1 /* polytopes --- Shows one of the six regular polytopes rotating in 4d */
4 static const char sccsid[] = "@(#)polytopes.c 1.2 05/09/28 xlockmore";
7 /* Copyright (c) 2003-2009 Carsten Steger <carsten@mirsanmir.org>. */
10 * Permission to use, copy, modify, and distribute this software and its
11 * documentation for any purpose and without fee is hereby granted,
12 * provided that the above copyright notice appear in all copies and that
13 * both that copyright notice and this permission notice appear in
14 * supporting documentation.
16 * This file is provided AS IS with no warranties of any kind. The author
17 * shall have no liability with respect to the infringement of copyrights,
18 * trade secrets or any patents by this file or any part thereof. In no
19 * event will the author be liable for any lost revenue or profits or
20 * other special, indirect and consequential damages.
23 * C. Steger - 03/08/10: Initial version
24 * C. Steger - 05/09/28: Added trackball support
25 * C. Steger - 07/01/23: Improved 4d trackball support
26 * C. Steger - 09/08/23: Removed check-config.pl warnings
30 * This program shows one of the six regular 4D polytopes rotating in 4D.
31 * Written by Carsten Steger, inspired by H.S.M Coxeter's book "Regular
32 * Polytopes", 3rd Edition, Dover Publications, Inc., 1973, and Thomas
33 * Banchoff's book "Beyond the Third Dimension: Geometry, Computer
34 * Graphics, and Higher Dimensions", Scientific American Library, 1990.
38 #define M_PI 3.14159265358979323846
41 #define SQRT15OVER4 1.93649167310370844259 /* sqrt(15/4) */
42 #define SQRT10OVER3 1.82574185835055371152 /* sqrt(10/3) */
43 #define SQRT5OVER2 1.58113883008418966600 /* sqrt(5/2) */
44 #define SQRT5OVER6 0.91287092917527685576 /* sqrt(5/6) */
45 #define SQRT5OVER12 0.64549722436790281420 /* sqrt(5/12) */
46 #define SQRT2 1.41421356237309504880 /* sqrt(2) */
47 #define GOLDEN 1.61803398874989484820 /* (sqrt(5)+1)/2 */
48 #define GOLDENINV 0.61803398874989484820 /* (sqrt(5)-1)/2 */
49 #define SQRT2INV 0.70710678118654752440 /* sqrt(1/2) */
50 #define GOLDEN2 1.14412280563536859520 /* ((sqrt(5)+1)/2)/sqrt(2) */
51 #define GOLDENINV2 0.43701602444882107080 /* ((sqrt(5)-1)/2)/sqrt(2) */
52 #define GOLDEN22 1.85122958682191611960 /* (((sqrt(5)+1)/2)^2)/sqrt(2) */
53 #define GOLDENINV22 0.27009075673772645360 /* (((sqrt(5)-1)/2)^2)/sqrt(2) */
55 #define DISP_WIREFRAME 0
56 #define DISP_SURFACE 1
57 #define DISP_TRANSPARENT 2
59 #define POLYTOPE_RANDOM -1
60 #define POLYTOPE_5_CELL 0
61 #define POLYTOPE_8_CELL 1
62 #define POLYTOPE_16_CELL 2
63 #define POLYTOPE_24_CELL 3
64 #define POLYTOPE_120_CELL 4
65 #define POLYTOPE_600_CELL 5
66 #define POLYTOPE_LAST_CELL POLYTOPE_600_CELL
68 #define COLORS_SINGLE 0
69 #define COLORS_DEPTH 1
71 #define DISP_3D_PERSPECTIVE 0
72 #define DISP_3D_ORTHOGRAPHIC 1
74 #define DISP_4D_PERSPECTIVE 0
75 #define DISP_4D_PERSPECTIVE_STR "0"
76 #define DISP_4D_ORTHOGRAPHIC 1
77 #define DISP_4D_ORTHOGRAPHIC_STR "1"
79 #define DEF_DISPLAY_MODE "transparent"
80 #define DEF_POLYTOPE "random"
81 #define DEF_COLORS "depth"
82 #define DEF_PROJECTION_3D "perspective"
83 #define DEF_PROJECTION_4D "perspective"
84 #define DEF_SPEEDWX "1.1"
85 #define DEF_SPEEDWY "1.3"
86 #define DEF_SPEEDWZ "1.5"
87 #define DEF_SPEEDXY "1.7"
88 #define DEF_SPEEDXZ "1.9"
89 #define DEF_SPEEDYZ "2.1"
92 # define DEFAULTS "*delay: 25000 \n" \
93 "*showFPS: False \n" \
94 "*suppressRotationAnimation: True\n" \
96 # define refresh_polytopes 0
97 # include "xlockmore.h" /* from the xscreensaver distribution */
98 #else /* !STANDALONE */
99 # include "xlock.h" /* from the xlockmore distribution */
100 #endif /* !STANDALONE */
105 # include <X11/keysym.h>
107 #include "gltrackball.h"
111 ModStruct polytopes_description =
112 {"polytopes", "init_polytopes", "draw_polytopes", "release_polytopes",
113 "draw_polytopes", "change_polytopes", NULL, &polytopes_opts,
114 25000, 1, 1, 1, 1.0, 4, "",
115 "Shows one of the six regular 4d polytopes rotating in 4d", 0, NULL};
121 static int display_mode;
122 static char *poly_str;
124 static char *color_str;
125 static int color_mode;
126 static char *proj_3d;
127 static int projection_3d;
128 static char *proj_4d;
129 static int projection_4d;
130 static float speed_wx;
131 static float speed_wy;
132 static float speed_wz;
133 static float speed_xy;
134 static float speed_xz;
135 static float speed_yz;
137 static const float offset4d[4] = { 0.0, 0.0, 0.0, 3.0 };
138 static const float offset3d[4] = { 0.0, 0.0, -2.0, 0.0 };
141 static XrmOptionDescRec opts[] =
143 {"-mode", ".displayMode", XrmoptionSepArg, 0 },
144 {"-wireframe", ".displayMode", XrmoptionNoArg, "wireframe" },
145 {"-surface", ".displayMode", XrmoptionNoArg, "surface" },
146 {"-transparent", ".displayMode", XrmoptionNoArg, "transparent" },
147 {"-polytope", ".polytope", XrmoptionSepArg, 0 },
148 {"-random", ".polytope", XrmoptionNoArg, "random" },
149 {"-5-cell", ".polytope", XrmoptionNoArg, "5-cell" },
150 {"-8-cell", ".polytope", XrmoptionNoArg, "8-cell" },
151 {"-16-cell", ".polytope", XrmoptionNoArg, "16-cell" },
152 {"-24-cell", ".polytope", XrmoptionNoArg, "24-cell" },
153 {"-120-cell", ".polytope", XrmoptionNoArg, "120-cell" },
154 {"-600-cell", ".polytope", XrmoptionNoArg, "600-cell" },
155 {"-single-color", ".colors", XrmoptionNoArg, "single" },
156 {"-depth-colors", ".colors", XrmoptionNoArg, "depth" },
157 {"-perspective-3d", ".projection3d", XrmoptionNoArg, "perspective" },
158 {"-orthographic-3d", ".projection3d", XrmoptionNoArg, "orthographic" },
159 {"-perspective-4d", ".projection4d", XrmoptionNoArg, "perspective" },
160 {"-orthographic-4d", ".projection4d", XrmoptionNoArg, "orthographic" },
161 {"-speed-wx", ".speedwx", XrmoptionSepArg, 0 },
162 {"-speed-wy", ".speedwy", XrmoptionSepArg, 0 },
163 {"-speed-wz", ".speedwz", XrmoptionSepArg, 0 },
164 {"-speed-xy", ".speedxy", XrmoptionSepArg, 0 },
165 {"-speed-xz", ".speedxz", XrmoptionSepArg, 0 },
166 {"-speed-yz", ".speedyz", XrmoptionSepArg, 0 }
169 static argtype vars[] =
171 { &mode, "displayMode", "DisplayMode", DEF_DISPLAY_MODE, t_String },
172 { &poly_str, "polytope", "Polytope", DEF_POLYTOPE, t_String },
173 { &color_str, "colors", "Colors", DEF_COLORS, t_String },
174 { &proj_3d, "projection3d", "Projection3d",DEF_PROJECTION_3D, t_String },
175 { &proj_4d, "projection4d", "Projection4d",DEF_PROJECTION_4D, t_String },
176 { &speed_wx, "speedwx", "Speedwx", DEF_SPEEDWX, t_Float},
177 { &speed_wy, "speedwy", "Speedwy", DEF_SPEEDWY, t_Float},
178 { &speed_wz, "speedwz", "Speedwz", DEF_SPEEDWZ, t_Float},
179 { &speed_xy, "speedxy", "Speedxy", DEF_SPEEDXY, t_Float},
180 { &speed_xz, "speedxz", "Speedxz", DEF_SPEEDXZ, t_Float},
181 { &speed_yz, "speedyz", "Speedyz", DEF_SPEEDYZ, t_Float}
184 static OptionStruct desc[] =
186 { "-wireframe", "display the polytope as a wireframe mesh" },
187 { "-surface", "display the polytope as a solid surface" },
188 { "-transparent", "display the polytope as a transparent surface" },
189 { "-solid", "display the polytope as a solid object" },
190 { "-bands", "display the polytope as see-through bands" },
191 { "-twosided", "display the polytope with two colors" },
192 { "-colorwheel", "display the polytope with a smooth color wheel" },
193 { "-perspective-3d", "project the polytope perspectively from 3d to 2d" },
194 { "-orthographic-3d", "project the polytope orthographically from 3d to 2d"},
195 { "-perspective-4d", "project the polytope perspectively from 4d to 3d" },
196 { "-orthographic-4d", "project the polytope orthographically from 4d to 3d"},
197 { "-speed-wx <arg>", "rotation speed around the wx plane" },
198 { "-speed-wy <arg>", "rotation speed around the wy plane" },
199 { "-speed-wz <arg>", "rotation speed around the wz plane" },
200 { "-speed-xy <arg>", "rotation speed around the xy plane" },
201 { "-speed-xz <arg>", "rotation speed around the xz plane" },
202 { "-speed-yz <arg>", "rotation speed around the yz plane" }
205 ENTRYPOINT ModeSpecOpt polytopes_opts =
206 {sizeof opts / sizeof opts[0], opts, sizeof vars / sizeof vars[0], vars, desc};
211 #define NUM_EDGE_5 10
212 #define NUM_FACE_5 10
213 #define VERT_PER_FACE_5 3
215 #define MIN_EDGE_DEPTH_5 (-0.5)
216 #define MAX_EDGE_DEPTH_5 0.75
217 #define MIN_FACE_DEPTH_5 (-0.5)
218 #define MAX_FACE_DEPTH_5 (1.0/3.0)
222 #define NUM_VERT_8 16
223 #define NUM_EDGE_8 32
224 #define NUM_FACE_8 24
225 #define VERT_PER_FACE_8 4
227 #define MIN_EDGE_DEPTH_8 (-1.0)
228 #define MAX_EDGE_DEPTH_8 1.0
229 #define MIN_FACE_DEPTH_8 (-1.0)
230 #define MAX_FACE_DEPTH_8 1.0
232 /* 16-cell {3,3,4} */
233 #define NUM_VERT_16 8
234 #define NUM_EDGE_16 24
235 #define NUM_FACE_16 32
236 #define VERT_PER_FACE_16 3
238 #define MIN_EDGE_DEPTH_16 (-1.0)
239 #define MAX_EDGE_DEPTH_16 1.0
240 #define MIN_FACE_DEPTH_16 (-2.0/3.0)
241 #define MAX_FACE_DEPTH_16 (2.0/3.0)
244 /* 24-cell {3,4,3} */
245 #define NUM_VERT_24 24
246 #define NUM_EDGE_24 96
247 #define NUM_FACE_24 96
248 #define VERT_PER_FACE_24 3
250 #define MIN_EDGE_DEPTH_24 (-SQRT2)
251 #define MAX_EDGE_DEPTH_24 SQRT2
252 #define MIN_FACE_DEPTH_24 (-SQRT2)
253 #define MAX_FACE_DEPTH_24 SQRT2
256 /* 120-cell {5,3,3} */
257 #define NUM_VERT_120 600
258 #define NUM_EDGE_120 1200
259 #define NUM_FACE_120 720
260 #define VERT_PER_FACE_120 5
262 #define MIN_EDGE_DEPTH_120 (-GOLDEN22)
263 #define MAX_EDGE_DEPTH_120 GOLDEN22
264 #define MIN_FACE_DEPTH_120 (-GOLDEN22)
265 #define MAX_FACE_DEPTH_120 GOLDEN22
268 /* 600-cell {3,3,5} */
269 #define NUM_VERT_600 120
270 #define NUM_EDGE_600 720
271 #define NUM_FACE_600 1200
272 #define VERT_PER_FACE_600 3
274 #define MIN_EDGE_DEPTH_600 (-GOLDEN/2.0-1)
275 #define MAX_EDGE_DEPTH_600 (GOLDEN/2.0+1)
276 #define MIN_FACE_DEPTH_600 ((-2*GOLDEN-2)/3.0)
