6.09HEADmaster

1 files changed, 0 insertions, 2458 deletions

diff --git a/hacks/glx/polyhedra.c b/hacks/glx/polyhedra.c
deleted file mode 100644
index 98e6891..0000000
--- a/hacks/glx/polyhedra.c
+++ /dev/null
@@ -1,2458 +0,0 @@
-/*****************************************************************************
- * #ident "Id: main.c,v 3.27 2002-01-06 16:23:01+02 rl Exp "
- * kaleido
- *
- *	Kaleidoscopic construction of uniform polyhedra
- *	Copyright (c) 1991-2002 Dr. Zvi Har'El <rl@math.technion.ac.il>
- *
- *	Redistribution and use in source and binary forms, with or without
- *	modification, are permitted provided that the following conditions
- *	are met:
- *
- *	1. Redistributions of source code must retain the above copyright
- *	   notice, this list of conditions and the following disclaimer.
- *
- *	2. Redistributions in binary form must reproduce the above copyright
- *	   notice, this list of conditions and the following disclaimer in
- *	   the documentation and/or other materials provided with the
- *	   distribution.
- *
- *	3. The end-user documentation included with the redistribution,
- *	   if any, must include the following acknowledgment:
- *		"This product includes software developed by
- *		 Dr. Zvi Har'El (http://www.math.technion.ac.il/~rl/)."
- *	   Alternately, this acknowledgment may appear in the software itself,
- *	   if and wherever such third-party acknowledgments normally appear.
- *
- *	This software is provided 'as-is', without any express or implied
- *	warranty.  In no event will the author be held liable for any
- *	damages arising from the use of this software.
- *
- *	Author:
- *		Dr. Zvi Har'El,
- *		Deptartment of Mathematics,
- *		Technion, Israel Institue of Technology,
- *		Haifa 32000, Israel.
- *		E-Mail: rl@math.technion.ac.il
- *
- *	ftp://ftp.math.technion.ac.il/kaleido/
- *	http://www.mathconsult.ch/showroom/unipoly/
- *
- *	Adapted for xscreensaver by Jamie Zawinski <jwz@jwz.org> 25-Apr-2004
- *
- *****************************************************************************
- */
-
-#ifdef HAVE_CONFIG_H
-# include "config.h"
-#endif
-
-#include <math.h>
-#include <stdio.h>
-#include <ctype.h>
-#include <string.h>
-#include <stdlib.h>
-#include <errno.h>
-
-#include "polyhedra.h"
-
-extern const char *progname;
-
-#ifndef MAXLONG
-#define MAXLONG 0x7FFFFFFF
-#endif
-#ifndef MAXDIGITS
-#define MAXDIGITS 10 /* (int)log10((double)MAXLONG) + 1 */
-#endif
-
-#ifndef DBL_EPSILON
-#define DBL_EPSILON 2.2204460492503131e-16
-#endif
-#define BIG_EPSILON 3e-2
-#define AZ M_PI/7  /* axis azimuth */
-#define EL M_PI/17 /* axis elevation */
-
-#define Err(x) do {\
-	fprintf (stderr, "%s: %s\n", progname, (x)); \
-	exit (1); \
-    } while(0)
-
-#define Free(lvalue) do {\
-	if (lvalue) {\
-	    free((char*) lvalue);\
-	    lvalue=0;\
-	}\
-    } while(0)
-
-#define Matfree(lvalue,n) do {\
-	if (lvalue) \
-	    matfree((char*) lvalue, n);\
-	lvalue=0;\
-    } while(0)
-
-#define Malloc(lvalue,n,type) do {\
-	if (!(lvalue = (type*) calloc((n), sizeof(type)))) \
-	    abort();\
-    } while(0)
-
-#define Realloc(lvalue,n,type) do {\
-	if (!(lvalue = (type*) realloc(lvalue, (n) * sizeof(type)))) \
-	    abort();\
-    } while(0)
-
-#define Calloc(lvalue,n,type) do {\
-	if (!(lvalue = (type*) calloc(n, sizeof(type))))\
-	    abort();\
-    } while(0)
-
-#define Matalloc(lvalue,n,m,type) do {\
-	if (!(lvalue = (type**) matalloc(n, (m) * sizeof(type))))\
-	    abort();\
-    } while(0)
-
-#define Sprintfrac(lvalue,x) do {\
-	if (!(lvalue=sprintfrac(x)))\
-	    return 0;\
-    } while(0)
-
-#define numerator(x) (frac(x), frax.n)
-#define denominator(x) (frac(x), frax.d)
-#define compl(x) (frac(x), (double) frax.n / (frax.n-frax.d))
-
-typedef struct {
-    double x, y, z;
-} Vector;
-
-typedef struct {
-  /* NOTE: some of the int's can be replaced by short's, char's,
-     or even bit fields, at the expense of readability!!!*/
-  int index; /* index to the standard list, the array uniform[] */
-  int N; /* number of faces types (atmost 5)*/
-  int M; /* vertex valency  (may be big for dihedral polyhedra) */
-  int V; /* vertex count */
-  int E; /* edge count */
-  int F; /* face count */
-  int D; /* density */
-  int chi; /* Euler characteristic */
-  int g; /* order of symmetry group */
-  int K; /* symmetry type: D=2, T=3, O=4, I=5 */
-  int hemi;/* flag hemi polyhedron */
-  int onesided;/* flag onesided polyhedron */
-  int even; /* removed face in pqr| */
-  int *Fi; /* face counts by type (array N)*/
-  int *rot; /* vertex configuration (array M of 0..N-1) */
-  int *snub; /* snub triangle configuration (array M of 0..1) */
-  int *firstrot; /* temporary for vertex generation (array V) */
-  int *anti; /* temporary for direction of ideal vertices (array E) */
-  int *ftype; /* face types (array F) */
-  int **e; /* edges (matrix 2 x E of 0..V-1)*/
-  int **dual_e; /* dual edges (matrix 2 x E of 0..F-1)*/
-  int **incid; /* vertex-face incidence (matrix M x V of 0..F-1)*/
-  int **adj; /* vertex-vertex adjacency (matrix M x V of 0..V-1)*/
-  double p[4]; /* p, q and r; |=0 */
-  double minr; /* smallest nonzero inradius */
-  double gon; /* basis type for dihedral polyhedra */
-  double *n; /* number of side of a face of each type (array N) */
-  double *m; /* number of faces at a vertex of each type (array N) */
-  double *gamma; /* fundamental angles in radians (array N) */
-  char *polyform; /* printable Wythoff symbol */
-  char *config; /* printable vertex configuration */
-  char *group; /* printable group name */
-  char *name; /* name, standard or manifuctured */
-  char *dual_name; /* dual name, standard or manifuctured */
-  char *class;
-  char *dual_class;
-  Vector *v; /* vertex coordinates (array V) */
-  Vector *f; /* face coordinates (array F)*/
-} Polyhedron;
-
-typedef struct {
-  long n,d;
-} Fraction;
-
-static Polyhedron *polyalloc(void);
-static Vector rotate(Vector vertex, Vector axis, double angle);
-
-static Vector sum3(Vector a, Vector b, Vector c);
-static Vector scale(double k, Vector a);
-static Vector sum(Vector a, Vector b);
-static Vector diff(Vector a, Vector b);
-static Vector pole (double r, Vector a, Vector b, Vector c);
-static Vector cross(Vector a, Vector b);
-static double dot(Vector a, Vector b);
-static int same(Vector a, Vector b, double epsilon);
-
-static char *sprintfrac(double x);
-
-static void frac(double x);
-static void matfree(void *mat, int rows);
-static void *matalloc(int rows, int row_size);
-
-static Fraction frax;
-
-
-static const struct {
-  char *Wythoff, *name, *dual, *group, *class, *dual_class;
-  short Coxeter, Wenninger;
-} uniform[] = {
-
-  /****************************************************************************
-   *		Dihedral Schwarz Triangles (D5 only)
-   ***************************************************************************/
-
-  /*  0 */	{"2 5|2",	"Pentagonal Prism",
-				"Pentagonal Dipyramid",
-				"Dihedral (D[1/5])",
-				"",
-				"",
-				0, 0},
-
-  /*  2 */	{"|2 2 5",	"Pentagonal Antiprism",
-				"Pentagonal Deltohedron",
-				"Dihedral (D[1/5])",
-				"",
-				"",
-				0, 0},
-							 /* (2 2 5/2) (D2/5) */
-  /*  4 */	{"2 5/2|2",	"Pentagrammic Prism",
-				"Pentagrammic Dipyramid",
-				"Dihedral (D[2/5])",
-				"",
-				"",
-				0, 0},
-
-  /*  6 */	{"|2 2 5/2",	"Pentagrammic Antiprism",
-				"Pentagrammic Deltohedron",
-				"Dihedral (D[2/5])",
-				"",
-				"",
-				0, 0},
-							 /* (5/3 2 2) (D3/5) */
-
-  /*  8 */	{"|2 2 5/3",	"Pentagrammic Crossed Antiprism",
-				"Pentagrammic Concave Deltohedron",
-				"Dihedral (D[3/5])",
-				"",
-				"",
-				0, 0},
-
-  /****************************************************************************
-   *		Tetrahedral
-   ***************************************************************************/
-
-							     /* (2 3 3) (T1) */
-  /*  10 */	{"3|2 3",	"Tetrahedron",
-				"Tetrahedron",
-				"Tetrahedral (T[1])",
-				"Platonic Solid",
-				"Platonic Solid",
-				15, 1},
-
-  /*  12 */	{"2 3|3",	"Truncated Tetrahedron",
-				"Triakistetrahedron",
-				"Tetrahedral (T[1])",
-				"Archimedean Solid",
-				"Catalan Solid",
-				16, 6},
-							   /* (3/2 3 3) (T2) */
-  /*  14 */	{"3/2 3|3",	"Octahemioctahedron",
-				"Octahemioctacron",
-				"Tetrahedral (T[2])",
-				"",
-				"",
-				37, 68},
-
-							   /* (3/2 2 3) (T3) */
-  /*  16 */	{"3/2 3|2",	"Tetrahemihexahedron",
-				"Tetrahemihexacron",
-				"Tetrahedral (T[3])",
-				"",
-				"",
-				36, 67},
-
-  /****************************************************************************
-   *		Octahedral
-   ***************************************************************************/
-
-							     /* (2 3 4) (O1) */
-  /* 18 */	{"4|2 3",	"Octahedron",
-				"Cube",
-				"Octahedral (O[1])",
-				"Platonic Solid",
-				"Platonic Solid",
-				17, 2},
-
-  /* 20 */	{"3|2 4",	"Cube",
-				"Octahedron",
-				"Octahedral (O[1])",
-				"Platonic Solid",
-				"Platonic Solid",
-				18, 3},
-
-  /* 22 */	{"2|3 4",	"Cuboctahedron",
-				"Rhombic Dodecahedron",
-				"Octahedral (O[1])",
-				"Archimedean Solid",
-				"Catalan Solid",
-				19, 11},
-
-  /* 24 */	{"2 4|3",	"Truncated Octahedron",
-				"Tetrakishexahedron",
-				"Octahedral (O[1])",
-				"Archimedean Solid",
-				"Catalan Solid",
-				20, 7},
-
-  /* 26 */	{"2 3|4",	"Truncated Cube",
-				"Triakisoctahedron",
-				"Octahedral (O[1])",
-				"Archimedean Solid",
-				"Catalan Solid",
-				21, 8},
-
-  /* 28 */	{"3 4|2",	"Rhombicuboctahedron",
-				"Deltoidal Icositetrahedron",
-				"Octahedral (O[1])",
-				"Archimedean Solid",
-				"Catalan Solid",
-				22, 13},
-
-  /* 30 */	{"2 3 4|",	"Truncated Cuboctahedron",
-				"Disdyakisdodecahedron",
-				"Octahedral (O[1])",
-				"Archimedean Solid",
-				"Catalan Solid",
-				23, 15},
-
-  /* 32, 33, 66, and 67 are chiral, existing in both left and right handed
-     (enantiomeric) forms, so it would make sense to display both versions.
