524, 528, 559, 578, 555 }, { 525, 528, 559, 579, 556 }, + { 526, 529, 559, 578, 557 }, { 527, 529, 559, 579, 558 }, + { 530, 560, 580, 581, 561 }, { 531, 560, 580, 582, 562 }, + { 532, 561, 581, 583, 563 }, { 533, 560, 580, 584, 564 }, + { 534, 561, 581, 585, 565 }, { 535, 562, 582, 586, 566 }, + { 536, 563, 583, 586, 566 }, { 537, 564, 584, 587, 567 }, + { 538, 565, 585, 587, 567 }, { 539, 562, 582, 588, 568 }, + { 540, 563, 583, 589, 569 }, { 541, 564, 584, 590, 570 }, + { 542, 565, 585, 591, 571 }, { 543, 566, 586, 592, 572 }, + { 544, 568, 588, 590, 570 }, { 545, 569, 589, 591, 571 }, + { 546, 567, 587, 593, 573 }, { 547, 568, 588, 594, 574 }, + { 548, 569, 589, 595, 575 }, { 549, 570, 590, 596, 576 }, + { 550, 571, 591, 597, 577 }, { 551, 572, 592, 594, 574 }, + { 552, 572, 592, 595, 575 }, { 553, 573, 593, 596, 576 }, + { 554, 573, 593, 597, 577 }, { 555, 574, 594, 598, 578 }, + { 556, 575, 595, 599, 579 }, { 557, 576, 596, 598, 578 }, + { 558, 577, 597, 599, 579 }, { 559, 578, 598, 599, 579 }, + { 580, 581, 583, 586, 582 }, { 580, 581, 585, 587, 584 }, + { 580, 582, 588, 590, 584 }, { 581, 583, 589, 591, 585 }, + { 582, 586, 592, 594, 588 }, { 583, 586, 592, 595, 589 }, + { 584, 587, 593, 596, 590 }, { 585, 587, 593, 597, 591 }, + { 588, 590, 596, 598, 594 }, { 589, 591, 597, 599, 595 }, + { 592, 594, 598, 599, 595 }, { 593, 596, 598, 599, 597 } +}; + + + +static const float vert_600[NUM_VERT_600][4] = { + { 0.0, 0.0, 0.0, -2.0 }, + { 0.0, -GOLDENINV, -1.0, -GOLDEN }, + { 0.0, GOLDENINV, -1.0, -GOLDEN }, + { -1.0, 0.0, -GOLDENINV, -GOLDEN }, + { 1.0, 0.0, -GOLDENINV, -GOLDEN }, + { -GOLDENINV, -1.0, 0.0, -GOLDEN }, + { GOLDENINV, -1.0, 0.0, -GOLDEN }, + { -GOLDENINV, 1.0, 0.0, -GOLDEN }, + { GOLDENINV, 1.0, 0.0, -GOLDEN }, + { -1.0, 0.0, GOLDENINV, -GOLDEN }, + { 1.0, 0.0, GOLDENINV, -GOLDEN }, + { 0.0, -GOLDENINV, 1.0, -GOLDEN }, + { 0.0, GOLDENINV, 1.0, -GOLDEN }, + { -GOLDENINV, 0.0, -GOLDEN, -1.0 }, + { GOLDENINV, 0.0, -GOLDEN, -1.0 }, + { -1.0, -1.0, -1.0, -1.0 }, + { 1.0, -1.0, -1.0, -1.0 }, + { -1.0, 1.0, -1.0, -1.0 }, + { 1.0, 1.0, -1.0, -1.0 }, + { 0.0, -GOLDEN, -GOLDENINV, -1.0 }, + { 0.0, GOLDEN, -GOLDENINV, -1.0 }, + { -GOLDEN, -GOLDENINV, 0.0, -1.0 }, + { GOLDEN, -GOLDENINV, 0.0, -1.0 }, + { -GOLDEN, GOLDENINV, 0.0, -1.0 }, + { GOLDEN, GOLDENINV, 0.0, -1.0 }, + { 0.0, -GOLDEN, GOLDENINV, -1.0 }, + { 0.0, GOLDEN, GOLDENINV, -1.0 }, + { -1.0, -1.0, 1.0, -1.0 }, + { 1.0, -1.0, 1.0, -1.0 }, + { -1.0, 1.0, 1.0, -1.0 }, + { 1.0, 1.0, 1.0, -1.0 }, + { -GOLDENINV, 0.0, GOLDEN, -1.0 }, + { GOLDENINV, 0.0, GOLDEN, -1.0 }, + { 0.0, -1.0, -GOLDEN, -GOLDENINV }, + { 0.0, 1.0, -GOLDEN, -GOLDENINV }, + { -GOLDEN, 0.0, -1.0, -GOLDENINV }, + { GOLDEN, 0.0, -1.0, -GOLDENINV }, + { -1.0, -GOLDEN, 0.0, -GOLDENINV }, + { 1.0, -GOLDEN, 0.0, -GOLDENINV }, + { -1.0, GOLDEN, 0.0, -GOLDENINV }, + { 1.0, GOLDEN, 0.0, -GOLDENINV }, + { -GOLDEN, 0.0, 1.0, -GOLDENINV }, + { GOLDEN, 0.0, 1.0, -GOLDENINV }, + { 0.0, -1.0, GOLDEN, -GOLDENINV }, + { 0.0, 1.0, GOLDEN, -GOLDENINV }, + { 0.0, 0.0, -2.0, 0.0 }, + { -1.0, -GOLDENINV, -GOLDEN, 0.0 }, + { 1.0, -GOLDENINV, -GOLDEN, 0.0 }, + { -1.0, GOLDENINV, -GOLDEN, 0.0 }, + { 1.0, GOLDENINV, -GOLDEN, 0.0 }, + { -GOLDENINV, -GOLDEN, -1.0, 0.0 }, + { GOLDENINV, -GOLDEN, -1.0, 0.0 }, + { -GOLDENINV, GOLDEN, -1.0, 0.0 }, + { GOLDENINV, GOLDEN, -1.0, 0.0 }, + { -GOLDEN, -1.0, -GOLDENINV, 0.0 }, + { GOLDEN, -1.0, -GOLDENINV, 0.0 }, + { -GOLDEN, 1.0, -GOLDENINV, 0.0 }, + { GOLDEN, 1.0, -GOLDENINV, 0.0 }, + { 0.0, -2.0, 0.0, 0.0 }, + { -2.0, 0.0, 0.0, 0.0 }, + { 2.0, 0.0, 0.0, 0.0 }, + { 0.0, 2.0, 0.0, 0.0 }, + { -GOLDEN, -1.0, GOLDENINV, 0.0 }, + { GOLDEN, -1.0, GOLDENINV, 0.0 }, + { -GOLDEN, 1.0, GOLDENINV, 0.0 }, + { GOLDEN, 1.0, GOLDENINV, 0.0 }, + { -GOLDENINV, -GOLDEN, 1.0, 0.0 }, + { GOLDENINV, -GOLDEN, 1.0, 0.0 }, + { -GOLDENINV, GOLDEN, 1.0, 0.0 }, + { GOLDENINV, GOLDEN, 1.0, 0.0 }, + { -1.0, -GOLDENINV, GOLDEN, 0.0 }, + { 1.0, -GOLDENINV, GOLDEN, 0.0 }, + { -1.0, GOLDENINV, GOLDEN, 0.0 }, + { 1.0, GOLDENINV, GOLDEN, 0.0 }, + { 0.0, 0.0, 2.0, 0.0 }, + { 0.0, -1.0, -GOLDEN, GOLDENINV }, + { 0.0, 1.0, -GOLDEN, GOLDENINV }, + { -GOLDEN, 0.0, -1.0, GOLDENINV }, + { GOLDEN, 0.0, -1.0, GOLDENINV }, + { -1.0, -GOLDEN, 0.0, GOLDENINV }, + { 1.0, -GOLDEN, 0.0, GOLDENINV }, + { -1.0, GOLDEN, 0.0, GOLDENINV }, + { 1.0, GOLDEN, 0.0, GOLDENINV }, + { -GOLDEN, 0.0, 1.0, GOLDENINV }, + { GOLDEN, 0.0, 1.0, GOLDENINV }, + { 0.0, -1.0, GOLDEN, GOLDENINV }, + { 0.0, 1.0, GOLDEN, GOLDENINV }, + { -GOLDENINV, 0.0, -GOLDEN, 1.0 }, + { GOLDENINV, 0.0, -GOLDEN, 1.0 }, + { -1.0, -1.0, -1.0, 1.0 }, + { 1.0, -1.0, -1.0, 1.0 }, + { -1.0, 1.0, -1.0, 1.0 }, + { 1.0, 1.0, -1.0, 1.0 }, + { 0.0, -GOLDEN, -GOLDENINV, 1.0 }, + { 0.0, GOLDEN, -GOLDENINV, 1.0 }, + { -GOLDEN, -GOLDENINV, 0.0, 1.0 }, + { GOLDEN, -GOLDENINV, 0.0, 1.0 }, + { -GOLDEN, GOLDENINV, 0.0, 1.0 }, + { GOLDEN, GOLDENINV, 0.0, 1.0 }, + { 0.0, -GOLDEN, GOLDENINV, 1.0 }, + { 0.0, GOLDEN, GOLDENINV, 1.0 }, + { -1.0, -1.0, 1.0, 1.0 }, + { 1.0, -1.0, 1.0, 1.0 }, + { -1.0, 1.0, 1.0, 1.0 }, + { 1.0, 1.0, 1.0, 1.0 }, + { -GOLDENINV, 0.0, GOLDEN, 1.0 }, + { GOLDENINV, 0.0, GOLDEN, 1.0 }, + { 0.0, -GOLDENINV, -1.0, GOLDEN }, + { 0.0, GOLDENINV, -1.0, GOLDEN }, + { -1.0, 0.0, -GOLDENINV, GOLDEN }, + { 1.0, 0.0, -GOLDENINV, GOLDEN }, + { -GOLDENINV, -1.0, 0.0, GOLDEN }, + { GOLDENINV, -1.0, 0.0, GOLDEN }, + { -GOLDENINV, 1.0, 0.0, GOLDEN }, + { GOLDENINV, 1.0, 0.0, GOLDEN }, + { -1.0, 0.0, GOLDENINV, GOLDEN }, + { 1.0, 0.0, GOLDENINV, GOLDEN }, + { 0.0, -GOLDENINV, 1.0, GOLDEN }, + { 0.0, GOLDENINV, 1.0, GOLDEN }, + { 0.0, 0.0, 0.0, 2.0 } +}; + +static const int edge_600[NUM_EDGE_600][2] = { + { 0, 1 }, { 0, 2 }, { 0, 3 }, { 0, 4 }, { 0, 5 }, + { 0, 6 }, { 0, 7 }, { 0, 8 }, { 0, 9 }, { 0, 10 }, + { 0, 11 }, { 0, 12 }, { 1, 2 }, { 1, 3 }, { 1, 4 }, + { 1, 5 }, { 1, 6 }, { 1, 13 }, { 1, 14 }, { 1, 15 }, + { 1, 16 }, { 1, 19 }, { 1, 33 }, { 2, 3 }, { 2, 4 }, + { 2, 7 }, { 2, 8 }, { 2, 13 }, { 2, 14 }, { 2, 17 }, + { 2, 18 }, { 2, 20 }, { 2, 34 }, { 3, 5 }, { 3, 7 }, + { 3, 9 }, { 3, 13 }, { 3, 15 }, { 3, 17 }, { 3, 21 }, + { 3, 23 }, { 3, 35 }, { 4, 6 }, { 4, 8 }, { 4, 10 }, + { 4, 14 }, { 4, 16 }, { 4, 18 }, { 4, 22 }, { 4, 24 }, + { 4, 36 }, { 5, 6 }, { 5, 9 }, { 5, 11 }, { 5, 15 }, + { 5, 19 }, { 5, 21 }, { 5, 25 }, { 5, 27 }, { 5, 37 }, + { 6, 10 }, { 6, 11 }, { 6, 16 }, { 6, 19 }, { 6, 22 }, + { 6, 25 }, { 6, 28 }, { 6, 38 }, { 7, 8 }, { 7, 9 }, + { 7, 12 }, { 7, 17 }, { 7, 20 }, { 7, 23 }, { 7, 26 }, + { 7, 29 }, { 7, 39 }, { 8, 10 }, { 8, 12 }, { 8, 18 }, + { 8, 20 }, { 8, 24 }, { 8, 26 }, { 8, 30 }, { 8, 40 }, + { 9, 11 }, { 9, 12 }, { 9, 21 }, { 9, 23 }, { 9, 27 }, + { 9, 29 }, { 9, 31 }, { 9, 41 }, { 10, 11 }, { 10, 12 }, + { 10, 22 }, { 10, 24 }, { 10, 28 }, { 10, 30 }, { 10, 32 }, + { 10, 42 }, { 11, 12 }, { 11, 25 }, { 11, 27 }, { 11, 28 }, + { 11, 31 }, { 11, 32 }, { 11, 43 }, { 12, 26 }, { 12, 29 }, + { 12, 30 }, { 12, 31 }, { 12, 32 }, { 12, 44 }, { 13, 14 }, + { 13, 15 }, { 13, 17 }, { 13, 33 }, { 13, 34 }, { 13, 35 }, + { 13, 45 }, { 13, 46 }, { 13, 48 }, { 14, 16 }, { 14, 18 }, + { 14, 33 }, { 14, 34 }, { 14, 36 }, { 14, 45 }, { 14, 47 }, + { 14, 49 }, { 15, 19 }, { 15, 21 }, { 15, 33 }, { 15, 35 }, + { 15, 37 }, { 15, 46 }, { 15, 50 }, { 15, 54 }, { 16, 19 }, + { 16, 22 }, { 16, 33 }, { 16, 36 }, { 16, 38 }, { 16, 47 }, + { 16, 51 }, { 16, 55 }, { 17, 20 }, { 17, 23 }, { 17, 34 }, + { 17, 35 }, { 17, 39 }, { 17, 48 }, { 17, 52 }, { 17, 56 }, + { 18, 20 }, { 18, 24 }, { 18, 34 }, { 18, 36 }, { 18, 40 }, + { 18, 49 }, { 18, 53 }, { 18, 57 }, { 19, 25 }, { 19, 33 }, + { 19, 37 }, { 19, 38 }, { 19, 50 }, { 19, 51 }, { 19, 58 }, + { 20, 26 }, { 20, 34 }, { 20, 39 }, { 20, 40 }, { 20, 52 }, + { 20, 53 }, { 20, 61 }, { 21, 23 }, { 21, 27 }, { 21, 35 }, + { 21, 37 }, { 21, 41 }, { 21, 54 }, { 21, 59 }, { 21, 62 }, + { 22, 24 }, { 22, 28 }, { 22, 36 }, { 22, 38 }, { 22, 42 }, + { 22, 55 }, { 22, 60 }, { 22, 63 }, { 23, 29 }, { 23, 35 }, + { 23, 39 }, { 23, 41 }, { 23, 56 }, { 23, 59 }, { 23, 64 }, + { 24, 30 }, { 24, 36 }, { 24, 40 }, { 24, 42 }, { 24, 57 }, + { 24, 60 }, { 24, 65 }, { 25, 27 }, { 25, 28 }, { 25, 37 }, + { 25, 38 }, { 25, 43 }, { 25, 58 }, { 25, 66 }, { 25, 67 }, + { 26, 29 }, { 26, 30 }, { 26, 39 }, { 26, 40 }, { 26, 44 }, + { 26, 61 }, { 26, 68 }, { 26, 69 }, { 27, 31 }, { 27, 37 }, + { 27, 41 }, { 27, 43 }, { 27, 62 }, { 27, 66 }, { 27, 70 }, + { 28, 32 }, { 28, 38 }, { 28, 42 }, { 28, 43 }, { 28, 63 }, + { 28, 67 }, { 28, 71 }, { 29, 31 }, { 29, 39 }, { 29, 41 }, + { 29, 44 }, { 29, 64 }, { 29, 68 }, { 29, 72 }, { 30, 32 }, + { 30, 40 }, { 30, 42 }, { 30, 44 }, { 30, 65 }, { 30, 69 }, + { 30, 73 }, { 31, 32 }, { 31, 41 }, { 31, 43 }, { 31, 44 }, + { 31, 70 }, { 31, 72 }, { 31, 74 }, { 32, 42 }, { 32, 43 }, + { 32, 44 }, { 32, 71 }, { 32, 73 }, { 32, 74 }, { 33, 45 }, + { 33, 46 }, { 33, 47 }, { 33, 50 }, { 33, 51 }, { 33, 75 }, + { 34, 45 }, { 34, 48 }, { 34, 49 }, { 34, 52 }, { 34, 53 }, + { 34, 76 }, { 35, 46 }, { 35, 48 }, { 35, 54 }, { 35, 56 }, + { 35, 59 }, { 35, 77 }, { 36, 47 }, { 36, 49 }, { 36, 55 }, + { 36, 57 }, { 36, 60 }, { 36, 78 }, { 37, 50 }, { 37, 54 }, + { 37, 58 }, { 37, 62 }, { 37, 66 }, { 37, 79 }, { 38, 51 }, + { 38, 55 }, { 38, 58 }, { 38, 63 }, { 38, 67 }, { 38, 80 }, + { 39, 52 }, { 39, 56 }, { 39, 61 }, { 39, 64 }, { 39, 68 }, + { 39, 81 }, { 40, 53 }, { 40, 57 }, { 40, 61 }, { 40, 65 }, + { 40, 69 }, { 40, 82 }, { 41, 59 }, { 41, 62 }, { 41, 64 }, + { 41, 70 }, { 41, 72 }, { 41, 83 }, { 42, 60 }, { 42, 63 }, + { 42, 65 }, { 42, 71 }, { 42, 73 }, { 42, 84 }, { 43, 66 }, + { 43, 67 }, { 43, 70 }, { 43, 71 }, { 43, 74 }, { 43, 85 }, + { 44, 68 }, { 44, 69 }, { 44, 72 }, { 44, 73 }, { 44, 74 }, + { 44, 86 }, { 45, 46 }, { 45, 47 }, { 45, 48 }, { 45, 49 }, + { 45, 75 }, { 45, 76 }, { 45, 87 }, { 45, 88 }, { 46, 48 }, + { 46, 50 }, { 46, 54 }, { 46, 75 }, { 46, 77 }, { 46, 87 }, + { 46, 89 }, { 47, 49 }, { 47, 51 }, { 47, 55 }, { 47, 75 }, + { 47, 78 }, { 47, 88 }, { 47, 90 }, { 48, 52 }, { 48, 56 }, + { 48, 76 }, { 48, 77 }, { 48, 87 }, { 48, 91 }, { 49, 53 }, + { 49, 57 }, { 49, 76 }, { 49, 78 }, { 49, 88 }, { 49, 92 }, + { 50, 51 }, { 50, 54 }, { 50, 58 }, { 50, 75 }, { 50, 79 }, + { 50, 89 }, { 50, 93 }, { 51, 55 }, { 51, 58 }, { 51, 75 }, + { 51, 80 }, { 51, 90 }, { 51, 93 }, { 52, 53 }, { 52, 56 }, + { 52, 61 }, { 52, 76 }, { 52, 81 }, { 52, 91 }, { 52, 94 }, + { 53, 57 }, { 53, 61 }, { 53, 76 }, { 53, 82 }, { 53, 92 }, + { 53, 94 }, { 54, 59 }, { 54, 62 }, { 54, 77 }, { 54, 79 }, + { 54, 89 }, { 54, 95 }, { 55, 60 }, { 55, 63 }, { 55, 78 }, + { 55, 80 }, { 55, 90 }, { 55, 96 }, { 56, 59 }, { 56, 64 }, + { 56, 77 }, { 56, 81 }, { 56, 91 }, { 56, 97 }, { 57, 60 }, + { 57, 65 }, { 57, 78 }, { 57, 82 }, { 57, 92 }, { 57, 98 }, + { 58, 66 }, { 58, 67 }, { 58, 79 }, { 58, 80 }, { 58, 93 }, + { 58, 99 }, { 59, 62 }, { 59, 64 }, { 59, 77 }, { 59, 83 }, + { 59, 95 }, { 59, 97 }, { 60, 63 }, { 60, 65 }, { 60, 78 }, + { 60, 84 }, { 60, 96 }, { 60, 98 }, { 61, 68 }, { 61, 69 }, + { 61, 81 }, { 61, 82 }, { 61, 94 }, { 61, 100 }, { 62, 66 }, + { 62, 70 }, { 62, 79 }, { 62, 83 }, { 62, 95 }, { 62, 101 }, + { 63, 67 }, { 63, 71 }, { 63, 80 }, { 63, 84 }, { 63, 96 }, + { 63, 102 }, { 64, 68 }, { 64, 72 }, { 64, 81 }, { 64, 83 }, + { 64, 97 }, { 64, 103 }, { 65, 69 }, { 65, 73 }, { 65, 82 }, + { 65, 84 }, { 65, 98 }, { 65, 104 }, { 66, 67 }, { 66, 70 }, + { 66, 79 }, { 66, 85 }, { 66, 99 }, { 66, 101 }, { 67, 71 }, + { 67, 80 }, { 67, 85 }, { 67, 99 }, { 67, 102 }, { 68, 69 }, + { 68, 72 }, { 68, 81 }, { 68, 86 }, { 68, 100 }, { 68, 103 }, + { 69, 73 }, { 69, 82 }, { 69, 86 }, { 69, 100 }, { 69, 104 }, + { 70, 72 }, { 70, 74 }, { 70, 83 }, { 70, 85 }, { 70, 101 }, + { 70, 105 }, { 71, 73 }, { 71, 74 }, { 71, 84 }, { 71, 85 }, + { 71, 102 }, { 71, 106 }, { 72, 74 }, { 72, 83 }, { 72, 86 }, + { 72, 103 }, { 72, 105 }, { 73, 74 }, { 73, 84 }, { 73, 86 }, + { 73, 104 }, { 73, 106 }, { 74, 85 }, { 74, 86 }, { 74, 105 }, + { 74, 106 }, { 75, 87 }, { 75, 88 }, { 75, 89 }, { 75, 90 }, + { 75, 93 }, { 75, 107 }, { 76, 87 }, { 76, 88 }, { 76, 91 }, + { 76, 92 }, { 76, 94 }, { 76, 108 }, { 77, 87 }, { 77, 89 }, + { 77, 91 }, { 77, 95 }, { 77, 97 }, { 77, 109 }, { 78, 88 }, + { 78, 90 }, { 78, 92 }, { 78, 96 }, { 78, 98 }, { 78, 110 }, + { 79, 89 }, { 79, 93 }, { 79, 95 }, { 79, 99 }, { 79, 101 }, + { 79, 111 }, { 80, 90 }, { 80, 93 }, { 80, 96 }, { 80, 99 }, + { 80, 102 }, { 80, 112 }, { 81, 91 }, { 81, 94 }, { 81, 97 }, + { 81, 100 }, { 81, 103 }, { 81, 113 }, { 82, 92 }, { 82, 94 }, + { 82, 98 }, { 82, 100 }, { 82, 104 }, { 82, 114 }, { 83, 95 }, + { 83, 97 }, { 83, 101 }, { 83, 103 }, { 83, 105 }, { 83, 115 }, + { 84, 96 }, { 84, 98 }, { 84, 102 }, { 84, 104 }, { 84, 106 }, + { 84, 116 }, { 85, 99 }, { 85, 101 }, { 85, 102 }, { 85, 105 }, + { 85, 106 }, { 85, 117 }, { 86, 100 }, { 86, 103 }, { 86, 104 }, + { 86, 105 }, { 86, 106 }, { 86, 118 }, { 87, 88 }, { 87, 89 }, + { 87, 91 }, { 87, 107 }, { 87, 108 }, { 87, 109 }, { 88, 90 }, + { 88, 92 }, { 88, 107 }, { 88, 108 }, { 88, 110 }, { 89, 93 }, + { 89, 95 }, { 89, 107 }, { 89, 109 }, { 89, 111 }, { 90, 93 }, + { 90, 96 }, { 90, 107 }, { 90, 110 }, { 90, 112 }, { 91, 94 }, + { 91, 97 }, { 91, 108 }, { 91, 109 }, { 91, 113 }, { 92, 94 }, + { 92, 98 }, { 92, 108 }, { 92, 110 }, { 92, 114 }, { 93, 99 }, + { 93, 107 }, { 93, 111 }, { 93, 112 }, { 94, 100 }, { 94, 108 }, + { 94, 113 }, { 94, 114 }, { 95, 97 }, { 95, 101 }, { 95, 109 }, + { 95, 111 }, { 95, 115 }, { 96, 98 }, { 96, 102 }, { 96, 110 }, + { 96, 112 }, { 96, 116 }, { 97, 103 }, { 97, 109 }, { 97, 113 }, + { 97, 115 }, { 98, 104 }, { 98, 110 }, { 98, 114 }, { 98, 116 }, + { 99, 101 }, { 99, 102 }, { 99, 111 }, { 99, 112 }, { 99, 117 }, + { 100, 103 }, { 100, 104 }, { 100, 113 }, { 100, 114 }, { 100, 118 }, + { 101, 105 }, { 101, 111 }, { 101, 115 }, { 101, 117 }, { 102, 106 }, + { 102, 112 }, { 102, 116 }, { 102, 117 }, { 103, 105 }, { 103, 113 }, + { 103, 115 }, { 103, 118 }, { 104, 106 }, { 104, 114 }, { 104, 116 }, + { 104, 118 }, { 105, 106 }, { 105, 115 }, { 105, 117 }, { 105, 118 }, + { 106, 116 }, { 106, 117 }, { 106, 118 }, { 107, 108 }, { 107, 109 }, + { 107, 110 }, { 107, 111 }, { 107, 112 }, { 107, 119 }, { 108, 109 }, + { 108, 110 }, { 108, 113 }, { 108, 114 }, { 108, 119 }, { 109, 111 }, + { 109, 113 }, { 109, 115 }, { 109, 119 }, { 110, 112 }, { 110, 114 }, + { 110, 116 }, { 110, 119 }, { 111, 112 }, { 111, 115 }, { 111, 117 }, + { 111, 119 }, { 112, 116 }, { 112, 117 }, { 112, 119 }, { 113, 114 }, + { 113, 115 }, { 113, 118 }, { 113, 119 }, { 114, 116 }, { 114, 118 }, + { 114, 119 }, { 115, 117 }, { 115, 118 }, { 115, 119 }, { 116, 117 }, + { 116, 118 }, { 116, 119 }, { 117, 118 }, { 117, 119 }, { 118, 119 } +}; + +static const int face_600[NUM_FACE_600][VERT_PER_FACE_600] = { + { 0, 1, 2 }, { 0, 1, 3 }, { 0, 1, 4 }, { 0, 1, 5 }, + { 0, 1, 6 }, { 0, 2, 3 }, { 0, 2, 4 }, { 0, 2, 7 }, + { 0, 2, 8 }, { 0, 3, 5 }, { 0, 3, 7 }, { 0, 3, 9 }, + { 0, 4, 6 }, { 0, 4, 8 }, { 0, 4, 10 }, { 0, 5, 6 }, + { 0, 5, 9 }, { 0, 5, 11 }, { 0, 6, 10 }, { 0, 6, 11 }, + { 0, 7, 8 }, { 0, 7, 9 }, { 0, 7, 12 }, { 0, 8, 10 }, + { 0, 8, 12 }, { 0, 9, 11 }, { 0, 9, 12 }, { 0, 10, 11 }, + { 0, 10, 12 }, { 0, 11, 12 }, { 1, 2, 3 }, { 1, 2, 4 }, + { 1, 2, 13 }, { 1, 2, 14 }, { 1, 3, 5 }, { 1, 3, 13 }, + { 1, 3, 15 }, { 1, 4, 6 }, { 1, 4, 14 }, { 1, 4, 16 }, + { 1, 5, 6 }, { 1, 5, 15 }, { 1, 5, 19 }, { 1, 6, 16 }, + { 1, 6, 19 }, { 1, 13, 14 }, { 1, 13, 15 }, { 1, 13, 33 }, + { 1, 14, 16 }, { 1, 14, 33 }, { 1, 15, 19 }, { 1, 15, 33 }, + { 1, 16, 19 }, { 1, 16, 33 }, { 1, 19, 33 }, { 2, 3, 7 }, + { 2, 3, 13 }, { 2, 3, 17 }, { 2, 4, 8 }, { 2, 4, 14 }, + { 2, 4, 18 }, { 2, 7, 8 }, { 2, 7, 17 }, { 2, 7, 20 }, + { 2, 8, 18 }, { 2, 8, 20 }, { 2, 13, 14 }, { 2, 13, 17 }, + { 2, 13, 34 }, { 2, 14, 18 }, { 2, 14, 34 }, { 2, 17, 20 }, + { 2, 17, 34 }, { 2, 18, 20 }, { 2, 18, 34 }, { 2, 20, 34 }, + { 3, 5, 9 }, { 3, 5, 15 }, { 3, 5, 21 }, { 3, 7, 9 }, + { 3, 7, 17 }, { 3, 7, 23 }, { 3, 9, 21 }, { 3, 9, 23 }, + { 3, 13, 15 }, { 3, 13, 17 }, { 3, 13, 35 }, { 3, 15, 21 }, + { 3, 15, 35 }, { 3, 17, 23 }, { 3, 17, 35 }, { 3, 21, 23 }, + { 3, 21, 35 }, { 3, 23, 35 }, { 4, 6, 10 }, { 4, 6, 16 }, + { 4, 6, 22 }, { 4, 8, 10 }, { 4, 8, 18 }, { 4, 8, 24 }, + { 4, 10, 22 }, { 4, 10, 24 }, { 4, 14, 16 }, { 4, 14, 18 }, + { 4, 14, 36 }, { 4, 16, 22 }, { 4, 16, 36 }, { 4, 18, 24 }, + { 4, 18, 36 }, { 4, 22, 24 }, { 4, 22, 36 }, { 4, 24, 36 }, + { 5, 6, 11 }, { 5, 6, 19 }, { 5, 6, 25 }, { 5, 9, 11 }, + { 5, 9, 21 }, { 5, 9, 27 }, { 5, 11, 25 }, { 5, 11, 27 }, + { 5, 15, 19 }, { 5, 15, 21 }, { 5, 15, 37 }, { 5, 19, 25 }, + { 5, 19, 37 }, { 5, 21, 27 }, { 5, 21, 37 }, { 5, 25, 27 }, + { 5, 25, 37 }, { 5, 27, 37 }, { 6, 10, 11 }, { 6, 10, 22 }, + { 6, 10, 28 }, { 6, 11, 25 }, { 6, 11, 28 }, { 6, 16, 19 }, + { 6, 16, 22 }, { 6, 16, 38 }, { 6, 19, 25 }, { 6, 19, 38 }, + { 6, 22, 28 }, { 6, 22, 38 }, { 6, 25, 28 }, { 6, 25, 38 }, + { 6, 28, 38 }, { 7, 8, 12 }, { 7, 8, 20 }, { 7, 8, 26 }, + { 7, 9, 12 }, { 7, 9, 23 }, { 7, 9, 29 }, { 7, 12, 26 }, + { 7, 12, 29 }, { 7, 17, 20 }, { 7, 17, 23 }, { 7, 17, 39 }, + { 7, 20, 26 }, { 7, 20, 39 }, { 7, 23, 29 }, { 7, 23, 39 }, + { 7, 26, 29 }, { 7, 26, 39 }, { 7, 29, 39 }, { 8, 10, 12 }, + { 8, 10, 24 }, { 8, 10, 30 }, { 8, 12, 26 }, { 8, 12, 30 }, + { 8, 18, 20 }, { 8, 18, 24 }, { 8, 18, 40 }, { 8, 20, 26 }, + { 8, 20, 40 }, { 8, 24, 30 }, { 8, 24, 40 }, { 8, 26, 30 }, + { 8, 26, 40 }, { 8, 30, 40 }, { 9, 11, 12 }, { 9, 11, 27 }, + { 9, 11, 31 }, { 9, 12, 29 }, { 9, 12, 31 }, { 9, 21, 23 }, + { 9, 21, 27 }, { 9, 21, 41 }, { 9, 23, 29 }, { 9, 23, 41 }, + { 9, 27, 31 }, { 9, 27, 41 }, { 9, 29, 31 }, { 9, 29, 41 }, + { 9, 31, 41 }, { 10, 11, 12 }, { 10, 11, 28 }, { 10, 11, 32 }, + { 10, 12, 30 }, { 10, 12, 32 }, { 10, 22, 24 }, { 10, 22, 28 }, + { 10, 22, 42 }, { 10, 24, 30 }, { 10, 24, 42 }, { 10, 28, 32 }, + { 10, 28, 42 }, { 10, 30, 32 }, { 10, 30, 42 }, { 10, 32, 42 }, + { 11, 12, 31 }, { 11, 12, 32 }, { 11, 25, 27 }, { 11, 25, 28 }, + { 11, 25, 43 }, { 11, 27, 31 }, { 11, 27, 43 }, { 11, 28, 32 }, + { 11, 28, 43 }, { 11, 31, 32 }, { 11, 31, 43 }, { 11, 32, 43 }, + { 12, 26, 29 }, { 12, 26, 30 }, { 12, 26, 44 }, { 12, 29, 31 }, + { 12, 29, 44 }, { 12, 30, 32 }, { 12, 30, 44 }, { 12, 31, 32 }, + { 12, 31, 44 }, { 12, 32, 44 }, { 13, 14, 33 }, { 13, 14, 34 }, + { 13, 14, 45 }, { 13, 15, 33 }, { 13, 15, 35 }, { 13, 15, 46 }, + { 13, 17, 34 }, { 13, 17, 35 }, { 13, 17, 48 }, { 13, 33, 45 }, + { 13, 33, 46 }, { 13, 34, 45 }, { 13, 34, 48 }, { 13, 35, 46 }, + { 13, 35, 48 }, { 13, 45, 46 }, { 13, 45, 48 }, { 13, 46, 48 }, + { 14, 16, 33 }, { 14, 16, 36 }, { 14, 16, 47 }, { 14, 18, 34 }, + { 14, 18, 36 }, { 14, 18, 49 }, { 14, 33, 45 }, { 14, 33, 47 }, + { 14, 34, 45 }, { 14, 34, 49 }, { 14, 36, 47 }, { 14, 36, 49 }, + { 14, 45, 47 }, { 14, 45, 49 }, { 14, 47, 49 }, { 15, 19, 33 }, + { 15, 19, 37 }, { 15, 19, 50 }, { 15, 21, 35 }, { 15, 21, 37 }, + { 15, 21, 54 }, { 15, 33, 46 }, { 15, 33, 50 }, { 15, 35, 46 }, + { 15, 35, 54 }, { 15, 37, 50 }, { 15, 37, 54 }, { 15, 46, 50 }, + { 15, 46, 54 }, { 15, 50, 54 }, { 16, 19, 33 }, { 16, 19, 38 }, + { 16, 19, 51 }, { 16, 22, 36 }, { 16, 22, 38 }, { 16, 22, 55 }, + { 16, 33, 47 }, { 16, 33, 51 }, { 16, 36, 47 }, { 16, 36, 55 }, + { 16, 38, 51 }, { 16, 38, 55 }, { 16, 47, 51 }, { 16, 47, 55 }, + { 16, 51, 55 }, { 17, 20, 34 }, { 17, 20, 39 }, { 17, 20, 52 }, + { 17, 23, 35 }, { 17, 23, 39 }, { 17, 23, 56 }, { 17, 34, 48 }, + { 17, 34, 52 }, { 17, 35, 48 }, { 17, 35, 56 }, { 17, 39, 52 }, + { 17, 39, 56 }, { 17, 48, 52 }, { 17, 48, 56 }, { 17, 52, 56 }, + { 18, 20, 34 }, { 18, 20, 40 }, { 18, 20, 53 }, { 18, 24, 36 }, + { 18, 24, 40 }, { 18, 24, 57 }, { 18, 34, 49 }, { 18, 34, 53 }, + { 18, 36, 49 }, { 18, 36, 57 }, { 18, 40, 53 }, { 18, 40, 57 }, + { 18, 49, 53 }, { 18, 49, 57 }, { 18, 53, 57 }, { 19, 25, 37 }, + { 19, 25, 38 }, { 19, 25, 58 }, { 19, 33, 50 }, { 19, 33, 51 }, + { 19, 37, 50 }, { 19, 37, 58 }, { 19, 38, 51 }, { 19, 38, 58 }, + { 19, 50, 51 }, { 19, 50, 58 }, { 19, 51, 58 }, { 20, 26, 39 }, + { 20, 26, 40 }, { 20, 26, 61 }, { 20, 34, 52 }, { 20, 34, 53 }, + { 20, 39, 52 }, { 20, 39, 61 }, { 20, 40, 53 }, { 20, 40, 61 }, + { 20, 52, 53 }, { 20, 52, 61 }, { 20, 53, 61 }, { 21, 23, 35 }, + { 21, 23, 41 }, { 21, 23, 59 }, { 21, 27, 37 }, { 21, 27, 41 }, + { 21, 27, 62 }, { 21, 35, 54 }, { 21, 35, 59 }, { 21, 37, 54 }, + { 21, 37, 62 }, { 21, 41, 59 }, { 21, 41, 62 }, { 21, 54, 59 }, + { 21, 54, 62 }, { 21, 59, 62 }, { 22, 24, 36 }, { 22, 24, 42 }, + { 22, 24, 60 }, { 22, 28, 38 }, { 22, 28, 42 }, { 22, 28, 63 }, + { 22, 36, 55 }, { 22, 36, 60 }, { 22, 38, 55 }, { 22, 38, 63 }, + { 22, 42, 60 }, { 22, 42, 63 }, { 22, 55, 60 }, { 22, 55, 63 }, + { 22, 60, 63 }, { 23, 29, 39 }, { 23, 29, 41 }, { 23, 29, 64 }, + { 23, 35, 56 }, { 23, 35, 59 }, { 23, 39, 56 }, { 23, 39, 64 }, + { 23, 41, 59 }, { 23, 41, 64 }, { 23, 56, 59 }, { 23, 56, 64 }, + { 23, 59, 64 }, { 24, 30, 40 }, { 24, 30, 42 }, { 24, 30, 65 }, + { 24, 36, 57 }, { 24, 36, 60 }, { 24, 40, 57 }, { 24, 40, 65 }, + { 24, 42, 60 }, { 24, 42, 65 }, { 24, 57, 60 }, { 24, 57, 65 }, + { 24, 60, 65 }, { 25, 27, 37 }, { 25, 27, 43 }, { 25, 27, 66 }, + { 25, 28, 38 }, { 25, 28, 43 }, { 25, 28, 67 }, { 25, 37, 58 }, + { 25, 37, 66 }, { 25, 38, 58 }, { 25, 38, 67 }, { 25, 43, 66 }, + { 25, 43, 67 }, { 25, 58, 66 }, { 25, 58, 