277 #define MAX_FACE_DEPTH_600 ((2*GOLDEN+2)/3.0)
282 GLXContext *glx_context;
283 /* 4D rotation angles */
284 float alpha, beta, delta, zeta, eta, theta;
285 /* Aspect ratio of the current window */
289 /* Trackball states */
290 trackball_state *trackballs[2];
291 int current_trackball;
294 float edge_color_5[NUM_EDGE_5][4];
295 float face_color_5[NUM_FACE_5][4];
296 float face_color_trans_5[NUM_FACE_5][4];
298 float edge_color_8[NUM_EDGE_8][4];
299 float face_color_8[NUM_FACE_8][4];
300 float face_color_trans_8[NUM_FACE_8][4];
302 float edge_color_16[NUM_EDGE_16][4];
303 float face_color_16[NUM_FACE_16][4];
304 float face_color_trans_16[NUM_FACE_16][4];
306 float edge_color_24[NUM_EDGE_24][4];
307 float face_color_24[NUM_FACE_24][4];
308 float face_color_trans_24[NUM_FACE_24][4];
310 float edge_color_120[NUM_EDGE_120][4];
311 float face_color_120[NUM_FACE_120][4];
312 float face_color_trans_120[NUM_FACE_120][4];
314 float edge_color_600[NUM_EDGE_600][4];
315 float face_color_600[NUM_FACE_600][4];
316 float face_color_trans_600[NUM_FACE_600][4];
322 static polytopesstruct *poly = (polytopesstruct *) NULL;
325 /* Vertex, edge, and face data for the six regular polytopes. All the
326 polytopes are constructed with coordinates chosen such that their 4d
327 circumsphere has a radius of 2. */
329 static const float vert_5[NUM_VERT_5][4] = {
330 { -SQRT5OVER2, -SQRT5OVER6, -SQRT5OVER12, -0.5 },
331 { SQRT5OVER2, -SQRT5OVER6, -SQRT5OVER12, -0.5 },
332 { 0.0, SQRT10OVER3, -SQRT5OVER12, -0.5 },
333 { 0.0, 0.0, SQRT15OVER4, -0.5 },
334 { 0.0, 0.0, 0.0, 2.0 }
337 static const int edge_5[NUM_EDGE_5][2] = {
338 { 0, 1 }, { 0, 2 }, { 0, 3 }, { 0, 4 }, { 1, 2 }, { 1, 3 }, { 1, 4 },
339 { 2, 3 }, { 2, 4 }, { 3, 4 }
342 static const int face_5[NUM_FACE_5][VERT_PER_FACE_5] = {
343 { 0, 1, 2 }, { 0, 1, 3 }, { 0, 1, 4 }, { 0, 2, 3 }, { 0, 2, 4 }, { 0, 3, 4 },
344 { 1, 2, 3 }, { 1, 2, 4 }, { 1, 3, 4 }, { 2, 3, 4 }
348 static const float vert_8[NUM_VERT_8][4] = {
349 { -1.0, -1.0, -1.0, -1.0 }, { 1.0, -1.0, -1.0, -1.0 },
350 { -1.0, 1.0, -1.0, -1.0 }, { 1.0, 1.0, -1.0, -1.0 },
351 { -1.0, -1.0, 1.0, -1.0 }, { 1.0, -1.0, 1.0, -1.0 },
352 { -1.0, 1.0, 1.0, -1.0 }, { 1.0, 1.0, 1.0, -1.0 },
353 { -1.0, -1.0, -1.0, 1.0 }, { 1.0, -1.0, -1.0, 1.0 },
354 { -1.0, 1.0, -1.0, 1.0 }, { 1.0, 1.0, -1.0, 1.0 },
355 { -1.0, -1.0, 1.0, 1.0 }, { 1.0, -1.0, 1.0, 1.0 },
356 { -1.0, 1.0, 1.0, 1.0 }, { 1.0, 1.0, 1.0, 1.0 }
359 static const int edge_8[NUM_EDGE_8][2] = {
360 { 0, 1 }, { 0, 2 }, { 0, 4 }, { 0, 8 }, { 1, 3 }, { 1, 5 },
361 { 1, 9 }, { 2, 3 }, { 2, 6 }, { 2, 10 }, { 3, 7 }, { 3, 11 },
362 { 4, 5 }, { 4, 6 }, { 4, 12 }, { 5, 7 }, { 5, 13 }, { 6, 7 },
363 { 6, 14 }, { 7, 15 }, { 8, 9 }, { 8, 10 }, { 8, 12 }, { 9, 11 },
364 { 9, 13 }, { 10, 11 }, { 10, 14 }, { 11, 15 }, { 12, 13 }, { 12, 14 },
365 { 13, 15 }, { 14, 15 }
368 static const int face_8[NUM_FACE_8][VERT_PER_FACE_8] = {
369 { 0, 1, 3, 2 }, { 0, 1, 5, 4 }, { 0, 1, 9, 8 },
370 { 0, 2, 6, 4 }, { 0, 2, 10, 8 }, { 0, 4, 12, 8 },
371 { 1, 3, 7, 5 }, { 1, 3, 11, 9 }, { 1, 5, 13, 9 },
372 { 2, 3, 7, 6 }, { 2, 3, 11, 10 }, { 2, 6, 14, 10 },
373 { 3, 7, 15, 11 }, { 4, 5, 7, 6 }, { 4, 5, 13, 12 },
374 { 4, 6, 14, 12 }, { 5, 7, 15, 13 }, { 6, 7, 15, 14 },
375 { 8, 9, 11, 10 }, { 8, 9, 13, 12 }, { 8, 10, 14, 12 },
376 { 9, 11, 15, 13 }, { 10, 11, 15, 14 }, { 12, 13, 15, 14 }
381 static const float vert_16[NUM_VERT_16][4] = {
382 { 0.0, 0.0, 0.0, -2.0 }, { 0.0, 0.0, -2.0, 0.0 },
383 { 0.0, -2.0, 0.0, 0.0 }, { -2.0, 0.0, 0.0, 0.0 },
384 { 2.0, 0.0, 0.0, 0.0 }, { 0.0, 2.0, 0.0, 0.0 },
385 { 0.0, 0.0, 2.0, 0.0 }, { 0.0, 0.0, 0.0, 2.0 }
388 static const int edge_16[NUM_EDGE_16][2] = {
389 { 0, 1 }, { 0, 2 }, { 0, 3 }, { 0, 4 }, { 0, 5 }, { 0, 6 }, { 1, 2 },
390 { 1, 3 }, { 1, 4 }, { 1, 5 }, { 1, 7 }, { 2, 3 }, { 2, 4 }, { 2, 6 },
391 { 2, 7 }, { 3, 5 }, { 3, 6 }, { 3, 7 }, { 4, 5 }, { 4, 6 }, { 4, 7 },
392 { 5, 6 }, { 5, 7 }, { 6, 7 }
395 static const int face_16[NUM_FACE_16][VERT_PER_FACE_16] = {
396 { 0, 1, 2 }, { 0, 1, 3 }, { 0, 1, 4 }, { 0, 1, 5 }, { 0, 2, 3 }, { 0, 2, 4 },
397 { 0, 2, 6 }, { 0, 3, 5 }, { 0, 3, 6 }, { 0, 4, 5 }, { 0, 4, 6 }, { 0, 5, 6 },
398 { 1, 2, 3 }, { 1, 2, 4 }, { 1, 2, 7 }, { 1, 3, 5 }, { 1, 3, 7 }, { 1, 4, 5 },
399 { 1, 4, 7 }, { 1, 5, 7 }, { 2, 3, 6 }, { 2, 3, 7 }, { 2, 4, 6 }, { 2, 4, 7 },
400 { 2, 6, 7 }, { 3, 5, 6 }, { 3, 5, 7 }, { 3, 6, 7 }, { 4, 5, 6 }, { 4, 5, 7 },
401 { 4, 6, 7 }, { 5, 6, 7 }
406 static const float vert_24[NUM_VERT_24][4] = {
407 { 0.0, 0.0, -SQRT2, -SQRT2 }, { 0.0, -SQRT2, 0.0, -SQRT2 },
408 { -SQRT2, 0.0, 0.0, -SQRT2 }, { SQRT2, 0.0, 0.0, -SQRT2 },
409 { 0.0, SQRT2, 0.0, -SQRT2 }, { 0.0, 0.0, SQRT2, -SQRT2 },
410 { 0.0, -SQRT2, -SQRT2, 0.0 }, { -SQRT2, 0.0, -SQRT2, 0.0 },
411 { SQRT2, 0.0, -SQRT2, 0.0 }, { 0.0, SQRT2, -SQRT2, 0.0 },
412 { -SQRT2, -SQRT2, 0.0, 0.0 }, { SQRT2, -SQRT2, 0.0, 0.0 },
413 { -SQRT2, SQRT2, 0.0, 0.0 }, { SQRT2, SQRT2, 0.0, 0.0 },
414 { 0.0, -SQRT2, SQRT2, 0.0 }, { -SQRT2, 0.0, SQRT2, 0.0 },
415 { SQRT2, 0.0, SQRT2, 0.0 }, { 0.0, SQRT2, SQRT2, 0.0 },
416 { 0.0, 0.0, -SQRT2, SQRT2 }, { 0.0, -SQRT2, 0.0, SQRT2 },
417 { -SQRT2, 0.0, 0.0, SQRT2 }, { SQRT2, 0.0, 0.0, SQRT2 },
418 { 0.0, SQRT2, 0.0, SQRT2 }, { 0.0, 0.0, SQRT2, SQRT2 }
421 static const int edge_24[NUM_EDGE_24][2] = {
422 { 0, 1 }, { 0, 2 }, { 0, 3 }, { 0, 4 }, { 0, 6 }, { 0, 7 },
423 { 0, 8 }, { 0, 9 }, { 1, 2 }, { 1, 3 }, { 1, 5 }, { 1, 6 },
424 { 1, 10 }, { 1, 11 }, { 1, 14 }, { 2, 4 }, { 2, 5 }, { 2, 7 },
425 { 2, 10 }, { 2, 12 }, { 2, 15 }, { 3, 4 }, { 3, 5 }, { 3, 8 },
426 { 3, 11 }, { 3, 13 }, { 3, 16 }, { 4, 5 }, { 4, 9 }, { 4, 12 },
427 { 4, 13 }, { 4, 17 }, { 5, 14 }, { 5, 15 }, { 5, 16 }, { 5, 17 },
428 { 6, 7 }, { 6, 8 }, { 6, 10 }, { 6, 11 }, { 6, 18 }, { 6, 19 },
429 { 7, 9 }, { 7, 10 }, { 7, 12 }, { 7, 18 }, { 7, 20 }, { 8, 9 },
430 { 8, 11 }, { 8, 13 }, { 8, 18 }, { 8, 21 }, { 9, 12 }, { 9, 13 },
431 { 9, 18 }, { 9, 22 }, { 10, 14 }, { 10, 15 }, { 10, 19 }, { 10, 20 },
432 { 11, 14 }, { 11, 16 }, { 11, 19 }, { 11, 21 }, { 12, 15 }, { 12, 17 },
433 { 12, 20 }, { 12, 22 }, { 13, 16 }, { 13, 17 }, { 13, 21 }, { 13, 22 },
434 { 14, 15 }, { 14, 16 }, { 14, 19 }, { 14, 23 }, { 15, 17 }, { 15, 20 },
435 { 15, 23 }, { 16, 17 }, { 16, 21 }, { 16, 23 }, { 17, 22 }, { 17, 23 },
436 { 18, 19 }, { 18, 20 }, { 18, 21 }, { 18, 22 }, { 19, 20 }, { 19, 21 },
437 { 19, 23 }, { 20, 22 }, { 20, 23 }, { 21, 22 }, { 21, 23 }, { 22, 23 }
440 static const int face_24[NUM_FACE_24][VERT_PER_FACE_24] = {
441 { 0, 1, 2 }, { 0, 1, 3 }, { 0, 1, 6 }, { 0, 2, 4 },
442 { 0, 2, 7 }, { 0, 3, 4 }, { 0, 3, 8 }, { 0, 4, 9 },
443 { 0, 6, 7 }, { 0, 6, 8 }, { 0, 7, 9 }, { 0, 8, 9 },
444 { 1, 2, 5 }, { 1, 2, 10 }, { 1, 3, 5 }, { 1, 3, 11 },
445 { 1, 5, 14 }, { 1, 6, 10 }, { 1, 6, 11 }, { 1, 10, 14 },
446 { 1, 11, 14 }, { 2, 4, 5 }, { 2, 4, 12 }, { 2, 5, 15 },
447 { 2, 7, 10 }, { 2, 7, 12 }, { 2, 10, 15 }, { 2, 12, 15 },
448 { 3, 4, 5 }, { 3, 4, 13 }, { 3, 5, 16 }, { 3, 8, 11 },
449 { 3, 8, 13 }, { 3, 11, 16 }, { 3, 13, 16 }, { 4, 5, 17 },
450 { 4, 9, 12 }, { 4, 9, 13 }, { 4, 12, 17 }, { 4, 13, 17 },
451 { 5, 14, 15 }, { 5, 14, 16 }, { 5, 15, 17 }, { 5, 16, 17 },
452 { 6, 7, 10 }, { 6, 7, 18 }, { 6, 8, 11 }, { 6, 8, 18 },
453 { 6, 10, 19 }, { 6, 11, 19 }, { 6, 18, 19 }, { 7, 9, 12 },
454 { 7, 9, 18 }, { 7, 10, 20 }, { 7, 12, 20 }, { 7, 18, 20 },
455 { 8, 9, 13 }, { 8, 9, 18 }, { 8, 11, 21 }, { 8, 13, 21 },
456 { 8, 18, 21 }, { 9, 12, 22 }, { 9, 13, 22 }, { 9, 18, 22 },
457 { 10, 14, 15 }, { 10, 14, 19 }, { 10, 15, 20 }, { 10, 19, 20 },
458 { 11, 14, 16 }, { 11, 14, 19 }, { 11, 16, 21 }, { 11, 19, 21 },
459 { 12, 15, 17 }, { 12, 15, 20 }, { 12, 17, 22 }, { 12, 20, 22 },
460 { 13, 16, 17 }, { 13, 16, 21 }, { 13, 17, 22 }, { 13, 21, 22 },
461 { 14, 15, 23 }, { 14, 16, 23 }, { 14, 19, 23 }, { 15, 17, 23 },
462 { 15, 20, 23 }, { 16, 17, 23 }, { 16, 21, 23 }, { 17, 22, 23 },
463 { 18, 19, 20 }, { 18, 19, 21 }, { 18, 20, 22 }, { 18, 21, 22 },
464 { 19, 20, 23 }, { 19, 21, 23 }, { 20, 22, 23 }, { 21, 22, 23 }
470 static const float vert_120[NUM_VERT_120][4] = {
471 { -GOLDENINV22, 0.0, -SQRT2INV, -GOLDEN22 },
472 { GOLDENINV22, 0.0, -SQRT2INV, -GOLDEN22 },
473 { -GOLDENINV2, -GOLDENINV2, -GOLDENINV2, -GOLDEN22 },
474 { GOLDENINV2, -GOLDENINV2, -GOLDENINV2, -GOLDEN22 },
475 { -GOLDENINV2, GOLDENINV2, -GOLDENINV2, -GOLDEN22 },
476 { GOLDENINV2, GOLDENINV2, -GOLDENINV2, -GOLDEN22 },
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687 { -GOLDENINV2, GOLDEN22, -GOLDENINV2, -GOLDENINV2 },
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696 { GOLDEN22, -GOLDENINV2, GOLDENINV2, -GOLDENINV2 },
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715 { -GOLDEN2, 0.0, SQRT5OVER2, -GOLDENINV2 },
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722 { SQRT2INV, 0.0, -GOLDEN22, -GOLDENINV22 },
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724 { GOLDEN2, -GOLDEN2, -GOLDEN2, -GOLDENINV22 },
725 { -GOLDEN2, GOLDEN2, -GOLDEN2, -GOLDENINV22 },
726 { GOLDEN2, GOLDEN2, -GOLDEN2, -GOLDENINV22 },
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728 { 0.0, GOLDEN22, -SQRT2INV, -GOLDENINV22 },
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730 { GOLDEN22, -SQRT2INV, 0.0, -GOLDENINV22 },
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735 { -GOLDEN2, -GOLDEN2, GOLDEN2, -GOLDENINV22 },
736 { GOLDEN2, -GOLDEN2, GOLDEN2, -GOLDENINV22 },
737 { -GOLDEN2, GOLDEN2, GOLDEN2, -GOLDENINV22 },
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747 { -GOLDENINV2, GOLDEN2, -SQRT5OVER2, 0.0 },
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750 { -SQRT2, 0.0, -SQRT2, 0.0 },
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1032 { GOLDENINV2, 0.0, -GOLDEN2, SQRT5OVER2 },
1033 { -SQRT2INV, -SQRT2INV, -SQRT2INV, SQRT5OVER2 },