-  */
-
-  /* 32 */	{"|2 3 4",	"Snub Cube",
-				"Pentagonal Icositetrahedron",
-				"Octahedral (O[1]), Chiral",
-				"Archimedean Solid",
-				"Catalan Solid",
-				24, 17},
-							  /* (3/2 4 4) (O2b) */
-
-  /* 34 */	{"3/2 4|4",	"Small Cubicuboctahedron",
-				"Small Hexacronic Icositetrahedron",
-				"Octahedral (O[2b])",
-				"",
-				"",
-				38, 69},
-							   /* (4/3 3 4) (O4) */
-
-  /* 36 */	{"3 4|4/3",	"Great Cubicuboctahedron",
-				"Great Hexacronic Icositetrahedron",
-				"Octahedral (O[4])",
-				"",
-				"",
-				50, 77},
-
-  /* 38 */	{"4/3 4|3",	"Cubohemioctahedron",
-				"Hexahemioctacron",
-				"Octahedral (O[4])",
-				"",
-				"",
-				51, 78},
-
-  /* 40 */	{"4/3 3 4|",	"Cubitruncated Cuboctahedron",
-				"Tetradyakishexahedron",
-				"Octahedral (O[4])",
-				"",
-				"",
-				52, 79},
-							   /* (3/2 2 4) (O5) */
-
-  /* 42 */	{"3/2 4|2",	"Great Rhombicuboctahedron",
-				"Great Deltoidal Icositetrahedron",
-				"Octahedral (O[5])",
-				"",
-				"",
-				59, 85},
-
-  /* 44 */	{"3/2 2 4|",	"Small Rhombihexahedron",
-				"Small Rhombihexacron",
-				"Octahedral (O[5])",
-				"",
-				"",
-				60, 86},
-							   /* (4/3 2 3) (O7) */
-
-  /* 46 */	{"2 3|4/3",	"Stellated Truncated Hexahedron",
-				"Great Triakisoctahedron",
-				"Octahedral (O[7])",
-				"",
-				"",
-				66, 92},
-
-  /* 48 */	{"4/3 2 3|",	"Great Truncated Cuboctahedron",
-				"Great Disdyakisdodecahedron",
-				"Octahedral (O[7])",
-				"",
-				"",
-				67, 93},
-							/* (4/3 3/2 2) (O11) */
-
-  /* 50 */	{"4/3 3/2 2|",	"Great Rhombihexahedron",
-				"Great Rhombihexacron",
-				"Octahedral (O[11])",
-				"",
-				"",
-				82, 103},
-
-  /****************************************************************************
-   *		Icosahedral
-   ***************************************************************************/
-
-							     /* (2 3 5) (I1) */
-  /* 52 */	{"5|2 3",	"Icosahedron",
-				"Dodecahedron",
-				"Icosahedral (I[1])",
-				"Platonic Solid",
-				"Platonic Solid",
-				25, 4},
-
-  /* 54 */	{"3|2 5",	"Dodecahedron",
-				"Icosahedron",
-				"Icosahedral (I[1])",
-				"Platonic Solid",
-				"Platonic Solid",
-				26, 5},
-
-  /* 56 */	{"2|3 5",	"Icosidodecahedron",
-				"Rhombic Triacontahedron",
-				"Icosahedral (I[1])",
-				"Archimedean Solid",
-				"Catalan Solid",
-				28, 12},
-
-  /* 58 */	{"2 5|3",	"Truncated Icosahedron",
-				"Pentakisdodecahedron",
-				"Icosahedral (I[1])",
-				"Archimedean Solid",
-				"Catalan Solid",
-				27, 9},
-
-  /* 60 */	{"2 3|5",	"Truncated Dodecahedron",
-				"Triakisicosahedron",
-				"Icosahedral (I[1])",
-				"Archimedean Solid",
-				"Catalan Solid",
-				29, 10},
-
-  /* 62 */	{"3 5|2",	"Rhombicosidodecahedron",
-				"Deltoidal Hexecontahedron",
-				"Icosahedral (I[1])",
-				"Archimedean Solid",
-				"Catalan Solid",
-				30, 14},
-
-  /* 64 */	{"2 3 5|",	"Truncated Icosidodecahedron",
-				"Disdyakistriacontahedron",
-				"Icosahedral (I[1])",
-				"Archimedean Solid",
-				"Catalan Solid",
-				31, 16},
-
-  /* 32, 33, 66, and 67 are chiral, existing in both left and right handed
-     (enantiomeric) forms, so it would make sense to display both versions.
-  */
-
-  /* 66 */	{"|2 3 5",	"Snub Dodecahedron",
-				"Pentagonal Hexecontahedron",
-				"Icosahedral (I[1]), Chiral",
-				"Archimedean Solid",
-				"Catalan Solid",
-				32, 18},
-							  /* (5/2 3 3) (I2a) */
-
-  /* 68 */	{"3|5/2 3",	"Small Ditrigonal Icosidodecahedron",
-				"Small Triambic Icosahedron",
-				"Icosahedral (I[2a])",
-				"",
-				"",
-				39, 70},
-
-  /* 70 */	{"5/2 3|3",	"Small Icosicosidodecahedron",
-				"Small Icosacronic Hexecontahedron",
-				"Icosahedral (I[2a])",
-				"",
-				"",
-				40, 71},
-
-  /* 72 */	{"|5/2 3 3",	"Small Snub Icosicosidodecahedron",
-				"Small Hexagonal Hexecontahedron",
-				"Icosahedral (I[2a])",
-				"",
-				"",
-				41, 110},
-							  /* (3/2 5 5) (I2b) */
-
-  /* 74 */	{"3/2 5|5",	"Small Dodecicosidodecahedron",
-				"Small Dodecacronic Hexecontahedron",
-				"Icosahedral (I[2b])",
-				"",
-				"",
-				42, 72},
-							   /* (2 5/2 5) (I3) */
-
-  /* 76 */	{"5|2 5/2",	"Small Stellated Dodecahedron",
-				"Great Dodecahedron",
-				"Icosahedral (I[3])",
-				"Kepler-Poinsot Solid",
-				"Kepler-Poinsot Solid",
-				43, 20},
-
-  /* 78 */	{"5/2|2 5",	"Great Dodecahedron",
-				"Small Stellated Dodecahedron",
-				"Icosahedral (I[3])",
-				"Kepler-Poinsot Solid",
-				"Kepler-Poinsot Solid",
-				44, 21},
-
-  /* 80 */	{"2|5/2 5",	"Great Dodecadodecahedron",
-				"Medial Rhombic Triacontahedron",
-				"Icosahedral (I[3])",
-				"",
-				"",
-				45, 73},
-
-  /* 82 */	{"2 5/2|5",	"Truncated Great Dodecahedron",
-				"Small Stellapentakisdodecahedron",
-				"Icosahedral (I[3])",
-				"",
-				"",
-				47, 75},
-
-  /* 84 */	{"5/2 5|2",	"Rhombidodecadodecahedron",
-				"Medial Deltoidal Hexecontahedron",
-				"Icosahedral (I[3])",
-				"",
-				"",
-				48, 76},
-
-  /* 86 */	{"2 5/2 5|",	"Small Rhombidodecahedron",
-				"Small Rhombidodecacron",
-				"Icosahedral (I[3])",
-				"",
-				"",
-				46, 74},
-
-  /* 88 */	{"|2 5/2 5",	"Snub Dodecadodecahedron",
-				"Medial Pentagonal Hexecontahedron",
-				"Icosahedral (I[3])",
-				"",
-				"",
-				49, 111},
-							   /* (5/3 3 5) (I4) */
-
-  /* 90 */	{"3|5/3 5",	"Ditrigonal Dodecadodecahedron",
-				"Medial Triambic Icosahedron",
-				"Icosahedral (I[4])",
-				"",
-				"",
-				53, 80},
-
-  /* 92 */	{"3 5|5/3",	"Great Ditrigonal Dodecicosidodecahedron",
-			       "Great Ditrigonal Dodecacronic Hexecontahedron",
-				"Icosahedral (I[4])",
-				"",
-				"",
-				54, 81},
-
-  /* 94 */	{"5/3 3|5",	"Small Ditrigonal Dodecicosidodecahedron",
-			       "Small Ditrigonal Dodecacronic Hexecontahedron",
-				"Icosahedral (I[4])",
-				"",
-				"",
-				55, 82},
-
-  /* 96 */	{"5/3 5|3",	"Icosidodecadodecahedron",
-				"Medial Icosacronic Hexecontahedron",
-				"Icosahedral (I[4])",
-				"",
-				"",
-				56, 83},
-
-  /* 98 */	{"5/3 3 5|",	"Icositruncated Dodecadodecahedron",
-				"Tridyakisicosahedron",
-				"Icosahedral (I[4])",
-				"",
-				"",
-				57, 84},
-
-  /* 100 */	{"|5/3 3 5",	"Snub Icosidodecadodecahedron",
-				"Medial Hexagonal Hexecontahedron",
-				"Icosahedral (I[4])",
-				"",
-				"",
-				58, 112},
-							  /* (3/2 3 5) (I6b) */
-
-  /* 102 */	{"3/2|3 5",	"Great Ditrigonal Icosidodecahedron",
-				"Great Triambic Icosahedron",
-				"Icosahedral (I[6b])",
-				"",
-				"",
-				61, 87},
-
-  /* 104 */	{"3/2 5|3",	"Great Icosicosidodecahedron",
-				"Great Icosacronic Hexecontahedron",
-				"Icosahedral (I[6b])",
-				"",
-				"",
-				62, 88},
-
-  /* 106 */	{"3/2 3|5",	"Small Icosihemidodecahedron",
-				"Small Icosihemidodecacron",
-				"Icosahedral (I[6b])",
-				"",
-				"",
-				63, 89},
-
-  /* 108 */	{"3/2 3 5|",	"Small Dodecicosahedron",
-				"Small Dodecicosacron",
-				"Icosahedral (I[6b])",
-				"",
-				"",
-				64, 90},
-							  /* (5/4 5 5) (I6c) */
-
-  /* 110 */	{"5/4 5|5",	"Small Dodecahemidodecahedron",
-				"Small Dodecahemidodecacron",
-				"Icosahedral (I[6c])",
-				"",
-				"",
-				65, 91},
-							   /* (2 5/2 3) (I7) */
-
-  /* 112 */	{"3|2 5/2",	"Great Stellated Dodecahedron",
-				"Great Icosahedron",
-				"Icosahedral (I[7])",
-				"Kepler-Poinsot Solid",
-				"Kepler-Poinsot Solid",
-				68, 22},
-
-  /* 114 */	{"5/2|2 3",	"Great Icosahedron",
-				"Great Stellated Dodecahedron",