67 }, { 25, 66, 67 }, + { 26, 29, 39 }, { 26, 29, 44 }, { 26, 29, 68 }, { 26, 30, 40 }, + { 26, 30, 44 }, { 26, 30, 69 }, { 26, 39, 61 }, { 26, 39, 68 }, + { 26, 40, 61 }, { 26, 40, 69 }, { 26, 44, 68 }, { 26, 44, 69 }, + { 26, 61, 68 }, { 26, 61, 69 }, { 26, 68, 69 }, { 27, 31, 41 }, + { 27, 31, 43 }, { 27, 31, 70 }, { 27, 37, 62 }, { 27, 37, 66 }, + { 27, 41, 62 }, { 27, 41, 70 }, { 27, 43, 66 }, { 27, 43, 70 }, + { 27, 62, 66 }, { 27, 62, 70 }, { 27, 66, 70 }, { 28, 32, 42 }, + { 28, 32, 43 }, { 28, 32, 71 }, { 28, 38, 63 }, { 28, 38, 67 }, + { 28, 42, 63 }, { 28, 42, 71 }, { 28, 43, 67 }, { 28, 43, 71 }, + { 28, 63, 67 }, { 28, 63, 71 }, { 28, 67, 71 }, { 29, 31, 41 }, + { 29, 31, 44 }, { 29, 31, 72 }, { 29, 39, 64 }, { 29, 39, 68 }, + { 29, 41, 64 }, { 29, 41, 72 }, { 29, 44, 68 }, { 29, 44, 72 }, + { 29, 64, 68 }, { 29, 64, 72 }, { 29, 68, 72 }, { 30, 32, 42 }, + { 30, 32, 44 }, { 30, 32, 73 }, { 30, 40, 65 }, { 30, 40, 69 }, + { 30, 42, 65 }, { 30, 42, 73 }, { 30, 44, 69 }, { 30, 44, 73 }, + { 30, 65, 69 }, { 30, 65, 73 }, { 30, 69, 73 }, { 31, 32, 43 }, + { 31, 32, 44 }, { 31, 32, 74 }, { 31, 41, 70 }, { 31, 41, 72 }, + { 31, 43, 70 }, { 31, 43, 74 }, { 31, 44, 72 }, { 31, 44, 74 }, + { 31, 70, 72 }, { 31, 70, 74 }, { 31, 72, 74 }, { 32, 42, 71 }, + { 32, 42, 73 }, { 32, 43, 71 }, { 32, 43, 74 }, { 32, 44, 73 }, + { 32, 44, 74 }, { 32, 71, 73 }, { 32, 71, 74 }, { 32, 73, 74 }, + { 33, 45, 46 }, { 33, 45, 47 }, { 33, 45, 75 }, { 33, 46, 50 }, + { 33, 46, 75 }, { 33, 47, 51 }, { 33, 47, 75 }, { 33, 50, 51 }, + { 33, 50, 75 }, { 33, 51, 75 }, { 34, 45, 48 }, { 34, 45, 49 }, + { 34, 45, 76 }, { 34, 48, 52 }, { 34, 48, 76 }, { 34, 49, 53 }, + { 34, 49, 76 }, { 34, 52, 53 }, { 34, 52, 76 }, { 34, 53, 76 }, + { 35, 46, 48 }, { 35, 46, 54 }, { 35, 46, 77 }, { 35, 48, 56 }, + { 35, 48, 77 }, { 35, 54, 59 }, { 35, 54, 77 }, { 35, 56, 59 }, + { 35, 56, 77 }, { 35, 59, 77 }, { 36, 47, 49 }, { 36, 47, 55 }, + { 36, 47, 78 }, { 36, 49, 57 }, { 36, 49, 78 }, { 36, 55, 60 }, + { 36, 55, 78 }, { 36, 57, 60 }, { 36, 57, 78 }, { 36, 60, 78 }, + { 37, 50, 54 }, { 37, 50, 58 }, { 37, 50, 79 }, { 37, 54, 62 }, + { 37, 54, 79 }, { 37, 58, 66 }, { 37, 58, 79 }, { 37, 62, 66 }, + { 37, 62, 79 }, { 37, 66, 79 }, { 38, 51, 55 }, { 38, 51, 58 }, + { 38, 51, 80 }, { 38, 55, 63 }, { 38, 55, 80 }, { 38, 58, 67 }, + { 38, 58, 80 }, { 38, 63, 67 }, { 38, 63, 80 }, { 38, 67, 80 }, + { 39, 52, 56 }, { 39, 52, 61 }, { 39, 52, 81 }, { 39, 56, 64 }, + { 39, 56, 81 }, { 39, 61, 68 }, { 39, 61, 81 }, { 39, 64, 68 }, + { 39, 64, 81 }, { 39, 68, 81 }, { 40, 53, 57 }, { 40, 53, 61 }, + { 40, 53, 82 }, { 40, 57, 65 }, { 40, 57, 82 }, { 40, 61, 69 }, + { 40, 61, 82 }, { 40, 65, 69 }, { 40, 65, 82 }, { 40, 69, 82 }, + { 41, 59, 62 }, { 41, 59, 64 }, { 41, 59, 83 }, { 41, 62, 70 }, + { 41, 62, 83 }, { 41, 64, 72 }, { 41, 64, 83 }, { 41, 70, 72 }, + { 41, 70, 83 }, { 41, 72, 83 }, { 42, 60, 63 }, { 42, 60, 65 }, + { 42, 60, 84 }, { 42, 63, 71 }, { 42, 63, 84 }, { 42, 65, 73 }, + { 42, 65, 84 }, { 42, 71, 73 }, { 42, 71, 84 }, { 42, 73, 84 }, + { 43, 66, 67 }, { 43, 66, 70 }, { 43, 66, 85 }, { 43, 67, 71 }, + { 43, 67, 85 }, { 43, 70, 74 }, { 43, 70, 85 }, { 43, 71, 74 }, + { 43, 71, 85 }, { 43, 74, 85 }, { 44, 68, 69 }, { 44, 68, 72 }, + { 44, 68, 86 }, { 44, 69, 73 }, { 44, 69, 86 }, { 44, 72, 74 }, + { 44, 72, 86 }, { 44, 73, 74 }, { 44, 73, 86 }, { 44, 74, 86 }, + { 45, 46, 48 }, { 45, 46, 75 }, { 45, 46, 87 }, { 45, 47, 49 }, + { 45, 47, 75 }, { 45, 47, 88 }, { 45, 48, 76 }, { 45, 48, 87 }, + { 45, 49, 76 }, { 45, 49, 88 }, { 45, 75, 87 }, { 45, 75, 88 }, + { 45, 76, 87 }, { 45, 76, 88 }, { 45, 87, 88 }, { 46, 48, 77 }, + { 46, 48, 87 }, { 46, 50, 54 }, { 46, 50, 75 }, { 46, 50, 89 }, + { 46, 54, 77 }, { 46, 54, 89 }, { 46, 75, 87 }, { 46, 75, 89 }, + { 46, 77, 87 }, { 46, 77, 89 }, { 46, 87, 89 }, { 47, 49, 78 }, + { 47, 49, 88 }, { 47, 51, 55 }, { 47, 51, 75 }, { 47, 51, 90 }, + { 47, 55, 78 }, { 47, 55, 90 }, { 47, 75, 88 }, { 47, 75, 90 }, + { 47, 78, 88 }, { 47, 78, 90 }, { 47, 88, 90 }, { 48, 52, 56 }, + { 48, 52, 76 }, { 48, 52, 91 }, { 48, 56, 77 }, { 48, 56, 91 }, + { 48, 76, 87 }, { 48, 76, 91 }, { 48, 77, 87 }, { 48, 77, 91 }, + { 48, 87, 91 }, { 49, 53, 57 }, { 49, 53, 76 }, { 49, 53, 92 }, + { 49, 57, 78 }, { 49, 57, 92 }, { 49, 76, 88 }, { 49, 76, 92 }, + { 49, 78, 88 }, { 49, 78, 92 }, { 49, 88, 92 }, { 50, 51, 58 }, + { 50, 51, 75 }, { 50, 51, 93 }, { 50, 54, 79 }, { 50, 54, 89 }, + { 50, 58, 79 }, { 50, 58, 93 }, { 50, 75, 89 }, { 50, 75, 93 }, + { 50, 79, 89 }, { 50, 79, 93 }, { 50, 89, 93 }, { 51, 55, 80 }, + { 51, 55, 90 }, { 51, 58, 80 }, { 51, 58, 93 }, { 51, 75, 90 }, + { 51, 75, 93 }, { 51, 80, 90 }, { 51, 80, 93 }, { 51, 90, 93 }, + { 52, 53, 61 }, { 52, 53, 76 }, { 52, 53, 94 }, { 52, 56, 81 }, + { 52, 56, 91 }, { 52, 61, 81 }, { 52, 61, 94 }, { 52, 76, 91 }, + { 52, 76, 94 }, { 52, 81, 91 }, { 52, 81, 94 }, { 52, 91, 94 }, + { 53, 57, 82 }, { 53, 57, 92 }, { 53, 61, 82 }, { 53, 61, 94 }, + { 53, 76, 92 }, { 53, 76, 94 }, { 53, 82, 92 }, { 53, 82, 94 }, + { 53, 92, 94 }, { 54, 59, 62 }, { 54, 59, 77 }, { 54, 59, 95 }, + { 54, 62, 79 }, { 54, 62, 95 }, { 54, 77, 89 }, { 54, 77, 95 }, + { 54, 79, 89 }, { 54, 79, 95 }, { 54, 89, 95 }, { 55, 60, 63 }, + { 55, 60, 78 }, { 55, 60, 96 }, { 55, 63, 80 }, { 55, 63, 96 }, + { 55, 78, 90 }, { 55, 78, 96 }, { 55, 80, 90 }, { 55, 80, 96 }, + { 55, 90, 96 }, { 56, 59, 64 }, { 56, 59, 77 }, { 56, 59, 97 }, + { 56, 64, 81 }, { 56, 64, 97 }, { 56, 77, 91 }, { 56, 77, 97 }, + { 56, 81, 91 }, { 56, 81, 97 }, { 56, 91, 97 }, { 57, 60, 65 }, + { 57, 60, 78 }, { 57, 60, 98 }, { 57, 65, 82 }, { 57, 65, 98 }, + { 57, 78, 92 }, { 57, 78, 98 }, { 57, 82, 92 }, { 57, 82, 98 }, + { 57, 92, 98 }, { 58, 66, 67 }, { 58, 66, 79 }, { 58, 66, 99 }, + { 58, 67, 80 }, { 58, 67, 99 }, { 58, 79, 93 }, { 58, 79, 99 }, + { 58, 80, 93 }, { 58, 80, 99 }, { 58, 93, 99 }, { 59, 62, 83 }, + { 59, 62, 95 }, { 59, 64, 83 }, { 59, 64, 97 }, { 59, 77, 95 }, + { 59, 77, 97 }, { 59, 83, 95 }, { 59, 83, 97 }, { 59, 95, 97 }, + { 60, 63, 84 }, { 60, 63, 96 }, { 60, 65, 84 }, { 60, 65, 98 }, + { 60, 78, 96 }, { 60, 78, 98 }, { 60, 84, 96 }, { 60, 84, 98 }, + { 60, 96, 98 }, { 61, 68, 69 }, { 61, 68, 81 }, { 61, 68, 100 }, + { 61, 69, 82 }, { 61, 69, 100 }, { 61, 81, 94 }, { 61, 81, 100 }, + { 61, 82, 94 }, { 61, 82, 100 }, { 61, 94, 100 }, { 62, 66, 70 }, + { 62, 66, 79 }, { 62, 66, 101 }, { 62, 70, 83 }, { 62, 70, 101 }, + { 62, 79, 95 }, { 62, 79, 101 }, { 62, 83, 95 }, { 62, 83, 101 }, + { 62, 95, 101 }, { 63, 67, 71 }, { 63, 67, 80 }, { 63, 67, 102 }, + { 63, 71, 84 }, { 63, 71, 102 }, { 63, 80, 96 }, { 63, 80, 102 }, + { 63, 84, 96 }, { 63, 84, 102 }, { 63, 96, 102 }, { 64, 68, 72 }, + { 64, 68, 81 }, { 64, 68, 103 }, { 64, 72, 83 }, { 64, 72, 103 }, + { 64, 81, 97 }, { 64, 81, 103 }, { 64, 83, 97 }, { 64, 83, 103 }, + { 64, 97, 103 }, { 65, 69, 73 }, { 65, 69, 82 }, { 65, 69, 104 }, + { 65, 73, 84 }, { 65, 73, 104 }, { 65, 82, 98 }, { 65, 82, 104 }, + { 65, 84, 98 }, { 65, 84, 104 }, { 65, 98, 104 }, { 66, 67, 85 }, + { 66, 67, 99 }, { 66, 70, 85 }, { 66, 70, 101 }, { 66, 79, 