1034 { SQRT2INV, -SQRT2INV, -SQRT2INV, SQRT5OVER2 },
1035 { -SQRT2INV, SQRT2INV, -SQRT2INV, SQRT5OVER2 },
1036 { SQRT2INV, SQRT2INV, -SQRT2INV, SQRT5OVER2 },
1037 { 0.0, -GOLDEN2, -GOLDENINV2, SQRT5OVER2 },
1038 { 0.0, GOLDEN2, -GOLDENINV2, SQRT5OVER2 },
1039 { -GOLDEN2, -GOLDENINV2, 0.0, SQRT5OVER2 },
1040 { GOLDEN2, -GOLDENINV2, 0.0, SQRT5OVER2 },
1041 { -GOLDEN2, GOLDENINV2, 0.0, SQRT5OVER2 },
1042 { GOLDEN2, GOLDENINV2, 0.0, SQRT5OVER2 },
1043 { 0.0, -GOLDEN2, GOLDENINV2, SQRT5OVER2 },
1044 { 0.0, GOLDEN2, GOLDENINV2, SQRT5OVER2 },
1045 { -SQRT2INV, -SQRT2INV, SQRT2INV, SQRT5OVER2 },
1046 { SQRT2INV, -SQRT2INV, SQRT2INV, SQRT5OVER2 },
1047 { -SQRT2INV, SQRT2INV, SQRT2INV, SQRT5OVER2 },
1048 { SQRT2INV, SQRT2INV, SQRT2INV, SQRT5OVER2 },
1049 { -GOLDENINV2, 0.0, GOLDEN2, SQRT5OVER2 },
1050 { GOLDENINV2, 0.0, GOLDEN2, SQRT5OVER2 },
1051 { -GOLDENINV22, 0.0, -SQRT2INV, GOLDEN22 },
1052 { GOLDENINV22, 0.0, -SQRT2INV, GOLDEN22 },
1053 { -GOLDENINV2, -GOLDENINV2, -GOLDENINV2, GOLDEN22 },
1054 { GOLDENINV2, -GOLDENINV2, -GOLDENINV2, GOLDEN22 },
1055 { -GOLDENINV2, GOLDENINV2, -GOLDENINV2, GOLDEN22 },
1056 { GOLDENINV2, GOLDENINV2, -GOLDENINV2, GOLDEN22 },
1057 { 0.0, -SQRT2INV, -GOLDENINV22, GOLDEN22 },
1058 { 0.0, SQRT2INV, -GOLDENINV22, GOLDEN22 },
1059 { -SQRT2INV, -GOLDENINV22, 0.0, GOLDEN22 },
1060 { SQRT2INV, -GOLDENINV22, 0.0, GOLDEN22 },
1061 { -SQRT2INV, GOLDENINV22, 0.0, GOLDEN22 },
1062 { SQRT2INV, GOLDENINV22, 0.0, GOLDEN22 },
1063 { 0.0, -SQRT2INV, GOLDENINV22, GOLDEN22 },
1064 { 0.0, SQRT2INV, GOLDENINV22, GOLDEN22 },
1065 { -GOLDENINV2, -GOLDENINV2, GOLDENINV2, GOLDEN22 },
1066 { GOLDENINV2, -GOLDENINV2, GOLDENINV2, GOLDEN22 },
1067 { -GOLDENINV2, GOLDENINV2, GOLDENINV2, GOLDEN22 },
1068 { GOLDENINV2, GOLDENINV2, GOLDENINV2, GOLDEN22 },
1069 { -GOLDENINV22, 0.0, SQRT2INV, GOLDEN22 },
1070 { GOLDENINV22, 0.0, SQRT2INV, GOLDEN22 }
1073 static const int edge_120[NUM_EDGE_120][2] = {
1074 { 0, 1 }, { 0, 2 }, { 0, 4 }, { 0, 20 }, { 1, 3 },
1075 { 1, 5 }, { 1, 21 }, { 2, 6 }, { 2, 8 }, { 2, 22 },
1076 { 3, 6 }, { 3, 9 }, { 3, 23 }, { 4, 7 }, { 4, 10 },
1077 { 4, 24 }, { 5, 7 }, { 5, 11 }, { 5, 25 }, { 6, 12 },
1078 { 6, 26 }, { 7, 13 }, { 7, 27 }, { 8, 10 }, { 8, 14 },
1079 { 8, 28 }, { 9, 11 }, { 9, 15 }, { 9, 29 }, { 10, 16 },
1080 { 10, 30 }, { 11, 17 }, { 11, 31 }, { 12, 14 }, { 12, 15 },
1081 { 12, 32 }, { 13, 16 }, { 13, 17 }, { 13, 33 }, { 14, 18 },
1082 { 14, 34 }, { 15, 19 }, { 15, 35 }, { 16, 18 }, { 16, 36 },
1083 { 17, 19 }, { 17, 37 }, { 18, 19 }, { 18, 38 }, { 19, 39 },
1084 { 20, 40 }, { 20, 41 }, { 20, 43 }, { 21, 40 }, { 21, 42 },
1085 { 21, 44 }, { 22, 41 }, { 22, 45 }, { 22, 49 }, { 23, 42 },
1086 { 23, 46 }, { 23, 50 }, { 24, 43 }, { 24, 47 }, { 24, 51 },
1087 { 25, 44 }, { 25, 48 }, { 25, 52 }, { 26, 45 }, { 26, 46 },
1088 { 26, 53 }, { 27, 47 }, { 27, 48 }, { 27, 56 }, { 28, 49 },
1089 { 28, 54 }, { 28, 57 }, { 29, 50 }, { 29, 55 }, { 29, 58 },
1090 { 30, 51 }, { 30, 54 }, { 30, 59 }, { 31, 52 }, { 31, 55 },
1091 { 31, 60 }, { 32, 53 }, { 32, 61 }, { 32, 62 }, { 33, 56 },
1092 { 33, 63 }, { 33, 64 }, { 34, 57 }, { 34, 61 }, { 34, 65 },
1093 { 35, 58 }, { 35, 62 }, { 35, 66 }, { 36, 59 }, { 36, 63 },
1094 { 36, 67 }, { 37, 60 }, { 37, 64 }, { 37, 68 }, { 38, 65 },
1095 { 38, 67 }, { 38, 69 }, { 39, 66 }, { 39, 68 }, { 39, 69 },
1096 { 40, 70 }, { 40, 71 }, { 41, 72 }, { 41, 78 }, { 42, 73 },
1097 { 42, 79 }, { 43, 74 }, { 43, 80 }, { 44, 75 }, { 44, 81 },
1098 { 45, 76 }, { 45, 88 }, { 46, 77 }, { 46, 89 }, { 47, 82 },
1099 { 47, 92 }, { 48, 83 }, { 48, 93 }, { 49, 84 }, { 49, 94 },
1100 { 50, 85 }, { 50, 95 }, { 51, 86 }, { 51, 96 }, { 52, 87 },
1101 { 52, 97 }, { 53, 98 }, { 53, 99 }, { 54, 90 }, { 54, 108 },
1102 { 55, 91 }, { 55, 109 }, { 56, 100 }, { 56, 101 }, { 57, 102 },
1103 { 57, 112 }, { 58, 103 }, { 58, 113 }, { 59, 104 }, { 59, 114 },
1104 { 60, 105 }, { 60, 115 }, { 61, 106 }, { 61, 116 }, { 62, 107 },
1105 { 62, 117 }, { 63, 110 }, { 63, 122 }, { 64, 111 }, { 64, 123 },
1106 { 65, 118 }, { 65, 124 }, { 66, 119 }, { 66, 125 }, { 67, 120 },
1107 { 67, 126 }, { 68, 121 }, { 68, 127 }, { 69, 128 }, { 69, 129 },
1108 { 70, 72 }, { 70, 73 }, { 70, 130 }, { 71, 74 }, { 71, 75 },
1109 { 71, 131 }, { 72, 76 }, { 72, 132 }, { 73, 77 }, { 73, 133 },
1110 { 74, 82 }, { 74, 134 }, { 75, 83 }, { 75, 135 }, { 76, 77 },
1111 { 76, 140 }, { 77, 141 }, { 78, 80 }, { 78, 84 }, { 78, 136 },
1112 { 79, 81 }, { 79, 85 }, { 79, 137 }, { 80, 86 }, { 80, 138 },
1113 { 81, 87 }, { 81, 139 }, { 82, 83 }, { 82, 142 }, { 83, 143 },
1114 { 84, 90 }, { 84, 146 }, { 85, 91 }, { 85, 147 }, { 86, 90 },
1115 { 86, 148 }, { 87, 91 }, { 87, 149 }, { 88, 94 }, { 88, 98 },
1116 { 88, 144 }, { 89, 95 }, { 89, 99 }, { 89, 145 }, { 90, 156 },
1117 { 91, 157 }, { 92, 96 }, { 92, 100 }, { 92, 150 }, { 93, 97 },
1118 { 93, 101 }, { 93, 151 }, { 94, 102 }, { 94, 152 }, { 95, 103 },
1119 { 95, 153 }, { 96, 104 }, { 96, 154 }, { 97, 105 }, { 97, 155 },
1120 { 98, 106 }, { 98, 158 }, { 99, 107 }, { 99, 159 }, { 100, 110 },
1121 { 100, 160 }, { 101, 111 }, { 101, 161 }, { 102, 106 }, { 102, 164 },
1122 { 103, 107 }, { 103, 165 }, { 104, 110 }, { 104, 166 }, { 105, 111 },
1123 { 105, 167 }, { 106, 168 }, { 107, 169 }, { 108, 112 }, { 108, 114 },
1124 { 108, 162 }, { 109, 113 }, { 109, 115 }, { 109, 163 }, { 110, 174 },
1125 { 111, 175 }, { 112, 118 }, { 112, 170 }, { 113, 119 }, { 113, 171 },
1126 { 114, 120 }, { 114, 172 }, { 115, 121 }, { 115, 173 }, { 116, 117 },
1127 { 116, 124 }, { 116, 176 }, { 117, 125 }, { 117, 177 }, { 118, 120 },
1128 { 118, 180 }, { 119, 121 }, { 119, 181 }, { 120, 182 }, { 121, 183 },
1129 { 122, 123 }, { 122, 126 }, { 122, 178 }, { 123, 127 }, { 123, 179 },
1130 { 124, 128 }, { 124, 184 }, { 125, 128 }, { 125, 185 }, { 126, 129 },
1131 { 126, 186 }, { 127, 129 }, { 127, 187 }, { 128, 188 }, { 129, 189 },
1132 { 130, 131 }, { 130, 190 }, { 130, 191 }, { 131, 192 }, { 131, 193 },
1133 { 132, 136 }, { 132, 190 }, { 132, 196 }, { 133, 137 }, { 133, 191 },
1134 { 133, 197 }, { 134, 138 }, { 134, 192 }, { 134, 198 }, { 135, 139 },
1135 { 135, 193 }, { 135, 199 }, { 136, 194 }, { 136, 201 }, { 137, 195 },
1136 { 137, 202 }, { 138, 194 }, { 138, 203 }, { 139, 195 }, { 139, 204 },
1137 { 140, 144 }, { 140, 196 }, { 140, 200 }, { 141, 145 }, { 141, 197 },
1138 { 141, 200 }, { 142, 150 }, { 142, 198 }, { 142, 205 }, { 143, 151 },
1139 { 143, 199 }, { 143, 205 }, { 144, 206 }, { 144, 210 }, { 145, 207 },
1140 { 145, 211 }, { 146, 152 }, { 146, 201 }, { 146, 212 }, { 147, 153 },
1141 { 147, 202 }, { 147, 213 }, { 148, 154 }, { 148, 203 }, { 148, 214 },
1142 { 149, 155 }, { 149, 204 }, { 149, 215 }, { 150, 208 }, { 150, 216 },
1143 { 151, 209 }, { 151, 217 }, { 152, 206 }, { 152, 218 }, { 153, 207 },
1144 { 153, 219 }, { 154, 208 }, { 154, 220 }, { 155, 209 }, { 155, 221 },
1145 { 156, 162 }, { 156, 212 }, { 156, 214 }, { 157, 163 }, { 157, 213 },
1146 { 157, 215 }, { 158, 159 }, { 158, 210 }, { 158, 222 }, { 159, 211 },
1147 { 159, 223 }, { 160, 161 }, { 160, 216 }, { 160, 228 }, { 161, 217 },
1148 { 161, 229 }, { 162, 224 }, { 162, 226 }, { 163, 225 }, { 163, 227 },
1149 { 164, 170 }, { 164, 218 }, { 164, 230 }, { 165, 171 }, { 165, 219 },
1150 { 165, 231 }, { 166, 172 }, { 166, 220 }, { 166, 232 }, { 167, 173 },
1151 { 167, 221 }, { 167, 233 }, { 168, 176 }, { 168, 222 }, { 168, 230 },
1152 { 169, 177 }, { 169, 223 }, { 169, 231 }, { 170, 224 }, { 170, 235 },
1153 { 171, 225 }, { 171, 236 }, { 172, 226 }, { 172, 237 }, { 173, 227 },
1154 { 173, 238 }, { 174, 178 }, { 174, 228 }, { 174, 232 }, { 175, 179 },
1155 { 175, 229 }, { 175, 233 }, { 176, 234 }, { 176, 240 }, { 177, 234 },
1156 { 177, 241 }, { 178, 239 }, { 178, 242 }, { 179, 239 }, { 179, 243 },
1157 { 180, 184 }, { 180, 235 }, { 180, 244 }, { 181, 185 }, { 181, 236 },
1158 { 181, 245 }, { 182, 186 }, { 182, 237 }, { 182, 244 }, { 183, 187 },
1159 { 183, 238 }, { 183, 245 }, { 184, 240 }, { 184, 246 }, { 185, 241 },
1160 { 185, 247 }, { 186, 242 }, { 186, 248 }, { 187, 243 }, { 187, 249 },
1161 { 188, 189 }, { 188, 246 }, { 188, 247 }, { 189, 248 }, { 189, 249 },
1162 { 190, 250 }, { 190, 270 }, { 191, 251 }, { 191, 271 }, { 192, 250 },
1163 { 192, 272 }, { 193, 251 }, { 193, 273 }, { 194, 250 }, { 194, 279 },
1164 { 195, 251 }, { 195, 280 }, { 196, 252 }, { 196, 274 }, { 197, 253 },
1165 { 197, 275 }, { 198, 254 }, { 198, 276 }, { 199, 255 }, { 199, 277 },
1166 { 200, 256 }, { 200, 278 }, { 201, 252 }, { 201, 282 }, { 202, 253 },
1167 { 202, 283 }, { 203, 254 }, { 203, 284 }, { 204, 255 }, { 204, 285 },
1168 { 205, 257 }, { 205, 281 }, { 206, 252 }, { 206, 290 }, { 207, 253 },
1169 { 207, 291 }, { 208, 254 }, { 208, 292 }, { 209, 255 }, { 209, 293 },
1170 { 210, 256 }, { 210, 294 }, { 211, 256 }, { 211, 295 }, { 212, 258 },
1171 { 212, 286 }, { 213, 259 }, { 213, 287 }, { 214, 260 }, { 214, 288 },
1172 { 215, 261 }, { 215, 289 }, { 216, 257 }, { 216, 296 }, { 217, 257 },
1173 { 217, 297 }, { 218, 258 }, { 218, 298 }, { 219, 259 }, { 219, 299 },
1174 { 220, 260 }, { 220, 300 }, { 221, 261 }, { 221, 301 }, { 222, 262 },
1175 { 222, 302 }, { 223, 262 }, { 223, 303 }, { 224, 258 }, { 224, 310 },
1176 { 225, 259 }, { 225, 311 }, { 226, 260 }, { 226, 312 }, { 227, 261 },
1177 { 227, 313 }, { 228, 263 }, { 228, 304 }, { 229, 263 }, { 229, 305 },
1178 { 230, 264 }, { 230, 306 }, { 231, 265 }, { 231, 307 }, { 232, 266 },
1179 { 232, 308 }, { 233, 267 }, { 233, 309 }, { 234, 262 }, { 234, 318 },
1180 { 235, 264 }, { 235, 314 }, { 236, 265 }, { 236, 315 }, { 237, 266 },
1181 { 237, 316 }, { 238, 267 }, { 238, 317 }, { 239, 263 }, { 239, 321 },
1182 { 240, 264 }, { 240, 322 }, { 241, 265 }, { 241, 323 }, { 242, 266 },
1183 { 242, 324 }, { 243, 267 }, { 243, 325 }, { 244, 268 }, { 244, 319 },