-				"Icosahedral (I[7])",
-				"Kepler-Poinsot Solid",
-				"Kepler-Poinsot Solid",
-				69, 41},
-
-  /* 116 */	{"2|5/2 3",	"Great Icosidodecahedron",
-				"Great Rhombic Triacontahedron",
-				"Icosahedral (I[7])",
-				"",
-				"",
-				70, 94},
-
-  /* 118 */	{"2 5/2|3",	"Great Truncated Icosahedron",
-				"Great Stellapentakisdodecahedron",
-				"Icosahedral (I[7])",
-				"",
-				"",
-				71, 95},
-
-  /* 120 */	{"2 5/2 3|",	"Rhombicosahedron",
-				"Rhombicosacron",
-				"Icosahedral (I[7])",
-				"",
-				"",
-				72, 96},
-
-  /* 122 */	{"|2 5/2 3",	"Great Snub Icosidodecahedron",
-				"Great Pentagonal Hexecontahedron",
-				"Icosahedral (I[7])",
-				"",
-				"",
-				73, 113},
-							   /* (5/3 2 5) (I9) */
-
-  /* 124 */	{"2 5|5/3",	"Small Stellated Truncated Dodecahedron",
-				"Great Pentakisdodecahedron",
-				"Icosahedral (I[9])",
-				"",
-				"",
-				74, 97},
-
-  /* 126 */	{"5/3 2 5|",	"Truncated Dodecadodecahedron",
-				"Medial Disdyakistriacontahedron",
-				"Icosahedral (I[9])",
-				"",
-				"",
-				75, 98},
-
-  /* 128 */	{"|5/3 2 5",	"Inverted Snub Dodecadodecahedron",
-				"Medial Inverted Pentagonal Hexecontahedron",
-				"Icosahedral (I[9])",
-				"",
-				"",
-				76, 114},
-						       /* (5/3 5/2 3) (I10a) */
-
-  /* 130 */	{"5/2 3|5/3",	"Great Dodecicosidodecahedron",
-				"Great Dodecacronic Hexecontahedron",
-				"Icosahedral (I[10a])",
-				"",
-				"",
-				77, 99},
-
-  /* 132 */	{"5/3 5/2|3",	"Small Dodecahemicosahedron",
-				"Small Dodecahemicosacron",
-				"Icosahedral (I[10a])",
-				"",
-				"",
-				78, 100},
-
-  /* 134 */	{"5/3 5/2 3|",	"Great Dodecicosahedron",
-				"Great Dodecicosacron",
-				"Icosahedral (I[10a])",
-				"",
-				"",
-				79, 101},
-
-  /* 136 */	{"|5/3 5/2 3",	"Great Snub Dodecicosidodecahedron",
-				"Great Hexagonal Hexecontahedron",
-				"Icosahedral (I[10a])",
-				"",
-				"",
-				80, 115},
-							 /* (5/4 3 5) (I10b) */
-
-  /* 138 */	{"5/4 5|3",	"Great Dodecahemicosahedron",
-				"Great Dodecahemicosacron",
-				"Icosahedral (I[10b])",
-				"",
-				"",
-				81, 102},
-							  /* (5/3 2 3) (I13) */
-
-  /* 140 */	{"2 3|5/3",	"Great Stellated Truncated Dodecahedron",
-				"Great Triakisicosahedron",
-				"Icosahedral (I[13])",
-				"",
-				"",
-				83, 104},
-
-  /* 142 */	{"5/3 3|2",	"Great Rhombicosidodecahedron",
-				"Great Deltoidal Hexecontahedron",
-				"Icosahedral (I[13])",
-				"",
-				"",
-				84, 105},
-
-  /* 144 */	{"5/3 2 3|",	"Great Truncated Icosidodecahedron",
-				"Great Disdyakistriacontahedron",
-				"Icosahedral (I[13])",
-				"",
-				"",
-				87, 108},
-
-  /* 146 */	{"|5/3 2 3",	"Great Inverted Snub Icosidodecahedron",
-				"Great Inverted Pentagonal Hexecontahedron",
-				"Icosahedral (I[13])",
-				"",
-				"",
-				88, 116},
-						     /* (5/3 5/3 5/2) (I18a) */
-
-  /* 148 */	{"5/3 5/2|5/3",	"Great Dodecahemidodecahedron",
-				"Great Dodecahemidodecacron",
-				"Icosahedral (I[18a])",
-				"",
-				"",
-				86, 107},
-						       /* (3/2 5/3 3) (I18b) */
-
-  /* 150 */	{"3/2 3|5/3",	"Great Icosihemidodecahedron",
-				"Great Icosihemidodecacron",
-				"Icosahedral (I[18b])",
-				"",
-				"",
-				85, 106},
-						      /* (3/2 3/2 5/3) (I22) */
-
-  /* 152 */	{"|3/2 3/2 5/2","Small Retrosnub Icosicosidodecahedron",
-				"Small Hexagrammic Hexecontahedron",
-				"Icosahedral (I[22])",
-				"",
-				"",
-				91, 118},
-							/* (3/2 5/3 2) (I23) */
-
-  /* 154 */	{"3/2 5/3 2|",	"Great Rhombidodecahedron",
-				"Great Rhombidodecacron",
-				"Icosahedral (I[23])",
-				"",
-				"",
-				89, 109},
-
-  /* 156 */	{"|3/2 5/3 2",	"Great Retrosnub Icosidodecahedron",
-				"Great Pentagrammic Hexecontahedron",
-				"Icosahedral (I[23])",
-				"",
-				"",
-				90, 117},
-
-  /****************************************************************************
-   *		Last But Not Least
-   ***************************************************************************/
-
-  /* 158 */    {"3/2 5/3 3 5/2",	"Great Dirhombicosidodecahedron",
-				"Great Dirhombicosidodecacron",
-				"Non-Wythoffian",
-				"",
-				"",
-				92, 119}
-};
-
-static int last_uniform = sizeof (uniform) / sizeof (uniform[0]);
-
-
-
-static int unpacksym(const char *sym, Polyhedron *P);
-static int moebius(Polyhedron *P);
-static int decompose(Polyhedron *P);
-static int guessname(Polyhedron *P);
-static int newton(Polyhedron *P, int need_approx);
-static int exceptions(Polyhedron *P);
-static int count(Polyhedron *P);
-static int configuration(Polyhedron *P);
-static int vertices(Polyhedron *P);
-static int faces(Polyhedron *P);
-static int edgelist(Polyhedron *P);
-
-static Polyhedron *
-kaleido(const char *sym,
-        int need_coordinates, int need_edgelist, int need_approx,
-	int just_list)
-{
-  Polyhedron *P;
-  /*
-   * Allocate a Polyhedron structure P.
-   */
-  if (!(P = polyalloc()))
-    return 0;
-  /*
-   * Unpack input symbol into P.
-   */
-  if (!unpacksym(sym, P))
-    return 0;
-  /*
-   * Find Mebius triangle, its density and Euler characteristic.
-   */
-  if (!moebius(P))
-    return 0;
-  /*
-   * Decompose Schwarz triangle.
-   */
-  if (!decompose(P))
-    return 0;
-  /*
-   * Find the names of the polyhedron and its dual.
-   */
-  if (!guessname(P))
-    return 0;
-  if (just_list)
-    return P;
-  /*
-   * Solve Fundamental triangles, optionally printing approximations.
-   */
-  if (!newton(P,need_approx))
-    return 0;
-  /*
-   * Deal with exceptional polyhedra.
-   */
-  if (!exceptions(P))
-    return 0;
-  /*
-   * Count edges and faces, update density and characteristic if needed.
-   */
-  if (!count(P))
-    return 0;
-  /*
-   * Generate printable vertex configuration.
-   */
-  if (!configuration(P))
-    return 0;
-  /*
-   * Compute coordinates.
-   */
-  if (!need_coordinates && !need_edgelist)
-    return P;
-  if (!vertices(P))
-    return 0;
-  if (!faces (P))
-    return 0;
-  /*
-   * Compute edgelist.
-   */
-  if (!need_edgelist)
-    return P;
-  if (!edgelist(P))
-    return 0;
-  return P;
-}
-
-/*
- * Allocate a blank Polyhedron structure and initialize some of its nonblank
- * fields.
- *
- * Array and matrix field are allocated when needed.
- */
-static Polyhedron *
-polyalloc()
-{
-  Polyhedron *P;
-  Calloc(P, 1, Polyhedron);
-  P->index = -1;
-  P->even = -1;
-  P->K = 2;
-  return P;
-}
-
-/*
- * Free the struture allocated by polyalloc(), as well as all the array and
- * matrix fields.
- */
-static void
-polyfree(Polyhedron *P)
-{
-  Free(P->Fi);
-  Free(P->n);
-  Free(P->m);
-  Free(P->gamma);
-  Free(P->rot);
-  Free(P->snub);
-  Free(P->firstrot);
-  Free(P->anti);
-  Free(P->ftype);
-  Free(P->polyform);
-  Free(P->config);
-  if (P->index < 0) {
-    Free(P->name);
-    Free(P->dual_name);
-  }
-  Free(P->v);
-  Free(P->f);
-  Matfree(P->e, 2);
-  Matfree(P->dual_e, 2);
-  Matfree(P->incid, P->M);
-  Matfree(P->adj, P->M);
-  free(P);
-}
-
-static void *
-matalloc(int rows, int row_size)
-{
-  void **mat;
-  int i = 0;
-  if (!(mat = malloc(rows * sizeof (void *))))
-    return 0;
-  while ((mat[i] = malloc(row_size)) && ++i < rows)
-    ;
-  if (i == rows)
-    return (void *)mat;
-  while (--i >= 0)
-    free(mat[i]);
-  free(mat);
-  return 0;
-}
-
-static void
-matfree(void *mat, int rows)
-{
-  while (--rows >= 0)
-    free(((void **)mat)[rows]);
-  free(mat);
-}
-
-/*
- * compute the mathematical modulus function.