99 }, + { 66, 79, 101 }, { 66, 85, 99 }, { 66, 85, 101 }, { 66, 99, 101 }, + { 67, 71, 85 }, { 67, 71, 102 }, { 67, 80, 99 }, { 67, 80, 102 }, + { 67, 85, 99 }, { 67, 85, 102 }, { 67, 99, 102 }, { 68, 69, 86 }, + { 68, 69, 100 }, { 68, 72, 86 }, { 68, 72, 103 }, { 68, 81, 100 }, + { 68, 81, 103 }, { 68, 86, 100 }, { 68, 86, 103 }, { 68, 100, 103 }, + { 69, 73, 86 }, { 69, 73, 104 }, { 69, 82, 100 }, { 69, 82, 104 }, + { 69, 86, 100 }, { 69, 86, 104 }, { 69, 100, 104 }, { 70, 72, 74 }, + { 70, 72, 83 }, { 70, 72, 105 }, { 70, 74, 85 }, { 70, 74, 105 }, + { 70, 83, 101 }, { 70, 83, 105 }, { 70, 85, 101 }, { 70, 85, 105 }, + { 70, 101, 105 }, { 71, 73, 74 }, { 71, 73, 84 }, { 71, 73, 106 }, + { 71, 74, 85 }, { 71, 74, 106 }, { 71, 84, 102 }, { 71, 84, 106 }, + { 71, 85, 102 }, { 71, 85, 106 }, { 71, 102, 106 }, { 72, 74, 86 }, + { 72, 74, 105 }, { 72, 83, 103 }, { 72, 83, 105 }, { 72, 86, 103 }, + { 72, 86, 105 }, { 72, 103, 105 }, { 73, 74, 86 }, { 73, 74, 106 }, + { 73, 84, 104 }, { 73, 84, 106 }, { 73, 86, 104 }, { 73, 86, 106 }, + { 73, 104, 106 }, { 74, 85, 105 }, { 74, 85, 106 }, { 74, 86, 105 }, + { 74, 86, 106 }, { 74, 105, 106 }, { 75, 87, 88 }, { 75, 87, 89 }, + { 75, 87, 107 }, { 75, 88, 90 }, { 75, 88, 107 }, { 75, 89, 93 }, + { 75, 89, 107 }, { 75, 90, 93 }, { 75, 90, 107 }, { 75, 93, 107 }, + { 76, 87, 88 }, { 76, 87, 91 }, { 76, 87, 108 }, { 76, 88, 92 }, + { 76, 88, 108 }, { 76, 91, 94 }, { 76, 91, 108 }, { 76, 92, 94 }, + { 76, 92, 108 }, { 76, 94, 108 }, { 77, 87, 89 }, { 77, 87, 91 }, + { 77, 87, 109 }, { 77, 89, 95 }, { 77, 89, 109 }, { 77, 91, 97 }, + { 77, 91, 109 }, { 77, 95, 97 }, { 77, 95, 109 }, { 77, 97, 109 }, + { 78, 88, 90 }, { 78, 88, 92 }, { 78, 88, 110 }, { 78, 90, 96 }, + { 78, 90, 110 }, { 78, 92, 98 }, { 78, 92, 110 }, { 78, 96, 98 }, + { 78, 96, 110 }, { 78, 98, 110 }, { 79, 89, 93 }, { 79, 89, 95 }, + { 79, 89, 111 }, { 79, 93, 99 }, { 79, 93, 111 }, { 79, 95, 101 }, + { 79, 95, 111 }, { 79, 99, 101 }, { 79, 99, 111 }, { 79, 101, 111 }, + { 80, 90, 93 }, { 80, 90, 96 }, { 80, 90, 112 }, { 80, 93, 99 }, + { 80, 93, 112 }, { 80, 96, 102 }, { 80, 96, 112 }, { 80, 99, 102 }, + { 80, 99, 112 }, { 80, 102, 112 }, { 81, 91, 94 }, { 81, 91, 97 }, + { 81, 91, 113 }, { 81, 94, 100 }, { 81, 94, 113 }, { 81, 97, 103 }, + { 81, 97, 113 }, { 81, 100, 103 }, { 81, 100, 113 }, { 81, 103, 113 }, + { 82, 92, 94 }, { 82, 92, 98 }, { 82, 92, 114 }, { 82, 94, 100 }, + { 82, 94, 114 }, { 82, 98, 104 }, { 82, 98, 114 }, { 82, 100, 104 }, + { 82, 100, 114 }, { 82, 104, 114 }, { 83, 95, 97 }, { 83, 95, 101 }, + { 83, 95, 115 }, { 83, 97, 103 }, { 83, 97, 115 }, { 83, 101, 105 }, + { 83, 101, 115 }, { 83, 103, 105 }, { 83, 103, 115 }, { 83, 105, 115 }, + { 84, 96, 98 }, { 84, 96, 102 }, { 84, 96, 116 }, { 84, 98, 104 }, + { 84, 98, 116 }, { 84, 102, 106 }, { 84, 102, 116 }, { 84, 104, 106 }, + { 84, 104, 116 }, { 84, 106, 116 }, { 85, 99, 101 }, { 85, 99, 102 }, + { 85, 99, 117 }, { 85, 101, 105 }, { 85, 101, 117 }, { 85, 102, 106 }, + { 85, 102, 117 }, { 85, 105, 106 }, { 85, 105, 117 }, { 85, 106, 117 }, + { 86, 100, 103 }, { 86, 100, 104 }, { 86, 100, 118 }, { 86, 103, 105 }, + { 86, 103, 118 }, { 86, 104, 106 }, { 86, 104, 118 }, { 86, 105, 106 }, + { 86, 105, 118 }, { 86, 106, 118 }, { 87, 88, 107 }, { 87, 88, 108 }, + { 87, 89, 107 }, { 87, 89, 109 }, { 87, 91, 108 }, { 87, 91, 109 }, + { 87, 107, 108 }, { 87, 107, 109 }, { 87, 108, 109 }, { 88, 90, 107 }, + { 88, 90, 110 }, { 88, 92, 108 }, { 88, 92, 110 }, { 88, 107, 108 }, + { 88, 107, 110 }, { 88, 108, 110 }, { 89, 93, 107 }, { 89, 93, 111 }, + { 89, 95, 109 }, { 89, 95, 111 }, { 89, 107, 109 }, { 89, 107, 111 }, + { 89, 109, 111 }, { 90, 93, 107 }, { 90, 93, 112 }, { 90, 96, 110 }, + { 90, 96, 112 }, { 90, 107, 110 }, { 90, 107, 112 }, { 90, 110, 112 }, + { 91, 94, 108 }, { 91, 94, 113 }, { 91, 97, 109 }, { 91, 97, 113 }, + { 91, 108, 109 }, { 91, 108, 113 }, { 91, 109, 113 }, { 92, 94, 108 }, + { 92, 94, 114 }, { 92, 98, 110 }, { 92, 98, 114 }, { 92, 108, 110 }, + { 92, 108, 114 }, { 92, 110, 114 }, { 93, 99, 111 }, { 93, 99, 112 }, + { 93, 107, 111 }, { 93, 107, 112 }, { 93, 111, 112 }, { 94, 100, 113 }, + { 94, 100, 114 }, { 94, 108, 113 }, { 94, 108, 114 }, { 94, 113, 114 }, + { 95, 97, 109 }, { 95, 97, 115 }, { 95, 101, 111 }, { 95, 101, 115 }, + { 95, 109, 111 }, { 95, 109, 115 }, { 95, 111, 115 }, { 96, 98, 110 }, + { 96, 98, 116 }, { 96, 102, 112 }, { 96, 102, 116 }, { 96, 110, 112 }, + { 96, 110, 116 }, { 96, 112, 116 }, { 97, 103, 113 }, { 97, 103, 115 }, + { 97, 109, 113 }, { 97, 109, 115 }, { 97, 113, 115 }, { 98, 104, 114 }, + { 98, 104, 116 }, { 98, 110, 114 }, { 98, 110, 116 }, { 98, 114, 116 }, + { 99, 101, 111 }, { 99, 101, 117 }, { 99, 102, 112 }, { 99, 102, 117 }, + { 99, 111, 112 }, { 99, 111, 117 }, { 99, 112, 117 }, { 100, 103, 113 }, + { 100, 103, 118 }, { 100, 104, 114 }, { 100, 104, 118 }, { 100, 113, 114 }, + { 100, 113, 118 }, { 100, 114, 118 }, { 101, 105, 115 }, { 101, 105, 117 }, + { 101, 111, 115 }, { 101, 111, 117 }, { 101, 115, 117 }, { 102, 106, 116 }, + { 102, 106, 117 }, { 102, 112, 116 }, { 102, 112, 117 }, { 102, 116, 117 }, + { 103, 105, 115 }, { 103, 105, 118 }, { 103, 113, 115 }, { 103, 113, 118 }, + { 103, 115, 118 }, { 104, 106, 116 }, { 104, 106, 118 }, { 104, 114, 116 }, + { 104, 114, 118 }, { 104, 116, 118 }, { 105, 106, 117 }, { 105, 106, 118 }, + { 105, 115, 117 }, { 105, 115, 118 }, { 105, 117, 118 }, { 106, 116, 117 }, + { 106, 116, 118 }, { 106, 117, 118 }, { 107, 108, 109 }, { 107, 108, 110 }, + { 107, 108, 119 }, { 107, 109, 111 }, { 107, 109, 119 }, { 107, 110, 112 }, + { 107, 110, 119 }, { 107, 111, 112 }, { 107, 111, 119 }, { 107, 112, 119 }, + { 108, 109, 113 }, { 108, 109, 119 }, { 108, 110, 114 }, { 108, 110, 119 }, + { 108, 113, 114 }, { 108, 113, 119 }, { 108, 114, 119 }, { 109, 111, 115 }, + { 109, 111, 119 }, { 109, 113, 115 }, { 109, 113, 119 }, { 109, 115, 119 }, + { 110, 112, 116 }, { 110, 112, 119 }, { 110, 114, 116 }, { 110, 114, 119 }, + { 110, 116, 119 }, { 111, 112, 117 }, { 111, 112, 119 }, { 111, 115, 117 }, + { 111, 115, 119 }, { 111, 117, 119 }, { 112, 116, 117 }, { 112, 116, 119 }, + { 112, 117, 119 }, { 113, 114, 118 }, { 113, 114, 119 }, { 113, 115, 118 }, + { 113, 115, 119 }, { 113, 118, 119 }, { 114, 116, 118 }, { 114, 116, 119 }, + { 114, 118, 119 }, { 115, 117, 118 }, { 115, 117, 119 }, { 115, 118, 119 }, + { 116, 117, 118 }, { 116, 117, 119 }, { 116, 118, 119 }, { 117, 118, 119 } +}; + + + +/* Add a rotation around the wx-plane to the matrix m. */ +static void rotatewx(float m[4][4], float phi) +{ + float c, s, u, v; + int i; + + phi *= M_PI/180.0; + c = cos(phi); + s = sin(phi); + for (i=0; i<4; i++) + { + u = m[i][1]; + v = m[i][2]; + m[i][1] = c*u+s*v; + m[i][2] = -s*u+c*v; + } +} + + +/* Add a rotation around the wy-plane to the matrix m. */ +static void rotatewy(float m[4][4], float phi) +{ + float c, s, u, v; + int i; + + phi *= M_PI/180.0; + c = cos(phi); + s = sin(phi); + for (i=0; i<4; i++) + { + u = m[i][0]; + v = m[i][2]; + m[i][0] = c*u-s*v; + m[i][2] = s*u+c*v; + } +} + + +/* Add a rotation around the wz-plane