1184 { 245, 269 }, { 245, 320 }, { 246, 268 }, { 246, 326 }, { 247, 269 },
1185 { 247, 327 }, { 248, 268 }, { 248, 328 }, { 249, 269 }, { 249, 329 },
1186 { 250, 330 }, { 251, 331 }, { 252, 332 }, { 253, 333 }, { 254, 334 },
1187 { 255, 335 }, { 256, 336 }, { 257, 337 }, { 258, 338 }, { 259, 339 },
1188 { 260, 340 }, { 261, 341 }, { 262, 342 }, { 263, 343 }, { 264, 344 },
1189 { 265, 345 }, { 266, 346 }, { 267, 347 }, { 268, 348 }, { 269, 349 },
1190 { 270, 271 }, { 270, 274 }, { 270, 350 }, { 271, 275 }, { 271, 351 },
1191 { 272, 273 }, { 272, 276 }, { 272, 352 }, { 273, 277 }, { 273, 353 },
1192 { 274, 278 }, { 274, 356 }, { 275, 278 }, { 275, 357 }, { 276, 281 },
1193 { 276, 358 }, { 277, 281 }, { 277, 359 }, { 278, 360 }, { 279, 282 },
1194 { 279, 284 }, { 279, 354 }, { 280, 283 }, { 280, 285 }, { 280, 355 },
1195 { 281, 365 }, { 282, 286 }, { 282, 361 }, { 283, 287 }, { 283, 362 },
1196 { 284, 288 }, { 284, 363 }, { 285, 289 }, { 285, 364 }, { 286, 288 },
1197 { 286, 372 }, { 287, 289 }, { 287, 373 }, { 288, 374 }, { 289, 375 },
1198 { 290, 294 }, { 290, 298 }, { 290, 366 }, { 291, 295 }, { 291, 299 },
1199 { 291, 367 }, { 292, 296 }, { 292, 300 }, { 292, 368 }, { 293, 297 },
1200 { 293, 301 }, { 293, 369 }, { 294, 302 }, { 294, 370 }, { 295, 303 },
1201 { 295, 371 }, { 296, 304 }, { 296, 376 }, { 297, 305 }, { 297, 377 },
1202 { 298, 306 }, { 298, 378 }, { 299, 307 }, { 299, 379 }, { 300, 308 },
1203 { 300, 380 }, { 301, 309 }, { 301, 381 }, { 302, 306 }, { 302, 382 },
1204 { 303, 307 }, { 303, 383 }, { 304, 308 }, { 304, 388 }, { 305, 309 },
1205 { 305, 389 }, { 306, 390 }, { 307, 391 }, { 308, 392 }, { 309, 393 },
1206 { 310, 312 }, { 310, 314 }, { 310, 384 }, { 311, 313 }, { 311, 315 },
1207 { 311, 385 }, { 312, 316 }, { 312, 386 }, { 313, 317 }, { 313, 387 },
1208 { 314, 319 }, { 314, 395 }, { 315, 320 }, { 315, 396 }, { 316, 319 },
1209 { 316, 397 }, { 317, 320 }, { 317, 398 }, { 318, 322 }, { 318, 323 },
1210 { 318, 394 }, { 319, 404 }, { 320, 405 }, { 321, 324 }, { 321, 325 },
1211 { 321, 399 }, { 322, 326 }, { 322, 400 }, { 323, 327 }, { 323, 401 },
1212 { 324, 328 }, { 324, 402 }, { 325, 329 }, { 325, 403 }, { 326, 327 },
1213 { 326, 406 }, { 327, 407 }, { 328, 329 }, { 328, 408 }, { 329, 409 },
1214 { 330, 350 }, { 330, 352 }, { 330, 354 }, { 331, 351 }, { 331, 353 },
1215 { 331, 355 }, { 332, 356 }, { 332, 361 }, { 332, 366 }, { 333, 357 },
1216 { 333, 362 }, { 333, 367 }, { 334, 358 }, { 334, 363 }, { 334, 368 },
1217 { 335, 359 }, { 335, 364 }, { 335, 369 }, { 336, 360 }, { 336, 370 },
1218 { 336, 371 }, { 337, 365 }, { 337, 376 }, { 337, 377 }, { 338, 372 },
1219 { 338, 378 }, { 338, 384 }, { 339, 373 }, { 339, 379 }, { 339, 385 },
1220 { 340, 374 }, { 340, 380 }, { 340, 386 }, { 341, 375 }, { 341, 381 },
1221 { 341, 387 }, { 342, 382 }, { 342, 383 }, { 342, 394 }, { 343, 388 },
1222 { 343, 389 }, { 343, 399 }, { 344, 390 }, { 344, 395 }, { 344, 400 },
1223 { 345, 391 }, { 345, 396 }, { 345, 401 }, { 346, 392 }, { 346, 397 },
1224 { 346, 402 }, { 347, 393 }, { 347, 398 }, { 347, 403 }, { 348, 404 },
1225 { 348, 406 }, { 348, 408 }, { 349, 405 }, { 349, 407 }, { 349, 409 },
1226 { 350, 410 }, { 350, 412 }, { 351, 410 }, { 351, 413 }, { 352, 411 },
1227 { 352, 414 }, { 353, 411 }, { 353, 415 }, { 354, 416 }, { 354, 418 },
1228 { 355, 417 }, { 355, 419 }, { 356, 412 }, { 356, 420 }, { 357, 413 },
1229 { 357, 421 }, { 358, 414 }, { 358, 422 }, { 359, 415 }, { 359, 423 },
1230 { 360, 420 }, { 360, 421 }, { 361, 416 }, { 361, 426 }, { 362, 417 },
1231 { 362, 427 }, { 363, 418 }, { 363, 428 }, { 364, 419 }, { 364, 429 },
1232 { 365, 422 }, { 365, 423 }, { 366, 424 }, { 366, 432 }, { 367, 425 },
1233 { 367, 433 }, { 368, 430 }, { 368, 434 }, { 369, 431 }, { 369, 435 },
1234 { 370, 424 }, { 370, 438 }, { 371, 425 }, { 371, 439 }, { 372, 426 },
1235 { 372, 436 }, { 373, 427 }, { 373, 437 }, { 374, 428 }, { 374, 436 },
1236 { 375, 429 }, { 375, 437 }, { 376, 430 }, { 376, 440 }, { 377, 431 },
1237 { 377, 441 }, { 378, 432 }, { 378, 444 }, { 379, 433 }, { 379, 445 },
1238 { 380, 434 }, { 380, 446 }, { 381, 435 }, { 381, 447 }, { 382, 438 },
1239 { 382, 448 }, { 383, 439 }, { 383, 449 }, { 384, 442 }, { 384, 450 },
1240 { 385, 443 }, { 385, 451 }, { 386, 442 }, { 386, 452 }, { 387, 443 },
1241 { 387, 453 }, { 388, 440 }, { 388, 454 }, { 389, 441 }, { 389, 455 },
1242 { 390, 444 }, { 390, 448 }, { 391, 445 }, { 391, 449 }, { 392, 446 },
1243 { 392, 454 }, { 393, 447 }, { 393, 455 }, { 394, 456 }, { 394, 457 },
1244 { 395, 450 }, { 395, 460 }, { 396, 451 }, { 396, 461 }, { 397, 452 },
1245 { 397, 462 }, { 398, 453 }, { 398, 463 }, { 399, 458 }, { 399, 459 },
1246 { 400, 456 }, { 400, 464 }, { 401, 457 }, { 401, 465 }, { 402, 458 },
1247 { 402, 466 }, { 403, 459 }, { 403, 467 }, { 404, 460 }, { 404, 462 },
1248 { 405, 461 }, { 405, 463 }, { 406, 464 }, { 406, 468 }, { 407, 465 },
1249 { 407, 468 }, { 408, 466 }, { 408, 469 }, { 409, 467 }, { 409, 469 },
1250 { 410, 411 }, { 410, 470 }, { 411, 471 }, { 412, 416 }, { 412, 472 },
1251 { 413, 417 }, { 413, 473 }, { 414, 418 }, { 414, 474 }, { 415, 419 },
1252 { 415, 475 }, { 416, 478 }, { 417, 479 }, { 418, 480 }, { 419, 481 },
1253 { 420, 424 }, { 420, 476 }, { 421, 425 }, { 421, 477 }, { 422, 430 },
1254 { 422, 482 }, { 423, 431 }, { 423, 483 }, { 424, 488 }, { 425, 489 },
1255 { 426, 432 }, { 426, 484 }, { 427, 433 }, { 427, 485 }, { 428, 434 },
1256 { 428, 486 }, { 429, 435 }, { 429, 487 }, { 430, 492 }, { 431, 493 },
1257 { 432, 494 }, { 433, 495 }, { 434, 496 }, { 435, 497 }, { 436, 442 },
1258 { 436, 490 }, { 437, 443 }, { 437, 491 }, { 438, 439 }, { 438, 498 },
1259 { 439, 499 }, { 440, 441 }, { 440, 500 }, { 441, 501 }, { 442, 508 },
1260 { 443, 509 }, { 444, 450 }, { 444, 502 }, { 445, 451 }, { 445, 503 },
1261 { 446, 452 }, { 446, 504 }, { 447, 453 }, { 447, 505 }, { 448, 456 },
1262 { 448, 506 }, { 449, 457 }, { 449, 507 }, { 450, 512 }, { 451, 513 },
1263 { 452, 514 }, { 453, 515 }, { 454, 458 }, { 454, 510 }, { 455, 459 },
1264 { 455, 511 }, { 456, 516 }, { 457, 517 }, { 458, 522 }, { 459, 523 },
1265 { 460, 464 }, { 460, 518 }, { 461, 465 }, { 461, 519 }, { 462, 466 },
1266 { 462, 520 }, { 463, 467 }, { 463, 521 }, { 464, 524 }, { 465, 525 },
1267 { 466, 526 }, { 467, 527 }, { 468, 469 }, { 468, 528 }, { 469, 529 },
1268 { 470, 472 }, { 470, 473 }, { 470, 530 }, { 471, 474 }, { 471, 475 },
1269 { 471, 530 }, { 472, 476 }, { 472, 531 }, { 473, 477 }, { 473, 532 },
1270 { 474, 482 }, { 474, 533 }, { 475, 483 }, { 475, 534 }, { 476, 477 },
1271 { 476, 535 }, { 477, 536 }, { 478, 480 }, { 478, 484 }, { 478, 531 },
1272 { 479, 481 }, { 479, 485 }, { 479, 532 }, { 480, 486 }, { 480, 533 },
1273 { 481, 487 }, { 481, 534 }, { 482, 483 }, { 482, 537 }, { 483, 538 },
1274 { 484, 490 }, { 484, 539 }, { 485, 491 }, { 485, 540 }, { 486, 490 },
1275 { 486, 541 }, { 487, 491 }, { 487, 542 }, { 488, 494 }, { 488, 498 },
1276 { 488, 535 }, { 489, 495 }, { 489, 499 }, { 489, 536 }, { 490, 544 },
1277 { 491, 545 }, { 492, 496 }, { 492, 500 }, { 492, 537 }, { 493, 497 },
1278 { 493, 501 }, { 493, 538 }, { 494, 502 }, { 494, 539 }, { 495, 503 },
1279 { 495, 540 }, { 496, 504 }, { 496, 541 }, { 497, 505 }, { 497, 542 },
1280 { 498, 506 }, { 498, 543 }, { 499, 507 }, { 499, 543 }, { 500, 510 },
1281 { 500, 546 }, { 501, 511 }, { 501, 546 }, { 502, 506 }, { 502, 547 },
1282 { 503, 507 }, { 503, 548 }, { 504, 510 }, { 504, 549 }, { 505, 511 },
1283 { 505, 550 }, { 506, 551 }, { 507, 552 }, { 508, 512 }, { 508, 514 },
1284 { 508, 544 }, { 509, 513 }, { 509, 515 }, { 509, 545 }, { 510, 553 },
1285 { 511, 554 }, { 512, 518 }, { 512, 547 }, { 513, 519 }, { 513, 548 },
1286 { 514, 520 }, { 514, 549 }, { 515, 521 }, { 515, 550 }, { 516, 517 },
1287 { 516, 524 }, { 516, 551 }, { 517, 525 }, { 517, 552 }, { 518, 520 },
1288 { 518, 555 }, { 519, 521 }, { 519, 556 }, { 520, 557 }, { 521, 558 },
1289 { 522, 523 }, { 522, 526 }, { 522, 553 }, { 523, 527 }, { 523, 554 },
1290 { 524, 528 }, { 524, 555 }, { 525, 528 }, { 525, 556 }, { 526, 529 },
1291 { 526, 557 }, { 527, 529 }, { 527, 558 }, { 528, 559 }, { 529, 559 },
1292 { 530, 560 }, { 530, 561 }, { 531, 560 }, { 531, 562 }, { 532, 561 },
1293 { 532, 563 }, { 533, 560 }, { 533, 564 }, { 534, 561 }, { 534, 565 },
1294 { 535, 562 }, { 535, 566 }, { 536, 563 }, { 536, 566 }, { 537, 564 },
1295 { 537, 567 }, { 538, 565 }, { 538, 567 }, { 539, 562 }, { 539, 568 },
1296 { 540, 563 }, { 540, 569 }, { 541, 564 }, { 541, 570 }, { 542, 565 },
1297 { 542, 571 }, { 543, 566 }, { 543, 572 }, { 544, 568 }, { 544, 570 },
1298 { 545, 569 }, { 545, 571 }, { 546, 567 }, { 546, 573 }, { 547, 568 },
1299 { 547, 574 }, { 548, 569 }, { 548, 575 }, { 549, 570 }, { 549, 576 },
1300 { 550, 571 }, { 550, 577 }, { 551, 572 }, { 551, 574 }, { 552, 572 },
1301 { 552, 575 }, { 553, 573 }, { 553, 576 }, { 554, 573 }, { 554, 577 },
1302 { 555, 574 }, { 555, 578 }, { 556, 575 }, { 556, 579 }, { 557, 576 },
1303 { 557, 578 }, { 558, 577 }, { 558, 579 }, { 559, 578 }, { 559, 579 },
1304 { 560, 580 }, { 561, 581 }, { 562, 582 }, { 563, 583 }, { 564, 584 },
1305 { 565, 585 }, { 566, 586 }, { 567, 587 }, { 568, 588 }, { 569, 589 },
1306 { 570, 590 }, { 571, 591 }, { 572, 592 }, { 573, 593 }, { 574, 594 },
1307 { 575, 595 }, { 576, 596 }, { 577, 597 }, { 578, 598 }, { 579, 599 },
1308 { 580, 581 }, { 580, 582 }, { 580, 584 }, { 581, 583 }, { 581, 585 },
1309 { 582, 586 }, { 582, 588 }, { 583, 586 }, { 583, 589 }, { 584, 587 },
1310 { 584, 590 }, { 585, 587 }, { 585, 591 }, { 586, 592 }, { 587, 593 },
1311 { 588, 590 }, { 588, 594 }, { 589, 591 }, { 589, 595 }, { 590, 596 },
1312 { 591, 597 }, { 592, 594 }, { 592, 595 }, { 593, 596 }, { 593, 597 },
1313 { 594, 598 }, { 595, 599 }, { 596, 598 }, { 597, 599 }, { 598, 599 }