- */
-static int
-mod (int i, int j)
-{
-  return (i%=j)>=0?i:j<0?i-j:i+j;
-}
-
-
-/*
- * Find the numerator and the denominator using the Euclidean algorithm.
- */
-static void
-frac(double x)
-{
-  static const Fraction zero = {0,1}, inf = {1,0};
-  Fraction r0, r;
-  long f;
-  double s = x;
-  r = zero;
-  frax = inf;
-  for (;;) {
-    if (fabs(s) > (double) MAXLONG)
-      return;
-    f = (long) floor (s);
-    r0 = r;
-    r = frax;
-    frax.n = frax.n * f + r0.n;
-    frax.d = frax.d * f + r0.d;
-    if (x == (double)frax.n/(double)frax.d)
-      return;
-    s = 1 / (s - f);
-  }
-}
-
-
-/*
- * Unpack input symbol: Wythoff symbol or an index to uniform[]. The symbol is
- * a # followed by a number, or a three fractions and a bar in some order. We
- * allow no bars only if it result from the input symbol #80.
- */
-static int
-unpacksym(const char *sym, Polyhedron *P)
-{
-  int i = 0, n, d, bars = 0;
-  char c;
-  while ((c = *sym++) && isspace(c))
-    ;
-  if (!c) Err("no data");
-  if (c == '#') {
-    while ((c = *sym++) && isspace(c))
-      ;
-    if (!c)
-      Err("no digit after #");
-    if (!isdigit(c))
-      Err("not a digit");
-    n = c - '0';
-    while ((c = *sym++) && isdigit(c))
-      n = n * 10 + c - '0';
-    if (!n)
-      Err("zero index");
-    if (n > last_uniform)
-      Err("index too big");
-    sym--;
-    while ((c = *sym++) && isspace(c))
-      ;
-    if (c)
-      Err("data exceeded");
-    sym = uniform[P->index = n - 1].Wythoff;
-  } else
-    sym--;
-
-  for (;;) {
-    while ((c = *sym++) && isspace(c))
-      ;
-    if (!c) {
-      if (i == 4 && (bars || P->index == last_uniform - 1))
-        return 1;
-      if (!bars)
-        Err("no bars");
-      Err("not enough fractions");
-    }
-    if (i == 4)
-      Err("data exceeded");
-    if (c == '|'){
-      if (++bars > 1)
-        Err("too many bars");
-      P->p[i++] = 0;
-      continue;
-    }
-    if (!isdigit(c))
-      Err("not a digit");
-    n = c - '0';
-    while ((c = *sym++) && isdigit(c))
-      n = n * 10 + c - '0';
-    if (c && isspace (c))
-      while ((c = *sym++) && isspace(c))
-        ;
-    if (c != '/') {
-      sym--;
-      if ((P->p[i++] = n) <= 1)
-        Err("fraction<=1");
-      continue;
-    }
-    while ((c = *sym++) && isspace(c))
-      ;
-    if (!c || !isdigit(c))
-      return 0;
-    d = c - '0';
-    while ((c = *sym++) && isdigit(c))
-      d = d * 10 + c - '0';
-    if (!d)
-      Err("zero denominator");
-    sym--;
-    if ((P->p[i++] = (double) n / d) <= 1)
-      Err("fraction<=1");
-  }
-}
-
-/*
- * Using Wythoff symbol (p|qr, pq|r, pqr| or |pqr), find the Moebius triangle
- * (2 3 K) (or (2 2 n)) of the Schwarz triangle (pqr), the order g of its
- * symmetry group, its Euler characteristic chi, and its covering density D.
- * g is the number of copies of (2 3 K) covering the sphere, i.e.,
- *
- *		g * pi * (1/2 + 1/3 + 1/K - 1) = 4 * pi
- *
- * D is the number of times g copies of (pqr) cover the sphere, i.e.
- *
- *		D * 4 * pi = g * pi * (1/p + 1/q + 1/r - 1)
- *
- * chi is V - E + F, where F = g is the number of triangles, E = 3*g/2 is the
- * number of triangle edges, and V = Vp+ Vq+ Vr, with Vp = g/(2*np) being the
- * number of vertices with angle pi/p (np is the numerator of p).
- */
-static int
-moebius(Polyhedron *P)
-{
-  int twos = 0, j, len = 1;
-  /*
-   * Arrange Wythoff symbol in a presentable form. In the same time check the
-   * restrictions on the three fractions: They all have to be greater then one,
-   * and the numerators 4 or 5 cannot occur together.  We count the ocurrences
-   * of 2 in `two', and save the largest numerator in `P->K', since they
-   * reflect on the symmetry group.
-   */
-  P->K = 2;
-  if (P->index == last_uniform - 1) {
-    Malloc(P->polyform, ++len, char);
-    strcpy(P->polyform, "|");
-  } else
-    Calloc(P->polyform, len, char);
-  for (j = 0; j < 4; j++) {
-    if (P->p[j]) {
-      char *s;
-      Sprintfrac(s, P->p[j]);
-      if (j && P->p[j-1]) {
-        Realloc(P->polyform, len += strlen (s) + 1, char);
-        strcat(P->polyform, " ");
-      } else
-        Realloc (P->polyform, len += strlen (s), char);
-      strcat(P->polyform, s);
-      free(s);
-      if (P->p[j] != 2) {
-        int k;
-        if ((k = numerator (P->p[j])) > P->K) {
-          if (P->K == 4)
-            break;
-          P->K = k;
-        } else if (k < P->K && k == 4)
-          break;
-      } else
-        twos++;
-    } else  {
-      Realloc(P->polyform, ++len, char);
-      strcat(P->polyform, "|");
-    }
-  }
-  /*
-   * Find the symmetry group P->K (where 2, 3, 4, 5 represent the dihedral,
-   * tetrahedral, octahedral and icosahedral groups, respectively), and its
-   * order P->g.
-   */
-  if (twos >= 2) {/* dihedral */
-    P->g = 4 * P->K;
-    P->K = 2;
-  } else {
-    if (P->K > 5)
-      Err("numerator too large");
-    P->g = 24 * P->K / (6 - P->K);
-  }
-  /*
-   * Compute the nominal density P->D and Euler characteristic P->chi.
-   * In few exceptional cases, these values will be modified later.
-   */
-  if (P->index != last_uniform - 1) {
-    int i;
-    P->D = P->chi = - P->g;
-    for (j = 0; j < 4; j++) if (P->p[j]) {
-      P->chi += i = P->g / numerator(P->p[j]);
-      P->D += i * denominator(P->p[j]);
-    }
-    P->chi /= 2;
-    P->D /= 4;
-    if (P->D <= 0)
-      Err("nonpositive density");
-  }
-  return 1;
-}
-
-/*
- * Decompose Schwarz triangle into N right triangles and compute the vertex
- * count V and the vertex valency M.  V is computed from the number g of
- * Schwarz triangles in the cover, divided by the number of triangles which
- * share a vertex. It is halved for one-sided polyhedra, because the
- * kaleidoscopic construction really produces a double orientable covering of
- * such polyhedra. All q' q|r are of the "hemi" type, i.e. have equatorial {2r}
- * faces, and therefore are (except 3/2 3|3 and the dihedra 2 2|r) one-sided. A
- * well known example is 3/2 3|4, the "one-sided heptahedron". Also, all p q r|
- * with one even denominator have a crossed parallelogram as a vertex figure,
- * and thus are one-sided as well.
- */
-static int
-decompose(Polyhedron *P)
-{
-  int j, J, *s, *t;
-  if (!P->p[1]) { /* p|q r */
-    P->N = 2;
-    P->M = 2 * numerator(P->p[0]);
-    P->V = P->g / P->M;
-    Malloc(P->n, P->N, double);
-    Malloc(P->m, P->N, double);
-    Malloc(P->rot, P->M, int);
-    s = P->rot;
-    for (j = 0; j < 2; j++) {
-      P->n[j] = P->p[j+2];
-      P->m[j] = P->p[0];
-    }
-    for (j = P->M / 2; j--;) {
-      *s++ = 0;
-      *s++ = 1;
-    }
-  } else if (!P->p[2]) { /* p q|r */
-    P->N = 3;
-    P->M = 4;
-    P->V = P->g / 2;
-    Malloc(P->n, P->N, double);
-    Malloc(P->m, P->N, double);
-    Malloc(P->rot, P->M, int);
-    s = P->rot;
-    P->n[0] = 2 * P->p[3];
-    P->m[0] = 2;
-    for (j = 1; j < 3; j++) {
-      P->n[j] = P->p[j-1];
-      P->m[j] = 1;
-      *s++ = 0;
-      *s++ = j;
-    }
-    if (fabs(P->p[0] - compl (P->p[1])) < DBL_EPSILON) {/* p = q' */
-      /* P->p[0]==compl(P->p[1]) should work.  However, MSDOS
-       * yeilds a 7e-17 difference! Reported by Jim Buddenhagen
-       * <jb1556@daditz.sbc.com> */
-      P->hemi = 1;
-      P->D = 0;
-      if (P->p[0] != 2 && !(P->p[3] == 3 && (P->p[0] == 3 ||
-                                             P->p[1] == 3))) {
-        P->onesided = 1;
-        P->V /= 2;
-        P->chi /= 2;
-      }
-    }
-  } else if (!P->p[3]) { /* p q r| */
-    P->M = P->N = 3;
-    P->V = P->g;
-    Malloc(P->n, P->N, double);
-    Malloc(P->m, P->N, double);
-    Malloc(P->rot, P->M, int);
-    s = P->rot;
-    for (j = 0; j < 3; j++) {
-      if (!(denominator(P->p[j]) % 2)) {
-        /* what happens if there is more then one even denominator? */
-        if (P->p[(j+1)%3] != P->p[(j+2)%3]) { /* needs postprocessing */
-          P->even = j;/* memorize the removed face */
-          P->chi -= P->g / numerator(P->p[j]) / 2;
-          P->onesided = 1;
-          P->D = 0;
-        } else {/* for p = q we get a double 2 2r|p */
-		/* noted by Roman Maeder <maeder@inf.ethz.ch> for 4 4 3/2| */
-		/* Euler characteristic is still wrong */
-          P->D /= 2;
-        }
-        P->V /= 2;
-      }
-      P->n[j] = 2 * P->p[j];
-      P->m[j] = 1;
-      *s++ = j;
-    }
-  } else { /* |p q r - snub polyhedron */
-    P->N = 4;
-    P->M = 6;
-    P->V = P->g / 2;/* Only "white" triangles carry a vertex */
-    Malloc(P->n, P->N, double);
-    Malloc(P->m, P->N, double);
-    Malloc(P->rot, P->M, int);
-    Malloc(P->snub, P->M, int);
-    s = P->rot;
-    t = P->snub;
-    P->m[0] = P->n[0] = 3;
-    for (j = 1; j < 4; j++) {
-      P->n[j] = P->p[j];
-      P->m[j] = 1;
-      *s++ = 0;
-      *s++ = j;
-      *t++ = 1;
-      *t++ = 0;
-    }
-  }
-  /*
-   * Sort the fundamental triangles (using bubble sort) according to decreasing
-   * n[i], while pushing the trivial triangles (n[i] = 2) to the end.