to the matrix m. */ +static void rotatewz(float m[4][4], float phi) +{ + float c, s, u, v; + int i; + + phi *= M_PI/180.0; + c = cos(phi); + s = sin(phi); + for (i=0; i<4; i++) + { + u = m[i][0]; + v = m[i][1]; + m[i][0] = c*u+s*v; + m[i][1] = -s*u+c*v; + } +} + + +/* Add a rotation around the xy-plane to the matrix m. */ +static void rotatexy(float m[4][4], float phi) +{ + float c, s, u, v; + int i; + + phi *= M_PI/180.0; + c = cos(phi); + s = sin(phi); + for (i=0; i<4; i++) + { + u = m[i][2]; + v = m[i][3]; + m[i][2] = c*u+s*v; + m[i][3] = -s*u+c*v; + } +} + + +/* Add a rotation around the xz-plane to the matrix m. */ +static void rotatexz(float m[4][4], float phi) +{ + float c, s, u, v; + int i; + + phi *= M_PI/180.0; + c = cos(phi); + s = sin(phi); + for (i=0; i<4; i++) + { + u = m[i][1]; + v = m[i][3]; + m[i][1] = c*u-s*v; + m[i][3] = s*u+c*v; + } +} + + +/* Add a rotation around the yz-plane to the matrix m. */ +static void rotateyz(float m[4][4], float phi) +{ + float c, s, u, v; + int i; + + phi *= M_PI/180.0; + c = cos(phi); + s = sin(phi); + for (i=0; i<4; i++) + { + u = m[i][0]; + v = m[i][3]; + m[i][0] = c*u-s*v; + m[i][3] = s*u+c*v; + } +} + + +/* Compute the rotation matrix m from the rotation angles. */ +static void rotateall(float al, float be, float de, float ze, float et, + float th, float m[4][4]) +{ + int i, j; + + for (i=0; i<4; i++) + for (j=0; j<4; j++) + m[i][j] = (i==j); + rotatewx(m,al); + rotatewy(m,be); + rotatewz(m,de); + rotatexz(m,et); + rotatexy(m,ze); + rotateyz(m,th); +} + + +/* Multiply two rotation matrices: o=m*n. */ +static void mult_rotmat(float m[4][4], float n[4][4], float o[4][4]) +{ + int i, j, k; + + for (i=0; i<4; i++) + { + for (j=0; j<4; j++) + { + o[i][j] = 0.0; + for (k=0; k<4; k++) + o[i][j] += m[i][k]*n[k][j]; + } + } +} + + +/* Compute a 4D rotation matrix from two unit quaternions. */ +static void quats_to_rotmat(float p[4], float q[4], float m[4][4]) +{ + double al, be, de, ze, et, th; + double r00, r01, r02, r12, r22; + + r00 = 1.0-2.0*(p[1]*p[1]+p[2]*p[2]); + r01 = 2.0*(p[0]*p[1]+p[2]*p[3]); + r02 = 2.0*(p[2]*p[0]-p[1]*p[3]); + r12 = 2.0*(p[1]*p[2]+p[0]*p[3]); + r22 = 1.0-2.0*(p[1]*p[1]+p[0]*p[0]); + + al = atan2(-r12,r22)*180.0/M_PI; + be = atan2(r02,sqrt(r00*r00+r01*r01))*180.0/M_PI; + de = atan2(-r01,r00)*180.0/M_PI; + + r00 = 1.0-2.0*(q[1]*q[1]+q[2]*q[2]); + r01 = 2.0*(q[0]*q[1]+q[2]*q[3]); + r02 = 2.0*(q[2]*q[0]-q[1]*q[3]); + r12 = 2.0*(q[1]*q[2]+q[0]*q[3]); + r22 = 1.0-2.0*(q[1]*q[1]+q[0]*q[0]); + + et = atan2(-r12,r22)*180.0/M_PI; + th = atan2(r02,sqrt(r00*r00+r01*r01))*180.0/M_PI; + ze = atan2(-r01,r00)*180.0/M_PI; + + rotateall(al,be,de,ze,et,-th,m); +} + + +/* Compute the normal vector of a plane based on three points in the plane. */ +static void normal(const float *p, const float *q, const float *r, + float *n) +{ + float u[3], v[3], t; + + u[0] = q[0]-p[0]; + u[1] = q[1]-p[1]; + u[2] = q[2]-p[2]; + v[0] = r[0]-p[0]; + v[1] = r[1]-p[1]; + v[2] = r[2]-p[2]; + n[0] = u[1]*v[2]-u[2]*v[1]; + n[1] = u[2]*v[0]-u[0]*v[2]; + n[2] = u[0]*v[1]-u[1]*v[0]; + t = sqrt(n[0]*n[0]+n[1]*n[1]+n[2]*n[2]); + n[0] /= t; + n[1] /= t; + n[2] /= t; +} + + +/* Project an array of vertices from 4d to 3d. */ +static void project(ModeInfo *mi, const float vert[][4], float v[][4], int num) +{ + float s, q1[4], q2[4], r1[4][4], r2[4][4], m[4][4]; + int i, j, k; + polytopesstruct *pp = &poly[MI_SCREEN(mi)]; + + rotateall(pp->alpha,pp->beta,pp->delta,pp->zeta,pp->eta,pp->theta,r1); + + gltrackball_get_quaternion(pp->trackballs[0],q1); + gltrackball_get_quaternion(pp->trackballs[1],q2); + quats_to_rotmat(q1,q2,r2); + + mult_rotmat(r2,r1,m); + + /* Project the vertices from 4d to 3d. */ + for (i=0; i<num; i++) + { + for (j=0; j<4; j++) + { + s = 0.0; + for (k=0; k<4; k++) + s += m[j][k]*vert[i][k]; + v[i][j] = s+offset4d[j]; + } + if (projection_4d == DISP_4D_ORTHOGRAPHIC) + { + for (j=0; j<3; j++) + v[i][j] /= 2.0; + v[i][3] = 1.0; + } + else + { + for (j=0; j<4; j++) + v[i][j] /= v[i][3]; + } + } + + /* Move the projected vertices along the z-axis so that they become visible + in the viewport. */ + for (i=0; i<num; i++) + { + for (j=0; j<4; j++) + v[i][j] += offset3d[j]; + } +} + + +/* Draw a single polytope. */ +static void draw(ModeInfo *mi, + float v[][4], + const int edge[][2], int num_edge, + const int face[], int num_face, + int vert_per_face, + float edge_color[][4], + float face_color[][4], + float face_color_trans[][4]) +{ + int i, j; + float n[3]; + GLfloat red[4] = { 1.0, 0.0, 0.0, 1.0 }; + GLfloat red_trans[4] = { 1.0, 0.0, 0.0, 1.0 }; + + mi->polygon_count = 0; + if (display_mode == DISP_WIREFRAME) + { + if (color_mode == COLORS_SINGLE) + glColor4fv(red); + glBegin(GL_LINES); + for (i=0; i<num_edge; i++) + { + if (color_mode == COLORS_DEPTH) + glColor4fv(edge_color[i]); + glVertex4fv(v[edge[i][0]]); + glVertex4fv(v[edge[i][1]]); + } + glEnd(); + mi->polygon_count = num_edge; + } + else + { + if (color_mode == COLORS_SINGLE) + { + red_trans[3] = face_color_trans[0][3]/2.0; + if (display_mode == DISP_TRANSPARENT) + glMaterialfv(GL_FRONT_AND_BACK,GL_AMBIENT_AND_DIFFUSE,red_trans); + else + glMaterialfv(GL_FRONT_AND_BACK,GL_AMBIENT_AND_DIFFUSE,red); + } + for (i=0; i<num_face; i++) + { + glBegin(GL_POLYGON); + if (color_mode == COLORS_DEPTH) + { + if (display_mode == DISP_TRANSPARENT) + glMaterialfv(GL_FRONT_AND_BACK,GL_AMBIENT_AND_DIFFUSE, + face_color_trans[i]); + else + glMaterialfv(GL_FRONT_AND_BACK,GL_AMBIENT_AND_DIFFUSE, + face_color[i]); + } + normal(v[face[i*vert_per_face]],v[face[i*vert_per_face+1]], + v[face[i*vert_per_face+2]],n); + glNormal3fv(n); + for (j=0; j<vert_per_face; j++) + glVertex4fv(v[face[i*vert_per_face+j]]); + glEnd(); + } + mi->polygon_count = num_face; + } +} + + +/* Draw a 5-cell {3,3,3} projected into 3d. */ +static void cell_5(ModeInfo *mi) +{ + polytopesstruct *hp = &poly[MI_SCREEN(mi)]; + float v[NUM_VERT_5][4]; + + project(mi,vert_5,v,NUM_VERT_5); + draw(mi,v,edge_5,NUM_EDGE_5,(int *)face_5,NUM_FACE_5, + VERT_PER_FACE_5,hp->edge_color_5,hp->face_color_5, + hp->face_color_trans_5); +} + + +/* Draw a 8-cell {4,3,3} projected into 3d. */ +static void cell_8(ModeInfo *mi) +{ + polytopesstruct *hp = &poly[MI_SCREEN(mi)]; + float v[NUM_VERT_8][4]; + + project(mi,vert_8,v,NUM_VERT_8); + draw(mi,v,edge_8,NUM_EDGE_8,(int *)face_8,NUM_FACE_8, + VERT_PER_FACE_8,hp->edge_color_8,hp->face_color_8, + hp->face_color_trans_8); +} + + +/* Draw a 16-cell {3,3,4} projected into 3d. */ +static void cell_16(ModeInfo *mi) +{ + polytopesstruct *hp = &poly[MI_SCREEN(mi)]; + float v[NUM_VERT_16][4]; + + project(mi,vert_16,v,NUM_VERT_16); + draw(mi,v,edge_16,NUM_EDGE_16,(int *)face_16,NUM_FACE_16, + VERT_PER_FACE_16,hp->edge_color_16,hp->face_color_16, + hp->face_color_trans_16); +} + + +/* Draw a 24-cell {3,4,3} projected into 3d. */ +static void cell_24(ModeInfo *mi) +{ + polytopesstruct *hp = &poly[MI_SCREEN(mi)]; + float v[NUM_VERT_24][4]; + + project(mi,vert_24,v,NUM_VERT_24); + draw(mi,v,edge_24,NUM_EDGE_24,(int *)face_24,NUM_FACE_24, + VERT_PER_FACE_24,hp->edge_color_24,hp->face_color_24, + hp->face_color_trans_24); +} + + +/* Draw