1316 static const int face_120[NUM_FACE_120][VERT_PER_FACE_120] = {
1317 { 0, 1, 3, 6, 2 }, { 0, 1, 5, 7, 4 },
1318 { 0, 1, 21, 40, 20 }, { 0, 2, 8, 10, 4 },
1319 { 0, 2, 22, 41, 20 }, { 0, 4, 24, 43, 20 },
1320 { 1, 3, 9, 11, 5 }, { 1, 3, 23, 42, 21 },
1321 { 1, 5, 25, 44, 21 }, { 2, 6, 12, 14, 8 },
1322 { 2, 6, 26, 45, 22 }, { 2, 8, 28, 49, 22 },
1323 { 3, 6, 12, 15, 9 }, { 3, 6, 26, 46, 23 },
1324 { 3, 9, 29, 50, 23 }, { 4, 7, 13, 16, 10 },
1325 { 4, 7, 27, 47, 24 }, { 4, 10, 30, 51, 24 },
1326 { 5, 7, 13, 17, 11 }, { 5, 7, 27, 48, 25 },
1327 { 5, 11, 31, 52, 25 }, { 6, 12, 32, 53, 26 },
1328 { 7, 13, 33, 56, 27 }, { 8, 10, 16, 18, 14 },
1329 { 8, 10, 30, 54, 28 }, { 8, 14, 34, 57, 28 },
1330 { 9, 11, 17, 19, 15 }, { 9, 11, 31, 55, 29 },
1331 { 9, 15, 35, 58, 29 }, { 10, 16, 36, 59, 30 },
1332 { 11, 17, 37, 60, 31 }, { 12, 14, 18, 19, 15 },
1333 { 12, 14, 34, 61, 32 }, { 12, 15, 35, 62, 32 },
1334 { 13, 16, 18, 19, 17 }, { 13, 16, 36, 63, 33 },
1335 { 13, 17, 37, 64, 33 }, { 14, 18, 38, 65, 34 },
1336 { 15, 19, 39, 66, 35 }, { 16, 18, 38, 67, 36 },
1337 { 17, 19, 39, 68, 37 }, { 18, 19, 39, 69, 38 },
1338 { 20, 40, 70, 72, 41 }, { 20, 40, 71, 74, 43 },
1339 { 20, 41, 78, 80, 43 }, { 21, 40, 70, 73, 42 },
1340 { 21, 40, 71, 75, 44 }, { 21, 42, 79, 81, 44 },
1341 { 22, 41, 72, 76, 45 }, { 22, 41, 78, 84, 49 },
1342 { 22, 45, 88, 94, 49 }, { 23, 42, 73, 77, 46 },
1343 { 23, 42, 79, 85, 50 }, { 23, 46, 89, 95, 50 },
1344 { 24, 43, 74, 82, 47 }, { 24, 43, 80, 86, 51 },
1345 { 24, 47, 92, 96, 51 }, { 25, 44, 75, 83, 48 },
1346 { 25, 44, 81, 87, 52 }, { 25, 48, 93, 97, 52 },
1347 { 26, 45, 76, 77, 46 }, { 26, 45, 88, 98, 53 },
1348 { 26, 46, 89, 99, 53 }, { 27, 47, 82, 83, 48 },
1349 { 27, 47, 92, 100, 56 }, { 27, 48, 93, 101, 56 },
1350 { 28, 49, 84, 90, 54 }, { 28, 49, 94, 102, 57 },
1351 { 28, 54, 108, 112, 57 }, { 29, 50, 85, 91, 55 },
1352 { 29, 50, 95, 103, 58 }, { 29, 55, 109, 113, 58 },
1353 { 30, 51, 86, 90, 54 }, { 30, 51, 96, 104, 59 },
1354 { 30, 54, 108, 114, 59 }, { 31, 52, 87, 91, 55 },
1355 { 31, 52, 97, 105, 60 }, { 31, 55, 109, 115, 60 },
1356 { 32, 53, 98, 106, 61 }, { 32, 53, 99, 107, 62 },
1357 { 32, 61, 116, 117, 62 }, { 33, 56, 100, 110, 63 },
1358 { 33, 56, 101, 111, 64 }, { 33, 63, 122, 123, 64 },
1359 { 34, 57, 102, 106, 61 }, { 34, 57, 112, 118, 65 },
1360 { 34, 61, 116, 124, 65 }, { 35, 58, 103, 107, 62 },
1361 { 35, 58, 113, 119, 66 }, { 35, 62, 117, 125, 66 },
1362 { 36, 59, 104, 110, 63 }, { 36, 59, 114, 120, 67 },
1363 { 36, 63, 122, 126, 67 }, { 37, 60, 105, 111, 64 },
1364 { 37, 60, 115, 121, 68 }, { 37, 64, 123, 127, 68 },
1365 { 38, 65, 118, 120, 67 }, { 38, 65, 124, 128, 69 },
1366 { 38, 67, 126, 129, 69 }, { 39, 66, 119, 121, 68 },
1367 { 39, 66, 125, 128, 69 }, { 39, 68, 127, 129, 69 },
1368 { 40, 70, 130, 131, 71 }, { 41, 72, 132, 136, 78 },
1369 { 42, 73, 133, 137, 79 }, { 43, 74, 134, 138, 80 },
1370 { 44, 75, 135, 139, 81 }, { 45, 76, 140, 144, 88 },
1371 { 46, 77, 141, 145, 89 }, { 47, 82, 142, 150, 92 },
1372 { 48, 83, 143, 151, 93 }, { 49, 84, 146, 152, 94 },
1373 { 50, 85, 147, 153, 95 }, { 51, 86, 148, 154, 96 },
1374 { 52, 87, 149, 155, 97 }, { 53, 98, 158, 159, 99 },
1375 { 54, 90, 156, 162, 108 }, { 55, 91, 157, 163, 109 },
1376 { 56, 100, 160, 161, 101 }, { 57, 102, 164, 170, 112 },
1377 { 58, 103, 165, 171, 113 }, { 59, 104, 166, 172, 114 },
1378 { 60, 105, 167, 173, 115 }, { 61, 106, 168, 176, 116 },
1379 { 62, 107, 169, 177, 117 }, { 63, 110, 174, 178, 122 },
1380 { 64, 111, 175, 179, 123 }, { 65, 118, 180, 184, 124 },
1381 { 66, 119, 181, 185, 125 }, { 67, 120, 182, 186, 126 },
1382 { 68, 121, 183, 187, 127 }, { 69, 128, 188, 189, 129 },
1383 { 70, 72, 76, 77, 73 }, { 70, 72, 132, 190, 130 },
1384 { 70, 73, 133, 191, 130 }, { 71, 74, 82, 83, 75 },
1385 { 71, 74, 134, 192, 131 }, { 71, 75, 135, 193, 131 },
1386 { 72, 76, 140, 196, 132 }, { 73, 77, 141, 197, 133 },
1387 { 74, 82, 142, 198, 134 }, { 75, 83, 143, 199, 135 },
1388 { 76, 77, 141, 200, 140 }, { 78, 80, 86, 90, 84 },
1389 { 78, 80, 138, 194, 136 }, { 78, 84, 146, 201, 136 },
1390 { 79, 81, 87, 91, 85 }, { 79, 81, 139, 195, 137 },
1391 { 79, 85, 147, 202, 137 }, { 80, 86, 148, 203, 138 },
1392 { 81, 87, 149, 204, 139 }, { 82, 83, 143, 205, 142 },
1393 { 84, 90, 156, 212, 146 }, { 85, 91, 157, 213, 147 },
1394 { 86, 90, 156, 214, 148 }, { 87, 91, 157, 215, 149 },
1395 { 88, 94, 102, 106, 98 }, { 88, 94, 152, 206, 144 },
1396 { 88, 98, 158, 210, 144 }, { 89, 95, 103, 107, 99 },
1397 { 89, 95, 153, 207, 145 }, { 89, 99, 159, 211, 145 },
1398 { 92, 96, 104, 110, 100 }, { 92, 96, 154, 208, 150 },
1399 { 92, 100, 160, 216, 150 }, { 93, 97, 105, 111, 101 },
1400 { 93, 97, 155, 209, 151 }, { 93, 101, 161, 217, 151 },
1401 { 94, 102, 164, 218, 152 }, { 95, 103, 165, 219, 153 },
1402 { 96, 104, 166, 220, 154 }, { 97, 105, 167, 221, 155 },
1403 { 98, 106, 168, 222, 158 }, { 99, 107, 169, 223, 159 },
1404 { 100, 110, 174, 228, 160 }, { 101, 111, 175, 229, 161 },
1405 { 102, 106, 168, 230, 164 }, { 103, 107, 169, 231, 165 },
1406 { 104, 110, 174, 232, 166 }, { 105, 111, 175, 233, 167 },
1407 { 108, 112, 118, 120, 114 }, { 108, 112, 170, 224, 162 },
1408 { 108, 114, 172, 226, 162 }, { 109, 113, 119, 121, 115 },
1409 { 109, 113, 171, 225, 163 }, { 109, 115, 173, 227, 163 },
1410 { 112, 118, 180, 235, 170 }, { 113, 119, 181, 236, 171 },
1411 { 114, 120, 182, 237, 172 }, { 115, 121, 183, 238, 173 },
1412 { 116, 117, 125, 128, 124 }, { 116, 117, 177, 234, 176 },
1413 { 116, 124, 184, 240, 176 }, { 117, 125, 185, 241, 177 },
1414 { 118, 120, 182, 244, 180 }, { 119, 121, 183, 245, 181 },
1415 { 122, 123, 127, 129, 126 }, { 122, 123, 179, 239, 178 },
1416 { 122, 126, 186, 242, 178 }, { 123, 127, 187, 243, 179 },
1417 { 124, 128, 188, 246, 184 }, { 125, 128, 188, 247, 185 },
1418 { 126, 129, 189, 248, 186 }, { 127, 129, 189, 249, 187 },
1419 { 130, 131, 192, 250, 190 }, { 130, 131, 193, 251, 191 },
1420 { 130, 190, 270, 271, 191 }, { 131, 192, 272, 273, 193 },
1421 { 132, 136, 194, 250, 190 }, { 132, 136, 201, 252, 196 },
1422 { 132, 190, 270, 274, 196 }, { 133, 137, 195, 251, 191 },
1423 { 133, 137, 202, 253, 197 }, { 133, 191, 271, 275, 197 },
1424 { 134, 138, 194, 250, 192 }, { 134, 138, 203, 254, 198 },
1425 { 134, 192, 272, 276, 198 }, { 135, 139, 195, 251, 193 },
1426 { 135, 139, 204, 255, 199 }, { 135, 193, 273, 277, 199 },
1427 { 136, 194, 279, 282, 201 }, { 137, 195, 280, 283, 202 },
1428 { 138, 194, 279, 284, 203 }, { 139, 195, 280, 285, 204 },
1429 { 140, 144, 206, 252, 196 }, { 140, 144, 210, 256, 200 },
1430 { 140, 196, 274, 278, 200 }, { 141, 145, 207, 253, 197 },
1431 { 141, 145, 211, 256, 200 }, { 141, 197, 275, 278, 200 },
1432 { 142, 150, 208, 254, 198 }, { 142, 150, 216, 257, 205 },
1433 { 142, 198, 276, 281, 205 }, { 143, 151, 209, 255, 199 },
1434 { 143, 151, 217, 257, 205 }, { 143, 199, 277, 281, 205 },
1435 { 144, 206, 290, 294, 210 }, { 145, 207, 291, 295, 211 },
1436 { 146, 152, 206, 252, 201 }, { 146, 152, 218, 258, 212 },
1437 { 146, 201, 282, 286, 212 }, { 147, 153, 207, 253, 202 },
1438 { 147, 153, 219, 259, 213 }, { 147, 202, 283, 287, 213 },
1439 { 148, 154, 208, 254, 203 }, { 148, 154, 220, 260, 214 },
1440 { 148, 203, 284, 288, 214 }, { 149, 155, 209, 255, 204 },
1441 { 149, 155, 221, 261, 215 }, { 149, 204, 285, 289, 215 },
1442 { 150, 208, 292, 296, 216 }, { 151, 209, 293, 297, 217 },
1443 { 152, 206, 290, 298, 218 }, { 153, 207, 291, 299, 219 },
1444 { 154, 208, 292, 300, 220 }, { 155, 209, 293, 301, 221 },
1445 { 156, 162, 224, 258, 212 }, { 156, 162, 226, 260, 214 },
1446 { 156, 212, 286, 288, 214 }, { 157, 163, 225, 259, 213 },
1447 { 157, 163, 227, 261, 215 }, { 157, 213, 287, 289, 215 },
1448 { 158, 159, 211, 256, 210 }, { 158, 159, 223, 262, 222 },
1449 { 158, 210, 294, 302, 222 }, { 159, 211, 295, 303, 223 },
1450 { 160, 161, 217, 257, 216 }, { 160, 161, 229, 263, 228 },
1451 { 160, 216, 296, 304, 228 }, { 161, 217, 297, 305, 229 },
1452 { 162, 224, 310, 312, 226 }, { 163, 225, 311, 313, 227 },
1453 { 164, 170, 224, 258, 218 }, { 164, 170, 235, 264, 230 },
1454 { 164, 218, 298, 306, 230 }, { 165, 171, 225, 259, 219 },
1455 { 165, 171, 236, 265, 231 }, { 165, 219, 299, 307, 231 },
1456 { 166, 172, 226, 260, 220 }, { 166, 172, 237, 266, 232 },
1457 { 166, 220, 300, 308, 232 }, { 167, 173, 227, 261, 221 },
1458 { 167, 173, 238, 267, 233 }, { 167, 221, 301, 309, 233 },
1459 { 168, 176, 234, 262, 222 }, { 168, 176, 240, 264, 230 },
1460 { 168, 222, 302, 306, 230 }, { 169, 177, 234, 262, 223 },
1461 { 169, 177, 241, 265, 231 }, { 169, 223, 303, 307, 231 },
1462 { 170, 224, 310, 314, 235 }, { 171, 225, 311, 315, 236 },
1463 { 172, 226, 312, 316, 237 }, { 173, 227, 313, 317, 238 },
1464 { 174, 178, 239, 263, 228 }, { 174, 178, 242, 266, 232 },
1465 { 174, 228, 304, 308, 232 }, { 175, 179, 239, 263, 229 },
1466 { 175, 179, 243, 267, 233 }, { 175, 229, 305, 309, 233 },
1467 { 176, 234, 318, 322, 240 }, { 177, 234, 318, 323, 241 },
1468 { 178, 239, 321, 324, 242 }, { 179, 239, 321, 325, 243 },
1469 { 180, 184, 240, 264, 235 }, { 180, 184, 246, 268, 244 },
1470 { 180, 235, 314, 319, 244 }, { 181, 185, 241, 265, 236 },
1471 { 181, 185, 247, 269, 245 }, { 181, 236, 315, 320, 245 },
1472 { 182, 186, 242, 266, 237 }, { 182, 186, 248, 268, 244 },
1473 { 182, 237, 316, 319, 244 }, { 183, 187, 243, 267, 238 },
1474 { 183, 187, 249, 269, 245 }, { 183, 238, 317, 320, 245 },
1475 { 184, 240, 322, 326, 246 }, { 185, 241, 323, 327, 247 },
1476 { 186, 242, 324, 328, 248 }, { 187, 243, 325, 329, 249 },
1477 { 188, 189, 248, 268, 246 }, { 188, 189, 249, 269, 247 },
1478 { 188, 246, 326, 327, 247 }, { 189, 248, 328, 329, 249 },
1479 { 190, 250, 330, 350, 270 }, { 191, 251, 331, 351, 271 },
1480 { 192, 250, 330, 352, 272 }, { 193, 251, 331, 353, 273 },