-   */
-  J = P->N - 1;
-  while (J) {
-    int last;
-    last = J;
-    J = 0;
-    for (j = 0; j < last; j++) {
-      if ((P->n[j] < P->n[j+1] || P->n[j] == 2) && P->n[j+1] != 2) {
-        int i;
-        double temp;
-        temp = P->n[j];
-        P->n[j] = P->n[j+1];
-        P->n[j+1] = temp;
-        temp = P->m[j];
-        P->m[j] = P->m[j+1];
-        P->m[j+1] = temp;
-        for (i = 0; i < P->M; i++) {
-          if (P->rot[i] == j)
-            P->rot[i] = j+1;
-          else if (P->rot[i] == j+1)
-            P->rot[i] = j;
-        }
-        if (P->even != -1) {
-          if (P->even == j)
-            P->even = j+1;
-          else if (P->even == j+1)
-            P->even = j;
-        }
-        J = j;
-      }
-    }
-  }
-  /*
-   *  Get rid of repeated triangles.
-   */
-  for (J = 0; J < P->N && P->n[J] != 2;J++) {
-    int k, i;
-    for (j = J+1; j < P->N && P->n[j]==P->n[J]; j++)
-      P->m[J] += P->m[j];
-    k = j - J - 1;
-    if (k) {
-      for (i = j; i < P->N; i++) {
-        P->n[i - k] = P->n[i];
-        P->m[i - k] = P->m[i];
-      }
-      P->N -= k;
-      for (i = 0; i < P->M; i++) {
-        if (P->rot[i] >= j)
-          P->rot[i] -= k;
-        else if (P->rot[i] > J)
-          P->rot[i] = J;
-      }
-      if (P->even >= j)
-        P->even -= k;
-    }
-  }
-  /*
-   * Get rid of trivial triangles.
-   */
-  if (!J)
-    J = 1; /* hosohedron */
-  if (J < P->N) {
-    int i;
-    P->N = J;
-    for (i = 0; i < P->M; i++) {
-      if (P->rot[i] >= P->N) {
-        for (j = i + 1; j < P->M; j++) {
-          P->rot[j-1] = P->rot[j];
-          if (P->snub)
-            P->snub[j-1] = P->snub[j];
-        }
-        P->M--;
-      }
-    }
-  }
-  /*
-   * Truncate arrays
-   */
-  Realloc(P->n, P->N, double);
-  Realloc(P->m, P->N, double);
-  Realloc(P->rot, P->M, int);
-  if (P->snub)
-    Realloc(P->snub, P->M, int);
-  return 1;
-}
-
-
-static int dihedral(Polyhedron *P, const char *name, const char *dual_name);
-
-
-/*
- * Get the polyhedron name, using standard list or guesswork. Ideally, we
- * should try to locate the Wythoff symbol in the standard list (unless, of
- * course, it is dihedral), after doing few normalizations, such as sorting
- * angles and splitting isoceles triangles.
- */
-static int
-guessname(Polyhedron *P)
-{
-  if (P->index != -1) {/* tabulated */
-    P->name = uniform[P->index].name;
-    P->dual_name = uniform[P->index].dual;
-    P->group = uniform[P->index].group;
-    P->class = uniform[P->index].class;
-    P->dual_class = uniform[P->index].dual_class;
-    return 1;
-  } else if (P->K == 2) {/* dihedral nontabulated */
-    if (!P->p[0]) {
-      if (P->N == 1) {
-        Malloc(P->name, sizeof ("Octahedron"), char);
-        Malloc(P->dual_name, sizeof ("Cube"), char);
-        strcpy(P->name, "Octahedron");
-        strcpy(P->dual_name, "Cube");
-        return 1;
-      }
-      P->gon = P->n[0] == 3 ? P->n[1] : P->n[0];
-      if (P->gon >= 2)
-        return dihedral(P, "Antiprism", "Deltohedron");
-      else
-        return dihedral(P, "Crossed Antiprism", "Concave Deltohedron");
-    } else if (!P->p[3] ||
-               (!P->p[2] &&
-                P->p[3] == 2)) {
-      if (P->N == 1) {
-        Malloc(P->name, sizeof("Cube"), char);
-        Malloc(P->dual_name, sizeof("Octahedron"), char);
-        strcpy(P->name, "Cube");
-        strcpy(P->dual_name, "Octahedron");
-        return 1;
-      }
-      P->gon = P->n[0] == 4 ? P->n[1] : P->n[0];
-      return dihedral(P, "Prism", "Dipyramid");
-    } else if (!P->p[1] && P->p[0] != 2) {
-      P->gon = P->m[0];
-      return dihedral(P, "Hosohedron", "Dihedron");
-    } else {
-      P->gon = P->n[0];
-      return dihedral(P, "Dihedron", "Hosohedron");
-    }
-  } else {/* other nontabulated */
-    static const char *pre[] = {"Tetr", "Oct", "Icos"};
-    Malloc(P->name, 50, char);
-    Malloc(P->dual_name, 50, char);
-    sprintf(P->name, "%sahedral ", pre[P->K - 3]);
-    if (P->onesided)
-      strcat (P->name, "One-Sided ");
-    else if (P->D == 1)
-      strcat(P->name, "Convex ");
-    else
-      strcat(P->name, "Nonconvex ");
-    strcpy(P->dual_name, P->name);
-    strcat(P->name, "Isogonal Polyhedron");
-    strcat(P->dual_name, "Isohedral Polyhedron");
-    Realloc(P->name, strlen (P->name) + 1, char);
-    Realloc(P->dual_name, strlen (P->dual_name) + 1, char);
-    return 1;
-  }
-}
-
-static int
-dihedral(Polyhedron *P, const char *name, const char *dual_name)
-{
-  char *s;
-  int i;
-  Sprintfrac(s, P->gon < 2 ? compl (P->gon) : P->gon);
-  i = strlen(s) + sizeof ("-gonal ");
-  Malloc(P->name, i + strlen (name), char);
-  Malloc(P->dual_name, i + strlen (dual_name), char);
-  sprintf(P->name, "%s-gonal %s", s, name);
-  sprintf(P->dual_name, "%s-gonal %s", s, dual_name);
-  free(s);
-  return 1;
-}
-
-/*
- * Solve the fundamental right spherical triangles.
- * If need_approx is set, print iterations on standard error.
- */
-static int
-newton(Polyhedron *P, int need_approx)
-{
-  /*
-   * First, we find initial approximations.
-   */
-  int j;
-  double cosa;
-  Malloc(P->gamma, P->N, double);
-  if (P->N == 1) {
-    P->gamma[0] = M_PI / P->m[0];
-    return 1;
-  }
-  for (j = 0; j < P->N; j++)
-    P->gamma[j] = M_PI / 2 - M_PI / P->n[j];
-  errno = 0; /* may be non-zero from some reason */
-  /*
-   * Next, iteratively find closer approximations for gamma[0] and compute
-   * other gamma[j]'s from Napier's equations.
-   */
-  if (need_approx)
-    fprintf(stderr, "Solving %s\n", P->polyform);
-  for (;;) {
-    double delta = M_PI, sigma = 0;
-    for (j = 0; j < P->N; j++) {
-      if (need_approx)
-        fprintf(stderr, "%-20.15f", P->gamma[j]);
-      delta -= P->m[j] * P->gamma[j];
-    }
-    if (need_approx)
-      printf("(%g)\n", delta);
-    if (fabs(delta) < 11 * DBL_EPSILON)
-      return 1;
-    /* On a RS/6000, fabs(delta)/DBL_EPSILON may occilate between 8 and
-     * 10. Reported by David W. Sanderson <dws@ssec.wisc.edu> */
-    for (j = 0; j < P->N; j++)
-      sigma += P->m[j] * tan(P->gamma[j]);
-    P->gamma[0] += delta * tan(P->gamma[0]) / sigma;
-    if (P->gamma[0] < 0 || P->gamma[0] > M_PI)
-      Err("gamma out of bounds");
-    cosa = cos(M_PI / P->n[0]) / sin(P->gamma[0]);
-    for (j = 1; j < P->N; j++)
-      P->gamma[j] = asin(cos(M_PI / P->n[j]) / cosa);
-    if (errno)
-      Err(strerror(errno));
-  }
-}
-
-/*
- * Postprocess pqr| where r has an even denominator (cf. Coxeter &al. Sec.9).
- * Remove the {2r} and add a retrograde {2p} and retrograde {2q}.
- */
-static int
-exceptions(Polyhedron *P)
-{
-  int j;
-  if (P->even != -1) {
-    P->M = P->N = 4;
-    Realloc(P->n, P->N, double);
-    Realloc(P->m, P->N, double);
-    Realloc(P->gamma, P->N, double);
-    Realloc(P->rot, P->M, int);
-    for (j = P->even + 1; j < 3; j++) {
-      P->n[j-1] = P->n[j];
-      P->gamma[j-1] = P->gamma[j];
-    }
-    P->n[2] = compl(P->n[1]);
-    P->gamma[2] = - P->gamma[1];
-    P->n[3] = compl(P->n[0]);
-    P->m[3] = 1;
-    P->gamma[3] = - P->gamma[0];
-    P->rot[0] = 0;
-    P->rot[1] = 1;
-    P->rot[2] = 3;
-    P->rot[3] = 2;
-  }
-
-  /*
-   * Postprocess the last polyhedron |3/2 5/3 3 5/2 by taking a |5/3 3 5/2,
-   * replacing the three snub triangles by four equatorial squares and adding
-   * the missing {3/2} (retrograde triangle, cf. Coxeter &al. Sec. 11).