a 120-cell {5,3,3} projected into 3d. */ +static void cell_120(ModeInfo *mi) +{ + polytopesstruct *hp = &poly[MI_SCREEN(mi)]; + float v[NUM_VERT_120][4]; + + project(mi,vert_120,v,NUM_VERT_120); + draw(mi,v,edge_120,NUM_EDGE_120,(int *)face_120,NUM_FACE_120, + VERT_PER_FACE_120,hp->edge_color_120,hp->face_color_120, + hp->face_color_trans_120); +} + + +/* Draw a 600-cell {3,3,5} projected into 3d. */ +static void cell_600(ModeInfo *mi) +{ + polytopesstruct *hp = &poly[MI_SCREEN(mi)]; + float v[NUM_VERT_600][4]; + + project(mi,vert_600,v,NUM_VERT_600); + draw(mi,v,edge_600,NUM_EDGE_600,(int *)face_600,NUM_FACE_600, + VERT_PER_FACE_600,hp->edge_color_600,hp->face_color_600, + hp->face_color_trans_600); +} + + +/* Compute a color based on the w-depth of a point. */ +static void color(float depth, float alpha, float min, float max, + float color[4]) +{ + double d, t; + int s; + + d = (depth-min)/(max-min); + s = floor(d*4.0); + t = d*4.0-s; + if (s < 0) + s += 6; + if (s >= 6) + s -= 6; + switch (s) + { + case 0: + color[0] = 1.0; + color[1] = t; + color[2] = 0.0; + break; + case 1: + color[0] = 1.0-t; + color[1] = 1.0; + color[2] = 0.0; + break; + case 2: + color[0] = 0.0; + color[1] = 1.0; + color[2] = t; + break; + case 3: + color[0] = 0.0; + color[1] = 1.0-t; + color[2] = 1.0; + break; + case 4: + color[0] = t; + color[1] = 0.0; + color[2] = 1.0; + break; + case 5: + color[0] = 1.0; + color[1] = 0.0; + color[2] = 1.0-t; + break; + } + color[3] = alpha; +} + + +/* Set the colors of a single polytope's edges and faces. */ +static void colors(const float vert[][4], + const int edge[][2], int num_edge, + const int face[], int num_face, + int vert_per_face, + float edge_color[][4], + float face_color[][4], + float face_color_trans[][4], + float alpha, + float min_edge_depth, float max_edge_depth, + float min_face_depth, float max_face_depth) +{ + int i, j; + float depth; + + for (i=0; i<num_edge; i++) + { + depth = (vert[edge[i][0]][3]+vert[edge[i][1]][3])/2.0; + color(depth,1.0,min_edge_depth,max_edge_depth,edge_color[i]); + } + for (i=0; i<num_face; i++) + { + depth = 0.0; + for (j=0; j<vert_per_face; j++) + depth += vert[face[i*vert_per_face+j]][3]; + depth /= vert_per_face; + color(depth,1.0,min_face_depth,max_face_depth,face_color[i]); + color(depth,alpha,min_face_depth,max_face_depth,face_color_trans[i]); + } +} + + +/* Set the colors of the polytopes' edges and faces. */ +static void set_colors(ModeInfo *mi) +{ + polytopesstruct *hp = &poly[MI_SCREEN(mi)]; + /* 5-cell. */ + colors(vert_5,edge_5,NUM_EDGE_5,(int *)face_5,NUM_FACE_5, + VERT_PER_FACE_5,hp->edge_color_5,hp->face_color_5, + hp->face_color_trans_5,0.5,MIN_EDGE_DEPTH_5, + MAX_EDGE_DEPTH_5,MIN_FACE_DEPTH_5,MAX_FACE_DEPTH_5); + + /* 8-cell. */ + colors(vert_8,edge_8,NUM_EDGE_8,(int *)face_8,NUM_FACE_8, + VERT_PER_FACE_8,hp->edge_color_8,hp->face_color_8, + hp->face_color_trans_8,0.4,MIN_EDGE_DEPTH_8, + MAX_EDGE_DEPTH_8,MIN_FACE_DEPTH_8,MAX_FACE_DEPTH_8); + + /* 16-cell. */ + colors(vert_16,edge_16,NUM_EDGE_16,(int *)face_16,NUM_FACE_16, + VERT_PER_FACE_16,hp->edge_color_16,hp->face_color_16, + hp->face_color_trans_16,0.25,MIN_EDGE_DEPTH_16, + MAX_EDGE_DEPTH_16,MIN_FACE_DEPTH_16,MAX_FACE_DEPTH_16); + + /* 24-cell. */ + colors(vert_24,edge_24,NUM_EDGE_24,(int *)face_24,NUM_FACE_24, + VERT_PER_FACE_24,hp->edge_color_24,hp->face_color_24, + hp->face_color_trans_24,0.25,MIN_EDGE_DEPTH_24, + MAX_EDGE_DEPTH_24,MIN_FACE_DEPTH_24,MAX_FACE_DEPTH_24); + + /* 120-cell. */ + colors(vert_120,edge_120,NUM_EDGE_120,(int *)face_120,NUM_FACE_120, + VERT_PER_FACE_120,hp->edge_color_120,hp->face_color_120, + hp->face_color_trans_120,0.15,MIN_EDGE_DEPTH_120, + MAX_EDGE_DEPTH_120,MIN_FACE_DEPTH_120,MAX_FACE_DEPTH_120); + + /* 600-cell. */ + colors(vert_600,edge_600,NUM_EDGE_600,(int *)face_600,NUM_FACE_600, + VERT_PER_FACE_600,hp->edge_color_600,hp->face_color_600, + hp->face_color_trans_600,0.06,MIN_EDGE_DEPTH_600, + MAX_EDGE_DEPTH_600,MIN_FACE_DEPTH_600,MAX_FACE_DEPTH_600); +} + + +static void init(ModeInfo *mi) +{ + polytopesstruct *pp = &poly[MI_SCREEN(mi)]; + + set_colors(mi); + + pp->alpha = 0.0; + pp->beta = 0.0; + pp->delta = 0.0; + pp->zeta = 0.0; + pp->eta = 0.0; + pp->theta = 0.0; + + pp->tick = 0; + pp->poly = 0; +} + + +/* Redisplay the polytopes. */ +static void display_polytopes(ModeInfo *mi) +{ + polytopesstruct *pp = &poly[MI_SCREEN(mi)]; + + if (!pp->button_pressed) + { + pp->alpha += speed_wx * pp->speed_scale; + if (pp->alpha >= 360.0) + pp->alpha -= 360.0; + pp->beta += speed_wy * pp->speed_scale; + if (pp->beta >= 360.0) + pp->beta -= 360.0; + pp->delta += speed_wz * pp->speed_scale; + if (pp->delta >= 360.0) + pp->delta -= 360.0; + pp->zeta += speed_xy * pp->speed_scale; + if (pp->zeta >= 360.0) + pp->zeta -= 360.0; + pp->eta += speed_xz * pp->speed_scale; + if (pp->eta >= 360.0) + pp->eta -= 360.0; + pp->theta += speed_yz * pp->speed_scale; + if (pp->theta >= 360.0) + pp->theta -= 360.0; + } + + glMatrixMode(GL_PROJECTION); + glLoadIdentity(); + if (projection_3d == DISP_3D_ORTHOGRAPHIC) + { + if (pp->aspect >= 1.0) + glOrtho(-pp->aspect,pp->aspect,-1.0,1.0,0.1,100.0); + else + glOrtho(-1.0,1.0,-1.0/pp->aspect,1.0/pp->aspect,0.1,100.0); + } + else + { + gluPerspective(60.0,pp->aspect,0.1,100.0); + } + + glMatrixMode(GL_MODELVIEW); + glLoadIdentity(); + + if (pp->tick == 0) + { + if (polytope == POLYTOPE_RANDOM) + pp->poly = random() % (POLYTOPE_LAST_CELL+1); + else + pp->poly = polytope; + } + if (++pp->tick > 1000) + pp->tick = 0; + + if (pp->poly == POLYTOPE_5_CELL) + cell_5(mi); + else if (pp->poly == POLYTOPE_8_CELL) + cell_8(mi); + else if (pp->poly == POLYTOPE_16_CELL) + cell_16(mi); + else if (pp->poly == POLYTOPE_24_CELL) + cell_24(mi); + else if (pp->poly == POLYTOPE_120_CELL) + cell_120(mi); + else if (pp->poly == POLYTOPE_600_CELL) + cell_600(mi); + else + abort(); +} + + +ENTRYPOINT void reshape_polytopes(ModeInfo *mi, int width, int height) +{ + polytopesstruct *pp = &poly[MI_SCREEN(mi)]; + int y = 0; + + if (width > height * 5) { /* tiny window: show middle */ + height = width; + y = -height/2; + } + + pp->WindW = (GLint)width; + pp->WindH = (GLint)height; + glViewport(0,y,width,height); + pp->aspect = (GLfloat)width/(GLfloat)height; +} + + +ENTRYPOINT Bool polytopes_handle_event(ModeInfo *mi, XEvent *event) +{ + polytopesstruct *pp = &poly[MI_SCREEN(mi)]; + KeySym sym = 0; + char c = 0; + + if (event->xany.type == KeyPress || event->xany.type == KeyRelease) + XLookupString (&event->xkey, &c, 1, &sym, 0); + + if (event->xany.type == ButtonPress && + event->xbutton.button == Button1) + { + pp->button_pressed = True; + gltrackball_start(pp->trackballs[pp->current_trackball], + event->xbutton.x, event->xbutton.y, + MI_WIDTH(mi), MI_HEIGHT(mi)); + return True; + } + else if (event->xany.type == ButtonRelease && + event->xbutton.button == Button1) + { + pp->button_pressed = False; + return True; + } + else if (event->xany.type == KeyPress) + { + if (sym == XK_Shift_L || sym == XK_Shift_R) + { + pp->current_trackball = 1; + if (pp->button_pressed) + gltrackball_start(pp->trackballs[pp->current_trackball], + event->xbutton.x, event->xbutton.y, + MI_WIDTH(mi), MI_HEIGHT(mi)); + return True; + } + } + else if (event->xany.type == KeyRelease) + { + if (sym == XK_Shift_L || sym == XK_Shift_R) + { + pp->current_trackball = 0; + if (pp->button_pressed) + gltrackball_start(pp->trackballs[pp->current_trackball], + event->xbutton.x, event->xbutton.y, + MI_WIDTH(mi), MI_HEIGHT(mi)); + return True; + } + } + else if (event->xany.type == MotionNotify && pp->button_pressed) + { + gltrackball_track(pp->trackballs[pp->current_trackball], + event->xmotion.x, event->xmotion.y, + MI_WIDTH(mi), MI_HEIGHT(mi)); + return True; + } + + return False; +} + + +/* + *----------------------------------------------------------------------------- + *----------------------------------------------------------------------------- + * Xlock hooks. + *----------------------------------------------------------------------------- + *----------------------------------------------------------------------------- + */ + +/* + *----------------------------------------------------------------------------- + * Initialize polytopes. Called each time the window changes. + *----------------------------------------------------------------------------- + */ + +ENTRYPOINT void init_polytopes(ModeInfo *mi) +{ + polytopesstruct *pp; + + MI_INIT(mi, poly); + pp = &poly[MI_SCREEN(mi)]; + + pp->trackballs[0] = gltrackball_init(True); + pp->trackballs[1] = gltrackball_init(True); + pp->current_trackball = 0; + pp->button_pressed = False; + + /* Set the display mode. */ + if (!strcasecmp(mode,"wireframe") || !strcasecmp(mode,"0")) + { + display_mode = DISP_WIREFRAME; + } + else if (!strcasecmp(mode,"surface") || !strcasecmp(mode,"1")) + { + display_mode = DISP_SURFACE; + } + else if (!strcasecmp(mode,"transparent") || !strcasecmp(mode,"2")) + { + display_mode = DISP_TRANSPARENT; + } + else + { + display_mode = DISP_TRANSPARENT; + } + + /* Set the Klein bottle. */ + if (!strcasecmp(poly_str,"random") || !strcasecmp(poly_str,"-1")) + { + polytope = POLYTOPE_RANDOM; + } + else if (!strcasecmp(poly_str,"5-cell") || !strcasecmp(poly_str,"0")) + { + polytope = POLYTOPE_5_CELL; + } + else if (!strcasecmp(poly_str,"8-cell") || !strcasecmp(poly_str,"1")) + { + polytope = POLYTOPE_8_CELL; + } + else if (!strcasecmp(poly_str,"16-cell") || !strcasecmp(poly_str,"2")) + { + polytope = POLYTOPE_16_CELL; + } + else if (!strcasecmp(poly_str,"24-cell") || !strcasecmp(poly_str,"3")) + { + polytope = POLYTOPE_24_CELL; + } + else if (!strcasecmp(poly_str,"120-cell") || !strcasecmp(poly_str,"4")) + { + polytope = POLYTOPE_120_CELL; + } + else if (!strcasecmp(poly_str,"600-cell") || !strcasecmp(poly_str,"5")) + { + polytope = POLYTOPE_600_CELL; + } + else + { + polytope = POLYTOPE_RANDOM; + } + + /* Set the color mode. */ + if (!strcasecmp(color_str,"single") || !strcasecmp(color_str,"0")) + { + color_mode = COLORS_SINGLE; + } + else if (!strcasecmp(color_str,"depth") || !strcasecmp(color_str,"1")) + { + color_mode = COLORS_DEPTH; + } + else + { + color_mode = COLORS_DEPTH; + } + + /* Set the 3d projection mode. */ + if (!strcasecmp(proj_3d,"perspective") || !strcasecmp(proj_3d,"0")) + { + projection_3d = DISP_3D_PERSPECTIVE; + } + else if (!strcasecmp(proj_3d,"orthographic") || !strcasecmp(proj_3d,"1")) + { + projection_3d = DISP_3D_ORTHOGRAPHIC; + } + else + { + projection_3d = DISP_3D_PERSPECTIVE; + } + + /* Set the 4d projection mode. */ + if (!strcasecmp(proj_4d,"perspective") || !strcasecmp(proj_4d,"0")) + { + projection_4d = DISP_4D_PERSPECTIVE; + } + else if (!strcasecmp(proj_4d,"orthographic") || !strcasecmp(proj_4d,"1")) + { + projection_4d = DISP_4D_ORTHOGRAPHIC; + } + else + { + projection_4d = DISP_4D_PERSPECTIVE; + } + + /* make multiple screens rotate at slightly different rates. */ + pp->speed_scale = 0.9 + frand(0.3); + + if ((pp->glx_context = init_GL(mi)) != NULL) + { + reshape_polytopes(mi,MI_WIDTH(mi),MI_HEIGHT(mi)); + glDrawBuffer(GL_BACK); + init(mi); + } + else + { + MI_CLEARWINDOW(mi); + } +} + +/* + *----------------------------------------------------------------------------- + * Called by the mainline code periodically to update the display. + *----------------------------------------------------------------------------- + */ +ENTRYPOINT void draw_polytopes(ModeInfo *mi) +{ + static const GLfloat light_ambient[] = { 0.0, 0.0, 0.0, 1.0 }; + static const GLfloat light_diffuse[] = { 1.0, 1.0, 1.0, 1.0 }; + static const GLfloat light_specular[] = { 0.0, 0.0, 0.0, 1.0 }; + static const GLfloat light_position[] = { 0.0, 0.0, 1.0, 0.0 }; + static const GLfloat mat_specular[] = { 1.0, 1.0, 1.0, 1.0 }; + + Display *display = MI_DISPLAY(mi); + Window window = MI_WINDOW(mi); + polytopesstruct *hp; + + if (poly == NULL) + return; + hp = &poly[MI_SCREEN(mi)]; + + MI_IS_DRAWN(mi) = True; + if (!hp->glx_context) + return; + + glXMakeCurrent(display,window,*(hp->glx_context)); + + + glMatrixMode(GL_PROJECTION); + glLoadIdentity(); + if (projection_3d == DISP_3D_PERSPECTIVE) + gluPerspective(60.0,1.0,0.1,100.0); + else + glOrtho(-1.0,1.0,-1.0,1.0,0.1,100.0);; + glMatrixMode(GL_MODELVIEW); + glLoadIdentity(); + + if (display_mode == DISP_WIREFRAME) + { + glDisable(GL_DEPTH_TEST); + glDisable(GL_LIGHTING); + glDisable(GL_LIGHT0); + glDisable(GL_BLEND); + } + else if (display_mode == DISP_SURFACE) + { + glEnable(GL_DEPTH_TEST); + glDepthFunc(GL_LESS); + glLightModeli(GL_LIGHT_MODEL_TWO_SIDE,GL_TRUE); + glEnable(GL_LIGHTING); + glEnable(GL_LIGHT0); + glLightfv(GL_LIGHT0,GL_AMBIENT,light_ambient); + glLightfv(GL_LIGHT0,GL_DIFFUSE,light_diffuse); + glLightfv(GL_LIGHT0,GL_SPECULAR,light_specular); + glLightfv(GL_LIGHT0,GL_POSITION,light_position); + glMaterialfv(GL_FRONT_AND_BACK,GL_SPECULAR,mat_specular); + glMaterialf(GL_FRONT_AND_BACK,GL_SHININESS,0.0); + glDepthMask(GL_TRUE); + glDisable(GL_BLEND); + } + else if (display_mode == DISP_TRANSPARENT) + { + glDisable(GL_DEPTH_TEST); + glLightModeli(GL_LIGHT_MODEL_TWO_SIDE,GL_TRUE); + glEnable(GL_LIGHTING); + glEnable(GL_LIGHT0); + glLightfv(GL_LIGHT0,GL_AMBIENT,light_ambient); + glLightfv(GL_LIGHT0,GL_DIFFUSE,light_diffuse); + glLightfv(GL_LIGHT0,GL_SPECULAR,light_specular); + glLightfv(GL_LIGHT0,GL_POSITION,light_position); + glMaterialfv(GL_FRONT_AND_BACK,GL_SPECULAR,mat_specular); + glMaterialf(GL_FRONT_AND_BACK,GL_SHININESS,0.0); + glDepthMask(GL_FALSE); + glEnable(GL_BLEND); + glBlendFunc(GL_SRC_ALPHA,GL_ONE); + } + else + { + glDisable(GL_DEPTH_TEST); + glDisable(GL_LIGHTING); + glDisable(GL_LIGHT0); + glDisable(GL_BLEND); + } + + + glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT); + glLoadIdentity(); + + display_polytopes(mi); + + if (MI_IS_FPS(mi)) + do_fps (mi); + + glFlush(); + + glXSwapBuffers(display,window); +} + + +#ifndef STANDALONE +ENTRYPOINT void change_polytopes(ModeInfo *mi) +{ + polytopesstruct *hp = &poly[MI_SCREEN(mi)]; + + if (!hp->glx_context) + return; + + glXMakeCurrent(MI_DISPLAY(mi),MI_WINDOW(mi),*(hp->glx_context)); + init(mi); +} +#endif /* !STANDALONE */ + +XSCREENSAVER_MODULE ("Polytopes", polytopes) + +#endif /* USE_GL */ |