1481 { 194, 250, 330, 354, 279 }, { 195, 251, 331, 355, 280 },
1482 { 196, 252, 332, 356, 274 }, { 197, 253, 333, 357, 275 },
1483 { 198, 254, 334, 358, 276 }, { 199, 255, 335, 359, 277 },
1484 { 200, 256, 336, 360, 278 }, { 201, 252, 332, 361, 282 },
1485 { 202, 253, 333, 362, 283 }, { 203, 254, 334, 363, 284 },
1486 { 204, 255, 335, 364, 285 }, { 205, 257, 337, 365, 281 },
1487 { 206, 252, 332, 366, 290 }, { 207, 253, 333, 367, 291 },
1488 { 208, 254, 334, 368, 292 }, { 209, 255, 335, 369, 293 },
1489 { 210, 256, 336, 370, 294 }, { 211, 256, 336, 371, 295 },
1490 { 212, 258, 338, 372, 286 }, { 213, 259, 339, 373, 287 },
1491 { 214, 260, 340, 374, 288 }, { 215, 261, 341, 375, 289 },
1492 { 216, 257, 337, 376, 296 }, { 217, 257, 337, 377, 297 },
1493 { 218, 258, 338, 378, 298 }, { 219, 259, 339, 379, 299 },
1494 { 220, 260, 340, 380, 300 }, { 221, 261, 341, 381, 301 },
1495 { 222, 262, 342, 382, 302 }, { 223, 262, 342, 383, 303 },
1496 { 224, 258, 338, 384, 310 }, { 225, 259, 339, 385, 311 },
1497 { 226, 260, 340, 386, 312 }, { 227, 261, 341, 387, 313 },
1498 { 228, 263, 343, 388, 304 }, { 229, 263, 343, 389, 305 },
1499 { 230, 264, 344, 390, 306 }, { 231, 265, 345, 391, 307 },
1500 { 232, 266, 346, 392, 308 }, { 233, 267, 347, 393, 309 },
1501 { 234, 262, 342, 394, 318 }, { 235, 264, 344, 395, 314 },
1502 { 236, 265, 345, 396, 315 }, { 237, 266, 346, 397, 316 },
1503 { 238, 267, 347, 398, 317 }, { 239, 263, 343, 399, 321 },
1504 { 240, 264, 344, 400, 322 }, { 241, 265, 345, 401, 323 },
1505 { 242, 266, 346, 402, 324 }, { 243, 267, 347, 403, 325 },
1506 { 244, 268, 348, 404, 319 }, { 245, 269, 349, 405, 320 },
1507 { 246, 268, 348, 406, 326 }, { 247, 269, 349, 407, 327 },
1508 { 248, 268, 348, 408, 328 }, { 249, 269, 349, 409, 329 },
1509 { 270, 271, 275, 278, 274 }, { 270, 271, 351, 410, 350 },
1510 { 270, 274, 356, 412, 350 }, { 271, 275, 357, 413, 351 },
1511 { 272, 273, 277, 281, 276 }, { 272, 273, 353, 411, 352 },
1512 { 272, 276, 358, 414, 352 }, { 273, 277, 359, 415, 353 },
1513 { 274, 278, 360, 420, 356 }, { 275, 278, 360, 421, 357 },
1514 { 276, 281, 365, 422, 358 }, { 277, 281, 365, 423, 359 },
1515 { 279, 282, 286, 288, 284 }, { 279, 282, 361, 416, 354 },
1516 { 279, 284, 363, 418, 354 }, { 280, 283, 287, 289, 285 },
1517 { 280, 283, 362, 417, 355 }, { 280, 285, 364, 419, 355 },
1518 { 282, 286, 372, 426, 361 }, { 283, 287, 373, 427, 362 },
1519 { 284, 288, 374, 428, 363 }, { 285, 289, 375, 429, 364 },
1520 { 286, 288, 374, 436, 372 }, { 287, 289, 375, 437, 373 },
1521 { 290, 294, 302, 306, 298 }, { 290, 294, 370, 424, 366 },
1522 { 290, 298, 378, 432, 366 }, { 291, 295, 303, 307, 299 },
1523 { 291, 295, 371, 425, 367 }, { 291, 299, 379, 433, 367 },
1524 { 292, 296, 304, 308, 300 }, { 292, 296, 376, 430, 368 },
1525 { 292, 300, 380, 434, 368 }, { 293, 297, 305, 309, 301 },
1526 { 293, 297, 377, 431, 369 }, { 293, 301, 381, 435, 369 },
1527 { 294, 302, 382, 438, 370 }, { 295, 303, 383, 439, 371 },
1528 { 296, 304, 388, 440, 376 }, { 297, 305, 389, 441, 377 },
1529 { 298, 306, 390, 444, 378 }, { 299, 307, 391, 445, 379 },
1530 { 300, 308, 392, 446, 380 }, { 301, 309, 393, 447, 381 },
1531 { 302, 306, 390, 448, 382 }, { 303, 307, 391, 449, 383 },
1532 { 304, 308, 392, 454, 388 }, { 305, 309, 393, 455, 389 },
1533 { 310, 312, 316, 319, 314 }, { 310, 312, 386, 442, 384 },
1534 { 310, 314, 395, 450, 384 }, { 311, 313, 317, 320, 315 },
1535 { 311, 313, 387, 443, 385 }, { 311, 315, 396, 451, 385 },
1536 { 312, 316, 397, 452, 386 }, { 313, 317, 398, 453, 387 },
1537 { 314, 319, 404, 460, 395 }, { 315, 320, 405, 461, 396 },
1538 { 316, 319, 404, 462, 397 }, { 317, 320, 405, 463, 398 },
1539 { 318, 322, 326, 327, 323 }, { 318, 322, 400, 456, 394 },
1540 { 318, 323, 401, 457, 394 }, { 321, 324, 328, 329, 325 },
1541 { 321, 324, 402, 458, 399 }, { 321, 325, 403, 459, 399 },
1542 { 322, 326, 406, 464, 400 }, { 323, 327, 407, 465, 401 },
1543 { 324, 328, 408, 466, 402 }, { 325, 329, 409, 467, 403 },
1544 { 326, 327, 407, 468, 406 }, { 328, 329, 409, 469, 408 },
1545 { 330, 350, 410, 411, 352 }, { 330, 350, 412, 416, 354 },
1546 { 330, 352, 414, 418, 354 }, { 331, 351, 410, 411, 353 },
1547 { 331, 351, 413, 417, 355 }, { 331, 353, 415, 419, 355 },
1548 { 332, 356, 412, 416, 361 }, { 332, 356, 420, 424, 366 },
1549 { 332, 361, 426, 432, 366 }, { 333, 357, 413, 417, 362 },
1550 { 333, 357, 421, 425, 367 }, { 333, 362, 427, 433, 367 },
1551 { 334, 358, 414, 418, 363 }, { 334, 358, 422, 430, 368 },
1552 { 334, 363, 428, 434, 368 }, { 335, 359, 415, 419, 364 },
1553 { 335, 359, 423, 431, 369 }, { 335, 364, 429, 435, 369 },
1554 { 336, 360, 420, 424, 370 }, { 336, 360, 421, 425, 371 },
1555 { 336, 370, 438, 439, 371 }, { 337, 365, 422, 430, 376 },
1556 { 337, 365, 423, 431, 377 }, { 337, 376, 440, 441, 377 },
1557 { 338, 372, 426, 432, 378 }, { 338, 372, 436, 442, 384 },
1558 { 338, 378, 444, 450, 384 }, { 339, 373, 427, 433, 379 },
1559 { 339, 373, 437, 443, 385 }, { 339, 379, 445, 451, 385 },
1560 { 340, 374, 428, 434, 380 }, { 340, 374, 436, 442, 386 },
1561 { 340, 380, 446, 452, 386 }, { 341, 375, 429, 435, 381 },
1562 { 341, 375, 437, 443, 387 }, { 341, 381, 447, 453, 387 },
1563 { 342, 382, 438, 439, 383 }, { 342, 382, 448, 456, 394 },
1564 { 342, 383, 449, 457, 394 }, { 343, 388, 440, 441, 389 },
1565 { 343, 388, 454, 458, 399 }, { 343, 389, 455, 459, 399 },
1566 { 344, 390, 444, 450, 395 }, { 344, 390, 448, 456, 400 },
1567 { 344, 395, 460, 464, 400 }, { 345, 391, 445, 451, 396 },
1568 { 345, 391, 449, 457, 401 }, { 345, 396, 461, 465, 401 },
1569 { 346, 392, 446, 452, 397 }, { 346, 392, 454, 458, 402 },
1570 { 346, 397, 462, 466, 402 }, { 347, 393, 447, 453, 398 },
1571 { 347, 393, 455, 459, 403 }, { 347, 398, 463, 467, 403 },
1572 { 348, 404, 460, 464, 406 }, { 348, 404, 462, 466, 408 },
1573 { 348, 406, 468, 469, 408 }, { 349, 405, 461, 465, 407 },
1574 { 349, 405, 463, 467, 409 }, { 349, 407, 468, 469, 409 },
1575 { 350, 410, 470, 472, 412 }, { 351, 410, 470, 473, 413 },
1576 { 352, 411, 471, 474, 414 }, { 353, 411, 471, 475, 415 },
1577 { 354, 416, 478, 480, 418 }, { 355, 417, 479, 481, 419 },
1578 { 356, 412, 472, 476, 420 }, { 357, 413, 473, 477, 421 },
1579 { 358, 414, 474, 482, 422 }, { 359, 415, 475, 483, 423 },
1580 { 360, 420, 476, 477, 421 }, { 361, 416, 478, 484, 426 },
1581 { 362, 417, 479, 485, 427 }, { 363, 418, 480, 486, 428 },
1582 { 364, 419, 481, 487, 429 }, { 365, 422, 482, 483, 423 },
1583 { 366, 424, 488, 494, 432 }, { 367, 425, 489, 495, 433 },
1584 { 368, 430, 492, 496, 434 }, { 369, 431, 493, 497, 435 },
1585 { 370, 424, 488, 498, 438 }, { 371, 425, 489, 499, 439 },
1586 { 372, 426, 484, 490, 436 }, { 373, 427, 485, 491, 437 },
1587 { 374, 428, 486, 490, 436 }, { 375, 429, 487, 491, 437 },
1588 { 376, 430, 492, 500, 440 }, { 377, 431, 493, 501, 441 },
1589 { 378, 432, 494, 502, 444 }, { 379, 433, 495, 503, 445 },
1590 { 380, 434, 496, 504, 446 }, { 381, 435, 497, 505, 447 },
1591 { 382, 438, 498, 506, 448 }, { 383, 439, 499, 507, 449 },
1592 { 384, 442, 508, 512, 450 }, { 385, 443, 509, 513, 451 },
1593 { 386, 442, 508, 514, 452 }, { 387, 443, 509, 515, 453 },
1594 { 388, 440, 500, 510, 454 }, { 389, 441, 501, 511, 455 },
1595 { 390, 444, 502, 506, 448 }, { 391, 445, 503, 507, 449 },
1596 { 392, 446, 504, 510, 454 }, { 393, 447, 505, 511, 455 },
1597 { 394, 456, 516, 517, 457 }, { 395, 450, 512, 518, 460 },
1598 { 396, 451, 513, 519, 461 }, { 397, 452, 514, 520, 462 },
1599 { 398, 453, 515, 521, 463 }, { 399, 458, 522, 523, 459 },
1600 { 400, 456, 516, 524, 464 }, { 401, 457, 517, 525, 465 },
1601 { 402, 458, 522, 526, 466 }, { 403, 459, 523, 527, 467 },
1602 { 404, 460, 518, 520, 462 }, { 405, 461, 519, 521, 463 },
1603 { 406, 464, 524, 528, 468 }, { 407, 465, 525, 528, 468 },
1604 { 408, 466, 526, 529, 469 }, { 409, 467, 527, 529, 469 },
1605 { 410, 411, 471, 530, 470 }, { 412, 416, 478, 531, 472 },
1606 { 413, 417, 479, 532, 473 }, { 414, 418, 480, 533, 474 },
1607 { 415, 419, 481, 534, 475 }, { 420, 424, 488, 535, 476 },
1608 { 421, 425, 489, 536, 477 }, { 422, 430, 492, 537, 482 },
1609 { 423, 431, 493, 538, 483 }, { 426, 432, 494, 539, 484 },
1610 { 427, 433, 495, 540, 485 }, { 428, 434, 496, 541, 486 },
1611 { 429, 435, 497, 542, 487 }, { 436, 442, 508, 544, 490 },
1612 { 437, 443, 509, 545, 491 }, { 438, 439, 499, 543, 498 },
1613 { 440, 441, 501, 546, 500 }, { 444, 450, 512, 547, 502 },
1614 { 445, 451, 513, 548, 503 }, { 446, 452, 514, 549, 504 },
1615 { 447, 453, 515, 550, 505 }, { 448, 456, 516, 551, 506 },
1616 { 449, 457, 517, 552, 507 }, { 454, 458, 522, 553, 510 },
1617 { 455, 459, 523, 554, 511 }, { 460, 464, 524, 555, 518 },
1618 { 461, 465, 525, 556, 519 }, { 462, 466, 526, 557, 520 },
1619 { 463, 467, 527, 558, 521 }, { 468, 469, 529, 559, 528 },
1620 { 470, 472, 476, 477, 473 }, { 470, 472, 531, 560, 530 },
1621 { 470, 473, 532, 561, 530 }, { 471, 474, 482, 483, 475 },
1622 { 471, 474, 533, 560, 530 }, { 471, 475, 534, 561, 530 },
1623 { 472, 476, 535, 562, 531 }, { 473, 477, 536, 563, 532 },
1624 { 474, 482, 537, 564, 533 }, { 475, 483, 538, 565, 534 },
1625 { 476, 477, 536, 566, 535 }, { 478, 480, 486, 490, 484 },
1626 { 478, 480, 533, 560, 531 }, { 478, 484, 539, 562, 531 },
1627 { 479, 481, 487, 491, 485 }, { 479, 481, 534, 561, 532 },
1628 { 479, 485, 540, 563, 532 }, { 480, 486, 541, 564, 533 },
1629 { 481, 487, 542, 565, 534 }, { 482, 483, 538, 567, 537 },
1630 { 484, 490, 544, 568, 539 }, { 485, 491, 545, 569, 540 },
1631 { 486, 490, 544, 570, 541 }, { 487, 491, 545, 571, 542 },
1632 { 488, 494, 502, 506, 498 }, { 488, 494, 539, 562, 535 },
1633 { 488, 498, 543, 566, 535 }, { 489, 495, 503, 507, 499 },
1634 { 489, 495, 540, 563, 536 }, { 489, 499, 543, 566, 536 },