-   */
-  if (P->index == last_uniform - 1) {
-    P->N = 5;
-    P->M = 8;
-    Realloc(P->n, P->N, double);
-    Realloc(P->m, P->N, double);
-    Realloc(P->gamma, P->N, double);
-    Realloc(P->rot, P->M, int);
-    Realloc(P->snub, P->M, int);
-    P->hemi = 1;
-    P->D = 0;
-    for (j = 3; j; j--) {
-      P->m[j] = 1;
-      P->n[j] = P->n[j-1];
-      P->gamma[j] = P->gamma[j-1];
-    }
-    P->m[0] = P->n[0] = 4;
-    P->gamma[0] = M_PI / 2;
-    P->m[4] = 1;
-    P->n[4] = compl(P->n[1]);
-    P->gamma[4] = - P->gamma[1];
-    for (j = 1; j < 6; j += 2) P->rot[j]++;
-    P->rot[6] = 0;
-    P->rot[7] = 4;
-    P->snub[6] = 1;
-    P->snub[7] = 0;
-  }
-  return 1;
-}
-
-/*
- * Compute edge and face counts, and update D and chi.  Update D in the few
- * cases the density of the polyhedron is meaningful but different than the
- * density of the corresponding Schwarz triangle (cf. Coxeter &al., p. 418 and
- * p. 425).
- * In these cases, spherical faces of one type are concave (bigger than a
- * hemisphere), and the actual density is the number of these faces less the
- * computed density.  Note that if j != 0, the assignment gamma[j] = asin(...)
- * implies gamma[j] cannot be obtuse.  Also, compute chi for the only
- * non-Wythoffian polyhedron.
- */
-static int
-count(Polyhedron *P)
-{
-  int j, temp;
-  Malloc(P->Fi, P->N, int);
-  for (j = 0; j < P->N; j++) {
-    P->E += temp = P->V * numerator(P->m[j]);
-    P->F += P->Fi[j] = temp / numerator(P->n[j]);
-  }
-  P->E /= 2;
-  if (P->D && P->gamma[0] > M_PI / 2)
-    P->D = P->Fi[0] - P->D;
-  if (P->index == last_uniform - 1)
-    P->chi = P->V - P->E + P->F;
-  return 1;
-}
-
-/*
- * Generate a printable vertex configuration symbol.
- */
-static int
-configuration(Polyhedron *P)
-{
-  int j, len = 2;
-  for (j = 0; j < P->M; j++) {
-    char *s;
-    Sprintfrac(s, P->n[P->rot[j]]);
-    len += strlen (s) + 2;
-    if (!j) {
-      Malloc(P->config, len, char);
-/*      strcpy(P->config, "(");*/
-      strcpy(P->config, "");
-    } else {
-      Realloc(P->config, len, char);
-      strcat(P->config, ", ");
-    }
-    strcat(P->config, s);
-    free(s);
-  }
-/*  strcat (P->config, ")");*/
-  if ((j = denominator (P->m[0])) != 1) {
-    char s[MAXDIGITS + 2];
-    sprintf(s, "/%d", j);
-    Realloc(P->config, len + strlen (s), char);
-    strcat(P->config, s);
-  }
-  return 1;
-}
-
-/*
- * Compute polyhedron vertices and vertex adjecency lists.
- * The vertices adjacent to v[i] are v[adj[0][i], v[adj[1][i], ...
- * v[adj[M-1][i], ordered counterclockwise.  The algorith is a BFS on the
- * vertices, in such a way that the vetices adjacent to a givem vertex are
- * obtained from its BFS parent by a cyclic sequence of rotations. firstrot[i]
- * points to the first  rotaion in the sequence when applied to v[i]. Note that
- * for non-snub polyhedra, the rotations at a child are opposite in sense when
- * compared to the rotations at the parent. Thus, we fill adj[*][i] from the
- * end to signify clockwise rotations. The firstrot[] array is not needed for
- * display thus it is freed after being used for face computations below.
- */
-static int
-vertices(Polyhedron *P)
-{
-  int i, newV = 2;
-  double cosa;
-  Malloc(P->v, P->V, Vector);
-  Matalloc(P->adj, P->M, P->V, int);
-  Malloc(P->firstrot, P->V, int); /* temporary , put in Polyhedron
-                                     structure so that may be freed on
-                                     error */
-  cosa = cos(M_PI / P->n[0]) / sin(P->gamma[0]);
-  P->v[0].x = 0;
-  P->v[0].y = 0;
-  P->v[0].z = 1;
-  P->firstrot[0] = 0;
-  P->adj[0][0] = 1;
-  P->v[1].x = 2 * cosa * sqrt(1 - cosa * cosa);
-  P->v[1].y = 0;
-  P->v[1].z = 2 * cosa * cosa - 1;
-  if (!P->snub) {
-    P->firstrot[1] = 0;
-    P->adj[0][1] = -1;/* start the other side */
-    P->adj[P->M-1][1] = 0;
-  } else {
-    P->firstrot[1] = P->snub[P->M-1] ? 0 : P->M-1 ;
-    P->adj[0][1] = 0;
-  }
-  for (i = 0; i < newV; i++) {
-    int j, k;
-    int last, one, start, limit;
-    if (P->adj[0][i] == -1) {
-      one = -1; start = P->M-2; limit = -1;
-    } else {
-      one = 1; start = 1; limit = P->M;
-    }
-    k = P->firstrot[i];
-    for (j = start; j != limit; j += one) {
-      Vector temp;
-      int J;
-      temp = rotate (P->v[P->adj[j-one][i]], P->v[i],
-                     one * 2 * P->gamma[P->rot[k]]);
-      for (J=0; J<newV && !same(P->v[J],temp,BIG_EPSILON); J++)
-        ;/* noop */
-      P->adj[j][i] = J;
-      last = k;
-      if (++k == P->M)
-        k = 0;
-      if (J == newV) { /* new vertex */
-        if (newV == P->V) Err ("too many vertices");
-        P->v[newV++] = temp;
-        if (!P->snub) {
-          P->firstrot[J] = k;
-          if (one > 0) {
-            P->adj[0][J] = -1;
-            P->adj[P->M-1][J] = i;
-          } else {
-            P->adj[0][J] = i;
-          }
-        } else {
-          P->firstrot[J] = !P->snub[last] ? last :
-            !P->snub[k] ? (k+1)%P->M : k ;
-          P->adj[0][J] = i;
-        }
-      }
-    }
-  }
-  return 1;
-}
-
-/*
- * Compute polyhedron faces (dual vertices) and incidence matrices.
- * For orientable polyhedra, we can distinguish between the two faces meeting
- * at a given directed edge and identify the face on the left and the face on
- * the right, as seen from the outside.  For one-sided polyhedra, the vertex
- * figure is a papillon (in Coxeter &al.  terminology, a crossed parallelogram)
- * and the two faces meeting at an edge can be identified as the side face
- * (n[1] or n[2]) and the diagonal face (n[0] or n[3]).
- */
-static int
-faces(Polyhedron *P)
-{
-  int i, newF = 0;
-  Malloc (P->f, P->F, Vector);
-  Malloc (P->ftype, P->F, int);
-  Matalloc (P->incid, P->M, P->V, int);
-  P->minr = 1 / fabs (tan (M_PI / P->n[P->hemi]) * tan (P->gamma[P->hemi]));
-  for (i = P->M; --i>=0;) {
-    int j;
-    for (j = P->V; --j>=0;)
-      P->incid[i][j] = -1;
-  }
-  for (i = 0; i < P->V; i++) {
-    int j;
-    for (j = 0; j < P->M; j++) {
-      int i0, J;
-      int pap=0;/* papillon edge type */
-      if (P->incid[j][i] != -1)
-        continue;
-      P->incid[j][i] = newF;
-      if (newF == P->F)
-        Err("too many faces");
-      P->f[newF] = pole(P->minr, P->v[i], P->v[P->adj[j][i]],
-                        P->v[P->adj[mod(j + 1, P->M)][i]]);
-      P->ftype[newF] = P->rot[mod(P->firstrot[i] + ((P->adj[0][i] <
-                                                     P->adj[P->M - 1][i])
-                                                    ?  j
-                                                    : -j - 2),
-                                  P->M)];
-      if (P->onesided)
-        pap = (P->firstrot[i] + j) % 2;
-      i0 = i;
-      J = j;
-      for (;;) {
-        int k;
-        k = i0;
-        if ((i0 = P->adj[J][k]) == i) break;
-        for (J = 0; J < P->M && P->adj[J][i0] != k; J++)
-          ;/* noop */
-        if (J == P->M)
-          Err("too many faces");
-        if (P->onesided && (J + P->firstrot[i0]) % 2 == pap) {
-          P->incid [J][i0] = newF;
-          if (++J >= P->M)
-            J = 0;
-        } else {
-          if (--J < 0)
-            J = P->M - 1;
-          P->incid [J][i0] = newF;
-        }
-      }
-      newF++;
-    }
-  }
-  Free(P->firstrot);
-  Free(P->rot);
-  Free(P->snub);
-  return 1;
-}
-
-/*
- * Compute edge list and graph polyhedron and dual.
- * If the polyhedron is of the "hemi" type, each edge has one finite vertex and
- * one ideal vertex. We make sure the latter is always the out-vertex, so that
- * the edge becomes a ray (half-line).  Each ideal vertex is represented by a
- * unit Vector, and the direction of the ray is either parallel or
- * anti-parallel this Vector. We flag this in the array P->anti[E].
- */
-static int
-edgelist(Polyhedron *P)
-{
-  int i, j, *s, *t, *u;
-  Matalloc(P->e, 2, P->E, int);
-  Matalloc(P->dual_e, 2, P->E, int);
-  s = P->e[0];
-  t = P->e[1];
-  for (i = 0; i < P->V; i++)
-    for (j = 0; j < P->M; j++)
-      if (i < P->adj[j][i]) {
-        *s++ = i;
-        *t++ = P->adj[j][i];
-      }
-  s = P->dual_e[0];
-  t = P->dual_e[1];
-  if (!P->hemi)
-    P->anti = 0;
-  else
-    Malloc(P->anti, P->E, int);
-  u = P->anti;
-  for (i = 0; i < P->V; i++)
-    for (j = 0; j < P->M; j++)
-      if (i < P->adj[j][i])
-        {
-          if (!u) {
-            *s++ = P->incid[mod(j-1,P->M)][i];
-            *t++ = P->incid[j][i];
-          } else {
-            if (P->ftype[P->incid[j][i]]) {
-              *s = P->incid[j][i];
-              *t = P->incid[mod(j-1,P->M)][i];
-            } else {
-              *s = P->incid[mod(j-1,P->M)][i];
-              *t = P->incid[j][i];
-            }
-            *u++ = dot(P->f[*s++], P->f[*t++]) > 0;
-          }
-        }
-  return 1;
-}
-
-
-static char *
-sprintfrac(double x)
-{
-  char *s;
-  frac (x);
-  if (!frax.d) {
-    Malloc(s, sizeof ("infinity"), char);
-    strcpy(s, "infinity");
-  } else if (frax.d == 1) {
-    char n[MAXDIGITS + 1];
-    sprintf(n, "%ld", frax.n);
-    Malloc(s, strlen (n) +  1, char);
-    strcpy(s, n);
-  } else {
-    char n[MAXDIGITS + 1], d[MAXDIGITS + 1];
-    sprintf(n, "%ld", frax.n);
-    sprintf(d, "%ld", frax.d);
-    Malloc(s, strlen (n) + strlen (d) + 2, char);
-    sprintf(s, "%s/%s", n, d);
-  }
-  return s;
-}
-
-static double
-dot(Vector a, Vector b)
-{
-  return a.x * b.x + a.y * b.y + a.z * b.z;
-}
-
-static Vector
-scale(double k, Vector a)
-{
-  a.x *= k;
-  a.y *= k;
-  a.z *= k;
-  return a;
-}
-
-static Vector
-diff(Vector a, Vector b)
-{
-  a.x -= b.x;
-  a.y -= b.y;
-  a.z -= b.z;
-  return a;
-}
-
-static Vector
-cross(Vector a, Vector b)
-{
-  Vector p;
-  p.x = a.y * b.z - a.z * b.y;
-  p.y = a.z * b.x - a.x * b.z;
-  p.z = a.x * b.y - a.y * b.x;
-  return p;
-}
-
-static Vector
-sum(Vector a, Vector b)
-{
-  a.x += b.x;
-  a.y += b.y;
-  a.z += b.z;
-  return a;
-}
-
-static Vector
-sum3(Vector a, Vector b, Vector c)
-{
-  a.x += b.x + c.x;
-  a.y += b.y + c.y;
-  a.z += b.z + c.z;
-  return a;
-}
-
-static Vector
-rotate(Vector vertex, Vector axis, double angle)
-{
-  Vector p;
-  p = scale(dot (axis, vertex), axis);
-  return sum3(p, scale(cos(angle), diff(vertex, p)),
-              scale(sin(angle), cross(axis, vertex)));
-}
-
-static Vector x, y, z;
-
-/*
- * rotate the standard frame
- */
-static void
-rotframe(double azimuth, double elevation, double angle)
-{
-  static const Vector X = {1,0,0}, Y = {0,1,0}, Z = {0,0,1};
-  Vector axis;
-
-  axis = rotate(rotate (X, Y, elevation), Z, azimuth);
-  x = rotate(X, axis, angle);
-  y = rotate(Y, axis, angle);
-  z = rotate(Z, axis, angle);
-}
-
-/*
- * rotate an array of n Vectors
- */
-static void
-rotarray(Vector *new, Vector *old, int n)
-{
-  while (n--) {
-    *new++ = sum3(scale(old->x, x), scale(old->y, y), scale(old->z, z));
-    old++;
-  }
-}
-
-static int
-same(Vector a, Vector b, double epsilon)
-{
-  return fabs(a.x - b.x) < epsilon && fabs(a.y - b.y) < epsilon
-    && fabs(a.z - b.z) < epsilon;
-}
-
-/*
- * Compute the polar reciprocal of the plane containing a, b and c:
- *
- * If this plane does not contain the origin, return p such that
- *	dot(p,a) = dot(p,b) = dot(p,b) = r.
- *
- * Otherwise, return p such that
- *	dot(p,a) = dot(p,b) = dot(p,c) = 0
- * and
- *	dot(p,p) = 1.
- */
-static Vector
-pole(double r, Vector a, Vector b, Vector c)
-{
-  Vector p;
-  double k;
-  p = cross(diff(b, a), diff(c, a));
-  k = dot(p, a);
-  if (fabs(k) < 1e-6)
-    return scale(1 / sqrt(dot(p, p)), p);
-  else
-    return scale(r/ k , p);
-}
-
-
-/* output */
-
-
-
-
-static void rotframe(double azimuth, double elevation, double angle);
-static void rotarray(Vector *new, Vector *old, int n);
-static int mod (int i, int j);
-
-
-static void
-push_point (polyhedron *p, Vector v)
-{
-  p->points[p->npoints].x = v.x;
-  p->points[p->npoints].y = v.y;
-  p->points[p->npoints].z = v.z;
-  p->npoints++;
-}
-
-static void
-push_face3 (polyhedron *p, int x, int y, int z)
-{
-  p->faces[p->nfaces].npoints = 3;
-  Malloc (p->faces[p->nfaces].points, 3, int);
-  p->faces[p->nfaces].points[0] = x;
-  p->faces[p->nfaces].points[1] = y;
-  p->faces[p->nfaces].points[2] = z;
-  p->nfaces++;
-}
-
-static void
-push_face4 (polyhedron *p, int x, int y, int z, int w)
-{
-  p->faces[p->nfaces].npoints = 4;
-  Malloc (p->faces[p->nfaces].points, 4, int);
-  p->faces[p->nfaces].points[0] = x;
-  p->faces[p->nfaces].points[1] = y;
-  p->faces[p->nfaces].points[2] = z;
-  p->faces[p->nfaces].points[3] = w;
-  p->nfaces++;
-}
-
-
-
-
-static polyhedron *
-construct_polyhedron (Polyhedron *P, Vector *v, int V, Vector *f, int F,
-                      const char *name, const char *dual,
-                      const char *class, const char *star,
-                      double azimuth, double elevation, double freeze)
-{
-  int i, j, k=0, l, ll, ii, *hit=0, facelets;
-
-  polyhedron *result;
-  Vector *temp;
-
-  Malloc (result, 1, polyhedron);
-  memset (result, 0, sizeof(*result));
-
-  /*
-   * Rotate polyhedron
-   */
-  rotframe(azimuth, elevation, freeze);
-  Malloc(temp, V, Vector);
-  rotarray(temp, v, V);
-  v = temp;
-  Malloc(temp, F, Vector);
-  rotarray(temp, f, F);
-  f = temp;
-
-  result->number = P->index + 1;
-  result->name = strdup (name);
-  result->dual = strdup (dual);
-  result->wythoff = strdup (P->polyform);
-  result->config = strdup (P->config);
-  result->group = strdup (P->group);
-  result->class = strdup (class);
-
-  /*
-   * Vertex list
-   */
-  Malloc (result->points, V + F * 13, point);
-  result->npoints = 0;
-
-  result->nedges = P->E;
-  result->logical_faces = F;
-  result->logical_vertices = V;
-  result->density = P->D;
-  result->chi = P->chi;
-
-  for (i = 0; i < V; i++)
-    push_point (result, v[i]);
-
-  /*
-   * Auxiliary vertices (needed because current VRML browsers cannot handle
-   * non-simple polygons, i.e., ploygons with self intersections): Each
-   * non-simple face is assigned an auxiliary vertex. By connecting it to the
-   * rest of the vertices the face is triangulated. The circum-center is used
-   * for the regular star faces of uniform polyhedra. The in-center is used for
-   * the pentagram (#79) and hexagram (#77) of the high-density snub duals, and
-   * for the pentagrams (#40, #58) and hexagram (#52) of the stellated duals
-   * with configuration (....)/2. Finally, the self-intersection of the crossed
-   * parallelogram is used for duals with form p q r| with an even denominator.
-   *
-   * This method do not work for the hemi-duals, whose faces are not
-   * star-shaped and have two self-intersections each.
-   *
-   * Thus, for each face we need six auxiliary vertices: The self intersections
-   * and the terminal points of the truncations of the infinite edges. The
-   * ideal vertices are listed, but are not used by the face-list.
-   *
-   * Note that the face of the last dual (#80) is octagonal, and constists of
-   * two quadrilaterals of the infinite type.
-   */
-
-  if (*star && P->even != -1)
-    Malloc(hit, F, int);
-  for (i = 0; i < F; i++)
-    if ((!*star &&
-         (frac(P->n[P->ftype[i]]), frax.d != 1 && frax.d != frax.n - 1)) ||
-        (*star &&
-         P->K == 5 &&
-         (P->D > 30 ||
-          denominator (P->m[0]) != 1))) {
-      /* find the center of the face */
-      double h;
-      if (!*star && P->hemi && !P->ftype[i])
-        h = 0;
-      else
-        h = P->minr / dot(f[i],f[i]);
-      push_point(result, scale (h, f[i]));
-
-    } else if (*star && P->even != -1) {
-      /* find the self-intersection of a crossed parallelogram.
-       * hit is set if v0v1 intersects v2v3*/
-      Vector v0, v1, v2, v3, c0, c1, p;
-      double d0, d1;
-      v0 = v[P->incid[0][i]];
-      v1 = v[P->incid[1][i]];
-      v2 = v[P->incid[2][i]];
-      v3 = v[P->incid[3][i]];
-      d0 = sqrt(dot(diff(v0, v2), diff(v0, v2)));
-      d1 = sqrt(dot (diff(v1, v3), diff(v1, v3)));
-      c0 = scale(d1, sum(v0, v2));
-      c1 = scale(d0, sum(v1, v3));
-      p = scale(0.5 / (d0 + d1), sum(c0, c1));
-      push_point (result, p);
-      p = cross(diff(p, v2), diff(p, v3));
-      hit[i] = (dot(p, p) < 1e-6);
-    } else if (*star && P->hemi && P->index != last_uniform - 1) {
-      /* find the terminal points of the truncation and the
-       * self-intersections.
-       *  v23       v0       v21
-       *  |  \     /  \     /  |
-       *  |   v0123    v0321   |
-       *  |  /     \  /     \  |
-       *  v01       v2       v03
-       */
-      Vector v0, v1, v2, v3, v01, v03, v21, v23, v0123, v0321 ;
-      Vector u;
-      double t = 1.5;/* truncation adjustment factor */
-      j = !P->ftype[P->incid[0][i]];
-      v0 = v[P->incid[j][i]];/* real vertex */
-      v1 = v[P->incid[j+1][i]];/* ideal vertex (unit vector) */
-      v2 = v[P->incid[j+2][i]];/* real */
-      v3 = v[P->incid[(j+3)%4][i]];/* ideal */
-      /* compute intersections
-       * this uses the following linear algebra:
-       * v0123 = v0 + a v1 = v2 + b v3
-       * v0 x v3 + a (v1 x v3) = v2 x v3
-       * a (v1 x v3) = (v2 - v0) x v3
-       * a (v1 x v3) . (v1 x v3) = (v2 - v0) x v3 . (v1 x v3)
-       */
-      u = cross(v1, v3);
-      v0123 = sum(v0, scale(dot(cross(diff(v2, v0), v3), u) / dot(u,u),
-                            v1));
-      v0321 = sum(v0, scale(dot(cross(diff(v0, v2), v1), u) / dot(u,u),
-                            v3));
-      /* compute truncations */
-      v01 = sum(v0 , scale(t, diff(v0123, v0)));
-      v23 = sum(v2 , scale(t, diff(v0123, v2)));
-      v03 = sum(v0 , scale(t, diff(v0321, v0)));
-      v21 = sum(v2 , scale(t, diff(v0321, v2)));
-
-      push_point(result, v01);
-      push_point(result, v23);
-      push_point(result, v0123);
-      push_point(result, v03);
-      push_point(result, v21);
-      push_point(result, v0321);
-
-    } else if (*star && P->index == last_uniform - 1) {
-      /* find the terminal points of the truncation and the
-       * self-intersections.