1635 { 492, 496, 504, 510, 500 }, { 492, 496, 541, 564, 537 },
1636 { 492, 500, 546, 567, 537 }, { 493, 497, 505, 511, 501 },
1637 { 493, 497, 542, 565, 538 }, { 493, 501, 546, 567, 538 },
1638 { 494, 502, 547, 568, 539 }, { 495, 503, 548, 569, 540 },
1639 { 496, 504, 549, 570, 541 }, { 497, 505, 550, 571, 542 },
1640 { 498, 506, 551, 572, 543 }, { 499, 507, 552, 572, 543 },
1641 { 500, 510, 553, 573, 546 }, { 501, 511, 554, 573, 546 },
1642 { 502, 506, 551, 574, 547 }, { 503, 507, 552, 575, 548 },
1643 { 504, 510, 553, 576, 549 }, { 505, 511, 554, 577, 550 },
1644 { 508, 512, 518, 520, 514 }, { 508, 512, 547, 568, 544 },
1645 { 508, 514, 549, 570, 544 }, { 509, 513, 519, 521, 515 },
1646 { 509, 513, 548, 569, 545 }, { 509, 515, 550, 571, 545 },
1647 { 512, 518, 555, 574, 547 }, { 513, 519, 556, 575, 548 },
1648 { 514, 520, 557, 576, 549 }, { 515, 521, 558, 577, 550 },
1649 { 516, 517, 525, 528, 524 }, { 516, 517, 552, 572, 551 },
1650 { 516, 524, 555, 574, 551 }, { 517, 525, 556, 575, 552 },
1651 { 518, 520, 557, 578, 555 }, { 519, 521, 558, 579, 556 },
1652 { 522, 523, 527, 529, 526 }, { 522, 523, 554, 573, 553 },
1653 { 522, 526, 557, 576, 553 }, { 523, 527, 558, 577, 554 },
1654 { 524, 528, 559, 578, 555 }, { 525, 528, 559, 579, 556 },
1655 { 526, 529, 559, 578, 557 }, { 527, 529, 559, 579, 558 },
1656 { 530, 560, 580, 581, 561 }, { 531, 560, 580, 582, 562 },
1657 { 532, 561, 581, 583, 563 }, { 533, 560, 580, 584, 564 },
1658 { 534, 561, 581, 585, 565 }, { 535, 562, 582, 586, 566 },
1659 { 536, 563, 583, 586, 566 }, { 537, 564, 584, 587, 567 },
1660 { 538, 565, 585, 587, 567 }, { 539, 562, 582, 588, 568 },
1661 { 540, 563, 583, 589, 569 }, { 541, 564, 584, 590, 570 },
1662 { 542, 565, 585, 591, 571 }, { 543, 566, 586, 592, 572 },
1663 { 544, 568, 588, 590, 570 }, { 545, 569, 589, 591, 571 },
1664 { 546, 567, 587, 593, 573 }, { 547, 568, 588, 594, 574 },
1665 { 548, 569, 589, 595, 575 }, { 549, 570, 590, 596, 576 },
1666 { 550, 571, 591, 597, 577 }, { 551, 572, 592, 594, 574 },
1667 { 552, 572, 592, 595, 575 }, { 553, 573, 593, 596, 576 },
1668 { 554, 573, 593, 597, 577 }, { 555, 574, 594, 598, 578 },
1669 { 556, 575, 595, 599, 579 }, { 557, 576, 596, 598, 578 },
1670 { 558, 577, 597, 599, 579 }, { 559, 578, 598, 599, 579 },
1671 { 580, 581, 583, 586, 582 }, { 580, 581, 585, 587, 584 },
1672 { 580, 582, 588, 590, 584 }, { 581, 583, 589, 591, 585 },
1673 { 582, 586, 592, 594, 588 }, { 583, 586, 592, 595, 589 },
1674 { 584, 587, 593, 596, 590 }, { 585, 587, 593, 597, 591 },
1675 { 588, 590, 596, 598, 594 }, { 589, 591, 597, 599, 595 },
1676 { 592, 594, 598, 599, 595 }, { 593, 596, 598, 599, 597 }
1681 static const float vert_600[NUM_VERT_600][4] = {
1682 { 0.0, 0.0, 0.0, -2.0 },
1683 { 0.0, -GOLDENINV, -1.0, -GOLDEN },
1684 { 0.0, GOLDENINV, -1.0, -GOLDEN },
1685 { -1.0, 0.0, -GOLDENINV, -GOLDEN },
1686 { 1.0, 0.0, -GOLDENINV, -GOLDEN },
1687 { -GOLDENINV, -1.0, 0.0, -GOLDEN },
1688 { GOLDENINV, -1.0, 0.0, -GOLDEN },
1689 { -GOLDENINV, 1.0, 0.0, -GOLDEN },
1690 { GOLDENINV, 1.0, 0.0, -GOLDEN },
1691 { -1.0, 0.0, GOLDENINV, -GOLDEN },
1692 { 1.0, 0.0, GOLDENINV, -GOLDEN },
1693 { 0.0, -GOLDENINV, 1.0, -GOLDEN },
1694 { 0.0, GOLDENINV, 1.0, -GOLDEN },
1695 { -GOLDENINV, 0.0, -GOLDEN, -1.0 },
1696 { GOLDENINV, 0.0, -GOLDEN, -1.0 },
1697 { -1.0, -1.0, -1.0, -1.0 },
1698 { 1.0, -1.0, -1.0, -1.0 },
1699 { -1.0, 1.0, -1.0, -1.0 },
1700 { 1.0, 1.0, -1.0, -1.0 },
1701 { 0.0, -GOLDEN, -GOLDENINV, -1.0 },
1702 { 0.0, GOLDEN, -GOLDENINV, -1.0 },
1703 { -GOLDEN, -GOLDENINV, 0.0, -1.0 },
1704 { GOLDEN, -GOLDENINV, 0.0, -1.0 },
1705 { -GOLDEN, GOLDENINV, 0.0, -1.0 },
1706 { GOLDEN, GOLDENINV, 0.0, -1.0 },
1707 { 0.0, -GOLDEN, GOLDENINV, -1.0 },
1708 { 0.0, GOLDEN, GOLDENINV, -1.0 },
1709 { -1.0, -1.0, 1.0, -1.0 },
1710 { 1.0, -1.0, 1.0, -1.0 },
1711 { -1.0, 1.0, 1.0, -1.0 },
1712 { 1.0, 1.0, 1.0, -1.0 },
1713 { -GOLDENINV, 0.0, GOLDEN, -1.0 },
1714 { GOLDENINV, 0.0, GOLDEN, -1.0 },
1715 { 0.0, -1.0, -GOLDEN, -GOLDENINV },
1716 { 0.0, 1.0, -GOLDEN, -GOLDENINV },
1717 { -GOLDEN, 0.0, -1.0, -GOLDENINV },
1718 { GOLDEN, 0.0, -1.0, -GOLDENINV },
1719 { -1.0, -GOLDEN, 0.0, -GOLDENINV },
1720 { 1.0, -GOLDEN, 0.0, -GOLDENINV },
1721 { -1.0, GOLDEN, 0.0, -GOLDENINV },
1722 { 1.0, GOLDEN, 0.0, -GOLDENINV },
1723 { -GOLDEN, 0.0, 1.0, -GOLDENINV },
1724 { GOLDEN, 0.0, 1.0, -GOLDENINV },
1725 { 0.0, -1.0, GOLDEN, -GOLDENINV },
1726 { 0.0, 1.0, GOLDEN, -GOLDENINV },
1727 { 0.0, 0.0, -2.0, 0.0 },
1728 { -1.0, -GOLDENINV, -GOLDEN, 0.0 },
1729 { 1.0, -GOLDENINV, -GOLDEN, 0.0 },
1730 { -1.0, GOLDENINV, -GOLDEN, 0.0 },
1731 { 1.0, GOLDENINV, -GOLDEN, 0.0 },
1732 { -GOLDENINV, -GOLDEN, -1.0, 0.0 },
1733 { GOLDENINV, -GOLDEN, -1.0, 0.0 },
1734 { -GOLDENINV, GOLDEN, -1.0, 0.0 },
1735 { GOLDENINV, GOLDEN, -1.0, 0.0 },
1736 { -GOLDEN, -1.0, -GOLDENINV, 0.0 },
1737 { GOLDEN, -1.0, -GOLDENINV, 0.0 },
1738 { -GOLDEN, 1.0, -GOLDENINV, 0.0 },
1739 { GOLDEN, 1.0, -GOLDENINV, 0.0 },
1740 { 0.0, -2.0, 0.0, 0.0 },
1741 { -2.0, 0.0, 0.0, 0.0 },
1742 { 2.0, 0.0, 0.0, 0.0 },
1743 { 0.0, 2.0, 0.0, 0.0 },
1744 { -GOLDEN, -1.0, GOLDENINV, 0.0 },
1745 { GOLDEN, -1.0, GOLDENINV, 0.0 },
1746 { -GOLDEN, 1.0, GOLDENINV, 0.0 },
1747 { GOLDEN, 1.0, GOLDENINV, 0.0 },
1748 { -GOLDENINV, -GOLDEN, 1.0, 0.0 },
1749 { GOLDENINV, -GOLDEN, 1.0, 0.0 },
1750 { -GOLDENINV, GOLDEN, 1.0, 0.0 },
1751 { GOLDENINV, GOLDEN, 1.0, 0.0 },
1752 { -1.0, -GOLDENINV, GOLDEN, 0.0 },
1753 { 1.0, -GOLDENINV, GOLDEN, 0.0 },
1754 { -1.0, GOLDENINV, GOLDEN, 0.0 },
1755 { 1.0, GOLDENINV, GOLDEN, 0.0 },
1756 { 0.0, 0.0, 2.0, 0.0 },
1757 { 0.0, -1.0, -GOLDEN, GOLDENINV },
1758 { 0.0, 1.0, -GOLDEN, GOLDENINV },
1759 { -GOLDEN, 0.0, -1.0, GOLDENINV },
1760 { GOLDEN, 0.0, -1.0, GOLDENINV },
1761 { -1.0, -GOLDEN, 0.0, GOLDENINV },
1762 { 1.0, -GOLDEN, 0.0, GOLDENINV },
1763 { -1.0, GOLDEN, 0.0, GOLDENINV },
1764 { 1.0, GOLDEN, 0.0, GOLDENINV },
1765 { -GOLDEN, 0.0, 1.0, GOLDENINV },
1766 { GOLDEN, 0.0, 1.0, GOLDENINV },
1767 { 0.0, -1.0, GOLDEN, GOLDENINV },
1768 { 0.0, 1.0, GOLDEN, GOLDENINV },
1769 { -GOLDENINV, 0.0, -GOLDEN, 1.0 },
1770 { GOLDENINV, 0.0, -GOLDEN, 1.0 },
1771 { -1.0, -1.0, -1.0, 1.0 },
1772 { 1.0, -1.0, -1.0, 1.0 },
1773 { -1.0, 1.0, -1.0, 1.0 },
1774 { 1.0, 1.0, -1.0, 1.0 },
1775 { 0.0, -GOLDEN, -GOLDENINV, 1.0 },
1776 { 0.0, GOLDEN, -GOLDENINV, 1.0 },
1777 { -GOLDEN, -GOLDENINV, 0.0, 1.0 },
1778 { GOLDEN, -GOLDENINV, 0.0, 1.0 },
1779 { -GOLDEN, GOLDENINV, 0.0, 1.0 },
1780 { GOLDEN, GOLDENINV, 0.0, 1.0 },
1781 { 0.0, -GOLDEN, GOLDENINV, 1.0 },
1782 { 0.0, GOLDEN, GOLDENINV, 1.0 },
1783 { -1.0, -1.0, 1.0, 1.0 },
1784 { 1.0, -1.0, 1.0, 1.0 },
1785 { -1.0, 1.0, 1.0, 1.0 },
1786 { 1.0, 1.0, 1.0, 1.0 },
1787 { -GOLDENINV, 0.0, GOLDEN, 1.0 },
1788 { GOLDENINV, 0.0, GOLDEN, 1.0 },
1789 { 0.0, -GOLDENINV, -1.0, GOLDEN },
1790 { 0.0, GOLDENINV, -1.0, GOLDEN },
1791 { -1.0, 0.0, -GOLDENINV, GOLDEN },
1792 { 1.0, 0.0, -GOLDENINV, GOLDEN },
1793 { -GOLDENINV, -1.0, 0.0, GOLDEN },
1794 { GOLDENINV, -1.0, 0.0, GOLDEN },
1795 { -GOLDENINV, 1.0, 0.0, GOLDEN },
1796 { GOLDENINV, 1.0, 0.0, GOLDEN },
1797 { -1.0, 0.0, GOLDENINV, GOLDEN },
1798 { 1.0, 0.0, GOLDENINV, GOLDEN },
1799 { 0.0, -GOLDENINV, 1.0, GOLDEN },
1800 { 0.0, GOLDENINV, 1.0, GOLDEN },
1801 { 0.0, 0.0, 0.0, 2.0 }
1804 static const int edge_600[NUM_EDGE_600][2] = {
1805 { 0, 1 }, { 0, 2 }, { 0, 3 }, { 0, 4 }, { 0, 5 },
1806 { 0, 6 }, { 0, 7 }, { 0, 8 }, { 0, 9 }, { 0, 10 },
1807 { 0, 11 }, { 0, 12 }, { 1, 2 }, { 1, 3 }, { 1, 4 },
1808 { 1, 5 }, { 1, 6 }, { 1, 13 }, { 1, 14 }, { 1, 15 },
1809 { 1, 16 }, { 1, 19 }, { 1, 33 }, { 2, 3 }, { 2, 4 },
1810 { 2, 7 }, { 2, 8 }, { 2, 13 }, { 2, 14 }, { 2, 17 },
1811 { 2, 18 }, { 2, 20 }, { 2, 34 }, { 3, 5 }, { 3, 7 },
1812 { 3, 9 }, { 3, 13 }, { 3, 15 }, { 3, 17 }, { 3, 21 },
1813 { 3, 23 }, { 3, 35 }, { 4, 6 }, { 4, 8 }, { 4, 10 },
1814 { 4, 14 }, { 4, 16 }, { 4, 18 }, { 4, 22 }, { 4, 24 },
1815 { 4, 36 }, { 5, 6 }, { 5, 9 }, { 5, 11 }, { 5, 15 },
1816 { 5, 19 }, { 5, 21 }, { 5, 25 }, { 5, 27 }, { 5, 37 },
1817 { 6, 10 }, { 6, 11 }, { 6, 16 }, { 6, 19 }, { 6, 22 },
1818 { 6, 25 }, { 6, 28 }, { 6, 38 }, { 7, 8 }, { 7, 9 },
1819 { 7, 12 }, { 7, 17 }, { 7, 20 }, { 7, 23 }, { 7, 26 },
1820 { 7, 29 }, { 7, 39 }, { 8, 10 }, { 8, 12 }, { 8, 18 },
1821 { 8, 20 }, { 8, 24 }, { 8, 26 }, { 8, 30 }, { 8, 40 },
1822 { 9, 11 }, { 9, 12 }, { 9, 21 }, { 9, 23 }, { 9, 27 },
1823 { 9, 29 }, { 9, 31 }, { 9, 41 }, { 10, 11 }, { 10, 12 },
1824 { 10, 22 }, { 10, 24 }, { 10, 28 }, { 10, 30 }, { 10, 32 },
1825 { 10, 42 }, { 11, 12 }, { 11, 25 }, { 11, 27 }, { 11, 28 },
1826 { 11, 31 }, { 11, 32 }, { 11, 43 }, { 12, 26 }, { 12, 29 },
1827 { 12, 30 }, { 12, 31 }, { 12, 32 }, { 12, 44 }, { 13, 14 },
1828 { 13, 15 }, { 13, 17 }, { 13, 33 }, { 13, 34 }, { 13, 35 },
1829 { 13, 45 }, { 13, 46 }, { 13, 48 }, { 14, 16 }, { 14, 18 },
1830 { 14, 33 }, { 14, 34 }, { 14, 36 }, { 14, 45 }, { 14, 47 },
1831 { 14, 49 }, { 15, 19 }, { 15, 21 }, { 15, 33 }, { 15, 35 },
1832 { 15, 37 }, { 15, 46 }, { 15, 50 }, { 15, 54 }, { 16, 19 },
1833 { 16, 22 }, { 16, 33 }, { 16, 36 }, { 16, 38 }, { 16, 47 },
1834 { 16, 51 }, { 16, 55 }, { 17, 20 }, { 17, 23 }, { 17, 34 },
1835 { 17, 35 }, { 17, 39 }, { 17, 48 }, { 17, 52 }, { 17, 56 },
1836 { 18, 20 }, { 18, 24 }, { 18, 34 }, { 18, 36 }, { 18, 40 },
1837 { 18, 49 }, { 18, 53 }, { 18, 57 }, { 19, 25 }, { 19, 33 },
1838 { 19, 37 }, { 19, 38 }, { 19, 50 }, { 19, 51 }, { 19, 58 },
1839 { 20, 26 }, { 20, 34 }, { 20, 39 }, { 20, 40 }, { 20, 52 },
1840 { 20, 53 }, { 20, 61 }, { 21, 23 }, { 21, 27 }, { 21, 35 },
1841 { 21, 37 }, { 21, 41 }, { 21, 54 }, { 21, 59 }, { 21, 62 },
1842 { 22, 24 }, { 22, 28 }, { 22, 36 }, { 22, 38 }, { 22, 42 },
1843 { 22, 55 }, { 22, 60 }, { 22, 63 }, { 23, 29 }, { 23, 35 },
1844 { 23, 39 }, { 23, 41 }, { 23, 56 }, { 23, 59 }, { 23, 64 },