-       *  v23       v0       v21
-       *  |  \     /  \     /  |
-       *  |   v0123    v0721   |
-       *  |  /     \  /     \  |
-       *  v01       v2       v07
-       *
-       *  v65       v4       v67
-       *  |  \     /  \     /  |
-       *  |   v4365    v4567   |
-       *  |  /     \  /     \  |
-       *  v43       v6       v45
-       */
-      Vector v0, v1, v2, v3, v4, v5, v6, v7, v01, v07, v21, v23;
-      Vector v43, v45, v65, v67, v0123, v0721, v4365, v4567;
-      double t = 1.5;/* truncation adjustment factor */
-      Vector u;
-      for (j = 0; j < 8; j++)
-        if (P->ftype[P->incid[j][i]] == 3)
-          break;
-      v0 = v[P->incid[j][i]];/* real {5/3} */
-      v1 = v[P->incid[(j+1)%8][i]];/* ideal */
-      v2 = v[P->incid[(j+2)%8][i]];/* real {3} */
-      v3 = v[P->incid[(j+3)%8][i]];/* ideal */
-      v4 = v[P->incid[(j+4)%8][i]];/* real {5/2} */
-      v5 = v[P->incid[(j+5)%8][i]];/* ideal */
-      v6 = v[P->incid[(j+6)%8][i]];/* real {3/2} */
-      v7 = v[P->incid[(j+7)%8][i]];/* ideal */
-      /* compute intersections */
-      u = cross(v1, v3);
-      v0123 = sum(v0, scale(dot(cross(diff(v2, v0), v3), u) / dot(u,u),
-                            v1));
-      u = cross(v7, v1);
-      v0721 = sum(v0, scale(dot(cross(diff(v2, v0), v1), u) / dot(u,u),
-                            v7));
-      u = cross(v5, v7);
-      v4567 = sum(v4, scale(dot(cross(diff(v6, v4), v7), u) / dot(u,u),
-                            v5));
-      u = cross(v3, v5);
-      v4365 = sum(v4, scale(dot(cross(diff(v6, v4), v5), u) / dot(u,u),
-                            v3));
-      /* compute truncations */
-      v01 = sum(v0 , scale(t, diff(v0123, v0)));
-      v23 = sum(v2 , scale(t, diff(v0123, v2)));
-      v07 = sum(v0 , scale(t, diff(v0721, v0)));
-      v21 = sum(v2 , scale(t, diff(v0721, v2)));
-      v45 = sum(v4 , scale(t, diff(v4567, v4)));
-      v67 = sum(v6 , scale(t, diff(v4567, v6)));
-      v43 = sum(v4 , scale(t, diff(v4365, v4)));
-      v65 = sum(v6 , scale(t, diff(v4365, v6)));
-
-      push_point(result, v01);
-      push_point(result, v23);
-      push_point(result, v0123);
-      push_point(result, v07);
-      push_point(result, v21);
-      push_point(result, v0721);
-      push_point(result, v45);
-      push_point(result, v67);
-      push_point(result, v4567);
-      push_point(result, v43);
-      push_point(result, v65);
-      push_point(result, v4365);
-    }
-
-  /*
-   * Face list:
-   * Each face is printed in a separate line, by listing the indices of its
-   * vertices. In the non-simple case, the polygon is represented by the
-   * triangulation, each triangle consists of two polyhedron vertices and one
-   * auxiliary vertex.
-   */
-  Malloc (result->faces, F * 10, face);
-  result->nfaces = 0;
-
-  ii = V;
-  facelets = 0;
-  for (i = 0; i < F; i++) {
-    if (*star) {
-      if (P->K == 5 &&
-          (P->D > 30 ||
-           denominator (P->m[0]) != 1)) {
-        for (j = 0; j < P->M - 1; j++) {
-          push_face3 (result, P->incid[j][i], P->incid[j+1][i],  ii);
-          facelets++;
-        }
-
-        push_face3 (result, P->incid[j][i], P->incid[0][i],  ii++);
-        facelets++;
-
-      } else if (P->even != -1) {
-        if (hit && hit[i]) {
-          push_face3 (result, P->incid[3][i], P->incid[0][i],  ii);
-          push_face3 (result, P->incid[1][i], P->incid[2][i],  ii);
-        } else {
-          push_face3 (result, P->incid[0][i], P->incid[1][i],  ii);
-          push_face3 (result, P->incid[2][i], P->incid[3][i],  ii);
-        }
-        ii++;
-        facelets += 2;
-
-      } else if (P->hemi && P->index != last_uniform - 1) {
-        j = !P->ftype[P->incid[0][i]];
-
-        push_face3 (result, ii, ii + 1, ii + 2);
-        push_face4 (result, P->incid[j][i], ii + 2, P->incid[j+2][i], ii + 5);
-        push_face3 (result, ii + 3, ii + 4, ii + 5);
-        ii += 6;
-        facelets += 3;
-      } else if (P->index == last_uniform - 1) {
-        for (j = 0; j < 8; j++)
-          if (P->ftype[P->incid[j][i]] == 3)
-            break;
-        push_face3 (result, ii, ii + 1, ii + 2);
-        push_face4 (result,
-                    P->incid[j][i], ii + 2, P->incid[(j+2)%8][i], ii + 5);
-        push_face3 (result, ii + 3, ii + 4, ii + 5);
-
-        push_face3 (result, ii + 6, ii + 7, ii + 8);
-        push_face4 (result,
-                    P->incid[(j+4)%8][i], ii + 8, P->incid[(j+6)%8][i],
-                    ii + 11);
-        push_face3 (result, ii + 9, ii + 10, ii + 11);
-        ii += 12;
-        facelets += 6;
-      } else {
-
-        result->faces[result->nfaces].npoints = P->M;
-        Malloc (result->faces[result->nfaces].points, P->M, int);
-        for (j = 0; j < P->M; j++)
-          result->faces[result->nfaces].points[j] = P->incid[j][i];
-        result->nfaces++;
-        facelets++;
-      }
-    } else {
-      int split = (frac(P->n[P->ftype[i]]),
-                   frax.d != 1 && frax.d != frax.n - 1);
-      for (j = 0; j < V; j++) {
-        for (k = 0; k < P->M; k++)
-          if (P->incid[k][j] == i)
-            break;
-        if (k != P->M)
-          break;
-      }
-      if (split) {
-        ll = j;
-        for (l = P->adj[k][j]; l != j; l = P->adj[k][l]) {
-          for (k = 0; k < P->M; k++)
-            if (P->incid[k][l] == i)
-              break;
-          if (P->adj[k][l] == ll)
-            k = mod(k + 1 , P->M);
-          push_face3 (result, ll, l, ii);
-          facelets++;
-          ll = l;
-        }
-        push_face3 (result, ll, j, ii++);
-        facelets++;
-
-      } else {
-
-        int *pp;
-        int pi = 0;
-        Malloc (pp, 100, int);
-
-        pp[pi++] = j;
-        ll = j;
-        for (l = P->adj[k][j]; l != j; l = P->adj[k][l]) {
-          for (k = 0; k < P->M; k++)
-            if (P->incid[k][l] == i)
-              break;
-          if (P->adj[k][l] == ll)
-            k = mod(k + 1 , P->M);
-          pp[pi++] = l;
-          ll = l;
-        }
-        result->faces[result->nfaces].npoints = pi;
-        result->faces[result->nfaces].points = pp;
-        result->nfaces++;
-        facelets++;
-      }
-    }
-  }
-
-  /*
-   * Face color indices - for polyhedra with multiple face types
-   * For non-simple faces, the index is repeated as many times as needed by the
-   * triangulation.
-   */
-  {
-    int ff = 0;
-    if (!*star && P->N != 1) {
-      for (i = 0; i < F; i++)
-        if (frac(P->n[P->ftype[i]]), frax.d == 1 || frax.d == frax.n - 1)
-          result->faces[ff++].color = P->ftype[i];
-        else
-          for (j = 0; j < frax.n; j++)
-            result->faces[ff++].color = P->ftype[i];
-    } else {
-      for (i = 0; i < facelets; i++)
-        result->faces[ff++].color = 0;
-    }
-  }
-
-  if (*star && P->even != -1)
-    free(hit);
-  free(v);
-  free(f);
-
-  return result;
-}
-
-
-
-/* External interface (jwz)
- */
-
-void
-free_polyhedron (polyhedron *p)
-{
-  if (!p) return;
-  Free (p->wythoff);
-  Free (p->name);
-  Free (p->group);
-  Free (p->class);
-  Free (p->points);
-  if (p->faces)
-    {
-      int i;
-      for (i = 0; i < p->nfaces; i++)
-        Free (p->faces[i].points);
-      Free (p->faces);
-    }
-  Free (p);
-}
-
-
-int
-construct_polyhedra (polyhedron ***polyhedra_ret)
-{
-  double freeze = 0;
-  double azimuth = AZ;
-  double elevation = EL;
-  int index = 0;
-
-  int count = 0;
-  polyhedron **result;
-  Malloc (result, last_uniform * 2 + 3, polyhedron*);
-
-  while (index < last_uniform) {
-    char sym[4];
-    Polyhedron *P;
-
-    sprintf(sym, "#%d", index + 1);
-    if (!(P = kaleido(sym, 1, 0, 0, 0))) {
-      Err (strerror(errno));
-    }
-
-    result[count++] = construct_polyhedron (P, P->v, P->V, P->f, P->F,
-                                            P->name, P->dual_name,
-                                            P->class, "",
-                                            azimuth, elevation, freeze);
-
-    result[count++] = construct_polyhedron (P, P->f, P->F, P->v, P->V,
-                                            P->dual_name, P->name,
-                                            P->dual_class, "*",
-                                            azimuth, elevation, freeze);
-    polyfree(P);
-    index++;
-  }
-
-  *polyhedra_ret = result;
-  count++; /* leave room for teapot */
-  return count;
-}