1845 { 24, 30 }, { 24, 36 }, { 24, 40 }, { 24, 42 }, { 24, 57 },
1846 { 24, 60 }, { 24, 65 }, { 25, 27 }, { 25, 28 }, { 25, 37 },
1847 { 25, 38 }, { 25, 43 }, { 25, 58 }, { 25, 66 }, { 25, 67 },
1848 { 26, 29 }, { 26, 30 }, { 26, 39 }, { 26, 40 }, { 26, 44 },
1849 { 26, 61 }, { 26, 68 }, { 26, 69 }, { 27, 31 }, { 27, 37 },
1850 { 27, 41 }, { 27, 43 }, { 27, 62 }, { 27, 66 }, { 27, 70 },
1851 { 28, 32 }, { 28, 38 }, { 28, 42 }, { 28, 43 }, { 28, 63 },
1852 { 28, 67 }, { 28, 71 }, { 29, 31 }, { 29, 39 }, { 29, 41 },
1853 { 29, 44 }, { 29, 64 }, { 29, 68 }, { 29, 72 }, { 30, 32 },
1854 { 30, 40 }, { 30, 42 }, { 30, 44 }, { 30, 65 }, { 30, 69 },
1855 { 30, 73 }, { 31, 32 }, { 31, 41 }, { 31, 43 }, { 31, 44 },
1856 { 31, 70 }, { 31, 72 }, { 31, 74 }, { 32, 42 }, { 32, 43 },
1857 { 32, 44 }, { 32, 71 }, { 32, 73 }, { 32, 74 }, { 33, 45 },
1858 { 33, 46 }, { 33, 47 }, { 33, 50 }, { 33, 51 }, { 33, 75 },
1859 { 34, 45 }, { 34, 48 }, { 34, 49 }, { 34, 52 }, { 34, 53 },
1860 { 34, 76 }, { 35, 46 }, { 35, 48 }, { 35, 54 }, { 35, 56 },
1861 { 35, 59 }, { 35, 77 }, { 36, 47 }, { 36, 49 }, { 36, 55 },
1862 { 36, 57 }, { 36, 60 }, { 36, 78 }, { 37, 50 }, { 37, 54 },
1863 { 37, 58 }, { 37, 62 }, { 37, 66 }, { 37, 79 }, { 38, 51 },
1864 { 38, 55 }, { 38, 58 }, { 38, 63 }, { 38, 67 }, { 38, 80 },
1865 { 39, 52 }, { 39, 56 }, { 39, 61 }, { 39, 64 }, { 39, 68 },
1866 { 39, 81 }, { 40, 53 }, { 40, 57 }, { 40, 61 }, { 40, 65 },
1867 { 40, 69 }, { 40, 82 }, { 41, 59 }, { 41, 62 }, { 41, 64 },
1868 { 41, 70 }, { 41, 72 }, { 41, 83 }, { 42, 60 }, { 42, 63 },
1869 { 42, 65 }, { 42, 71 }, { 42, 73 }, { 42, 84 }, { 43, 66 },
1870 { 43, 67 }, { 43, 70 }, { 43, 71 }, { 43, 74 }, { 43, 85 },
1871 { 44, 68 }, { 44, 69 }, { 44, 72 }, { 44, 73 }, { 44, 74 },
1872 { 44, 86 }, { 45, 46 }, { 45, 47 }, { 45, 48 }, { 45, 49 },
1873 { 45, 75 }, { 45, 76 }, { 45, 87 }, { 45, 88 }, { 46, 48 },
1874 { 46, 50 }, { 46, 54 }, { 46, 75 }, { 46, 77 }, { 46, 87 },
1875 { 46, 89 }, { 47, 49 }, { 47, 51 }, { 47, 55 }, { 47, 75 },
1876 { 47, 78 }, { 47, 88 }, { 47, 90 }, { 48, 52 }, { 48, 56 },
1877 { 48, 76 }, { 48, 77 }, { 48, 87 }, { 48, 91 }, { 49, 53 },
1878 { 49, 57 }, { 49, 76 }, { 49, 78 }, { 49, 88 }, { 49, 92 },
1879 { 50, 51 }, { 50, 54 }, { 50, 58 }, { 50, 75 }, { 50, 79 },
1880 { 50, 89 }, { 50, 93 }, { 51, 55 }, { 51, 58 }, { 51, 75 },
1881 { 51, 80 }, { 51, 90 }, { 51, 93 }, { 52, 53 }, { 52, 56 },
1882 { 52, 61 }, { 52, 76 }, { 52, 81 }, { 52, 91 }, { 52, 94 },
1883 { 53, 57 }, { 53, 61 }, { 53, 76 }, { 53, 82 }, { 53, 92 },
1884 { 53, 94 }, { 54, 59 }, { 54, 62 }, { 54, 77 }, { 54, 79 },
1885 { 54, 89 }, { 54, 95 }, { 55, 60 }, { 55, 63 }, { 55, 78 },
1886 { 55, 80 }, { 55, 90 }, { 55, 96 }, { 56, 59 }, { 56, 64 },
1887 { 56, 77 }, { 56, 81 }, { 56, 91 }, { 56, 97 }, { 57, 60 },
1888 { 57, 65 }, { 57, 78 }, { 57, 82 }, { 57, 92 }, { 57, 98 },
1889 { 58, 66 }, { 58, 67 }, { 58, 79 }, { 58, 80 }, { 58, 93 },
1890 { 58, 99 }, { 59, 62 }, { 59, 64 }, { 59, 77 }, { 59, 83 },
1891 { 59, 95 }, { 59, 97 }, { 60, 63 }, { 60, 65 }, { 60, 78 },
1892 { 60, 84 }, { 60, 96 }, { 60, 98 }, { 61, 68 }, { 61, 69 },
1893 { 61, 81 }, { 61, 82 }, { 61, 94 }, { 61, 100 }, { 62, 66 },
1894 { 62, 70 }, { 62, 79 }, { 62, 83 }, { 62, 95 }, { 62, 101 },
1895 { 63, 67 }, { 63, 71 }, { 63, 80 }, { 63, 84 }, { 63, 96 },
1896 { 63, 102 }, { 64, 68 }, { 64, 72 }, { 64, 81 }, { 64, 83 },
1897 { 64, 97 }, { 64, 103 }, { 65, 69 }, { 65, 73 }, { 65, 82 },
1898 { 65, 84 }, { 65, 98 }, { 65, 104 }, { 66, 67 }, { 66, 70 },
1899 { 66, 79 }, { 66, 85 }, { 66, 99 }, { 66, 101 }, { 67, 71 },
1900 { 67, 80 }, { 67, 85 }, { 67, 99 }, { 67, 102 }, { 68, 69 },
1901 { 68, 72 }, { 68, 81 }, { 68, 86 }, { 68, 100 }, { 68, 103 },
1902 { 69, 73 }, { 69, 82 }, { 69, 86 }, { 69, 100 }, { 69, 104 },
1903 { 70, 72 }, { 70, 74 }, { 70, 83 }, { 70, 85 }, { 70, 101 },
1904 { 70, 105 }, { 71, 73 }, { 71, 74 }, { 71, 84 }, { 71, 85 },
1905 { 71, 102 }, { 71, 106 }, { 72, 74 }, { 72, 83 }, { 72, 86 },
1906 { 72, 103 }, { 72, 105 }, { 73, 74 }, { 73, 84 }, { 73, 86 },
1907 { 73, 104 }, { 73, 106 }, { 74, 85 }, { 74, 86 }, { 74, 105 },
1908 { 74, 106 }, { 75, 87 }, { 75, 88 }, { 75, 89 }, { 75, 90 },
1909 { 75, 93 }, { 75, 107 }, { 76, 87 }, { 76, 88 }, { 76, 91 },
1910 { 76, 92 }, { 76, 94 }, { 76, 108 }, { 77, 87 }, { 77, 89 },
1911 { 77, 91 }, { 77, 95 }, { 77, 97 }, { 77, 109 }, { 78, 88 },
1912 { 78, 90 }, { 78, 92 }, { 78, 96 }, { 78, 98 }, { 78, 110 },
1913 { 79, 89 }, { 79, 93 }, { 79, 95 }, { 79, 99 }, { 79, 101 },
1914 { 79, 111 }, { 80, 90 }, { 80, 93 }, { 80, 96 }, { 80, 99 },
1915 { 80, 102 }, { 80, 112 }, { 81, 91 }, { 81, 94 }, { 81, 97 },
1916 { 81, 100 }, { 81, 103 }, { 81, 113 }, { 82, 92 }, { 82, 94 },
1917 { 82, 98 }, { 82, 100 }, { 82, 104 }, { 82, 114 }, { 83, 95 },
1918 { 83, 97 }, { 83, 101 }, { 83, 103 }, { 83, 105 }, { 83, 115 },
1919 { 84, 96 }, { 84, 98 }, { 84, 102 }, { 84, 104 }, { 84, 106 },
1920 { 84, 116 }, { 85, 99 }, { 85, 101 }, { 85, 102 }, { 85, 105 },
1921 { 85, 106 }, { 85, 117 }, { 86, 100 }, { 86, 103 }, { 86, 104 },
1922 { 86, 105 }, { 86, 106 }, { 86, 118 }, { 87, 88 }, { 87, 89 },
1923 { 87, 91 }, { 87, 107 }, { 87, 108 }, { 87, 109 }, { 88, 90 },
1924 { 88, 92 }, { 88, 107 }, { 88, 108 }, { 88, 110 }, { 89, 93 },
1925 { 89, 95 }, { 89, 107 }, { 89, 109 }, { 89, 111 }, { 90, 93 },
1926 { 90, 96 }, { 90, 107 }, { 90, 110 }, { 90, 112 }, { 91, 94 },
1927 { 91, 97 }, { 91, 108 }, { 91, 109 }, { 91, 113 }, { 92, 94 },
1928 { 92, 98 }, { 92, 108 }, { 92, 110 }, { 92, 114 }, { 93, 99 },
1929 { 93, 107 }, { 93, 111 }, { 93, 112 }, { 94, 100 }, { 94, 108 },
1930 { 94, 113 }, { 94, 114 }, { 95, 97 }, { 95, 101 }, { 95, 109 },
1931 { 95, 111 }, { 95, 115 }, { 96, 98 }, { 96, 102 }, { 96, 110 },
1932 { 96, 112 }, { 96, 116 }, { 97, 103 }, { 97, 109 }, { 97, 113 },
1933 { 97, 115 }, { 98, 104 }, { 98, 110 }, { 98, 114 }, { 98, 116 },
1934 { 99, 101 }, { 99, 102 }, { 99, 111 }, { 99, 112 }, { 99, 117 },
1935 { 100, 103 }, { 100, 104 }, { 100, 113 }, { 100, 114 }, { 100, 118 },
1936 { 101, 105 }, { 101, 111 }, { 101, 115 }, { 101, 117 }, { 102, 106 },
1937 { 102, 112 }, { 102, 116 }, { 102, 117 }, { 103, 105 }, { 103, 113 },
1938 { 103, 115 }, { 103, 118 }, { 104, 106 }, { 104, 114 }, { 104, 116 },
1939 { 104, 118 }, { 105, 106 }, { 105, 115 }, { 105, 117 }, { 105, 118 },
1940 { 106, 116 }, { 106, 117 }, { 106, 118 }, { 107, 108 }, { 107, 109 },
1941 { 107, 110 }, { 107, 111 }, { 107, 112 }, { 107, 119 }, { 108, 109 },
1942 { 108, 110 }, { 108, 113 }, { 108, 114 }, { 108, 119 }, { 109, 111 },
1943 { 109, 113 }, { 109, 115 }, { 109, 119 }, { 110, 112 }, { 110, 114 },
1944 { 110, 116 }, { 110, 119 }, { 111, 112 }, { 111, 115 }, { 111, 117 },
1945 { 111, 119 }, { 112, 116 }, { 112, 117 }, { 112, 119 }, { 113, 114 },
1946 { 113, 115 }, { 113, 118 }, { 113, 119 }, { 114, 116 }, { 114, 118 },
1947 { 114, 119 }, { 115, 117 }, { 115, 118 }, { 115, 119 }, { 116, 117 },
1948 { 116, 118 }, { 116, 119 }, { 117, 118 }, { 117, 119 }, { 118, 119 }
1951 static const int face_600[NUM_FACE_600][VERT_PER_FACE_600] = {
1952 { 0, 1, 2 }, { 0, 1, 3 }, { 0, 1, 4 }, { 0, 1, 5 },
1953 { 0, 1, 6 }, { 0, 2, 3 }, { 0, 2, 4 }, { 0, 2, 7 },
1954 { 0, 2, 8 }, { 0, 3, 5 }, { 0, 3, 7 }, { 0, 3, 9 },
1955 { 0, 4, 6 }, { 0, 4, 8 }, { 0, 4, 10 }, { 0, 5, 6 },
1956 { 0, 5, 9 }, { 0, 5, 11 }, { 0, 6, 10 }, { 0, 6, 11 },
1957 { 0, 7, 8 }, { 0, 7, 9 }, { 0, 7, 12 }, { 0, 8, 10 },
1958 { 0, 8, 12 }, { 0, 9, 11 }, { 0, 9, 12 }, { 0, 10, 11 },
1959 { 0, 10, 12 }, { 0, 11, 12 }, { 1, 2, 3 }, { 1, 2, 4 },
1960 { 1, 2, 13 }, { 1, 2, 14 }, { 1, 3, 5 }, { 1, 3, 13 },
1961 { 1, 3, 15 }, { 1, 4, 6 }, { 1, 4, 14 }, { 1, 4, 16 },
1962 { 1, 5, 6 }, { 1, 5, 15 }, { 1, 5, 19 }, { 1, 6, 16 },
1963 { 1, 6, 19 }, { 1, 13, 14 }, { 1, 13, 15 }, { 1, 13, 33 },
1964 { 1, 14, 16 }, { 1, 14, 33 }, { 1, 15, 19 }, { 1, 15, 33 },
1965 { 1, 16, 19 }, { 1, 16, 33 }, { 1, 19, 33 }, { 2, 3, 7 },
1966 { 2, 3, 13 }, { 2, 3, 17 }, { 2, 4, 8 }, { 2, 4, 14 },
1967 { 2, 4, 18 }, { 2, 7, 8 }, { 2, 7, 17 }, { 2, 7, 20 },
1968 { 2, 8, 18 }, { 2, 8, 20 }, { 2, 13, 14 }, { 2, 13, 17 },
1969 { 2, 13, 34 }, { 2, 14, 18 }, { 2, 14, 34 }, { 2, 17, 20 },
1970 { 2, 17, 34 }, { 2, 18, 20 }, { 2, 18, 34 }, { 2, 20, 34 },
1971 { 3, 5, 9 }, { 3, 5, 15 }, { 3, 5, 21 }, { 3, 7, 9 },
1972 { 3, 7, 17 }, { 3, 7, 23 }, { 3, 9, 21 }, { 3, 9, 23 },
1973 { 3, 13, 15 }, { 3, 13, 17 }, { 3, 13, 35 }, { 3, 15, 21 },
1974 { 3, 15, 35 }, { 3, 17, 23 }, { 3, 17, 35 }, { 3, 21, 23 },
1975 { 3, 21, 35 }, { 3, 23, 35 }, { 4, 6, 10 }, { 4, 6, 16 },
1976 { 4, 6, 22 }, { 4, 8, 10 }, { 4, 8, 18 }, { 4, 8, 24 },
1977 { 4, 10, 22 }, { 4, 10, 24 }, { 4, 14, 16 }, { 4, 14, 18 },
1978 { 4, 14, 36 }, { 4, 16, 22 }, { 4, 16, 36 }, { 4, 18, 24 },
1979 { 4, 18, 36 }, { 4, 22, 24 }, { 4, 22, 36 }, { 4, 24, 36 },
1980 { 5, 6, 11 }, { 5, 6, 19 }, { 5, 6, 25 }, { 5, 9, 11 },
1981 { 5, 9, 21 }, { 5, 9, 27 }, { 5, 11, 25 }, { 5, 11, 27 },
1982 { 5, 15, 19 }, { 5, 15, 21 }, { 5, 15, 37 }, { 5, 19, 25 },
1983 { 5, 19, 37 }, { 5, 21, 27 }, { 5, 21, 37 }, { 5, 25, 27 },
1984 { 5, 25, 37 }, { 5, 27, 37 }, { 6, 10, 11 }, { 6, 10, 22 },
1985 { 6, 10, 28 }, { 6, 11, 25 }, { 6, 11, 28 }, { 6, 16, 19 },
1986 { 6, 16, 22 }, { 6, 16, 38 }, { 6, 19, 25 }, { 6, 19, 38 },
1987 { 6, 22, 28 }, { 6, 22, 38 }, { 6, 25, 28 }, { 6, 25, 38 },
1988 { 6, 28, 38 }, { 7, 8, 12 }, { 7, 8, 20 }, { 7, 8, 26 },
1989 { 7, 9, 12 }, { 7, 9, 23 }, { 7, 9, 29 }, { 7, 12, 26 },
1990 { 7, 12, 29 }, { 7, 17, 20 }, { 7, 17, 23 }, { 7, 17, 39 },
1991 { 7, 20, 26 }, { 7, 20, 39 }, { 7, 23, 29 }, { 7, 23, 39 },
1992 { 7, 26, 29 }, { 7, 26, 39 }, { 7, 29, 39 }, { 8, 10, 12 },
1993 { 8, 10, 24 }, { 8, 10, 30 }, { 8, 12, 26 }, { 8, 12, 30 },
1994 { 8, 18, 20 }, { 8, 18, 24 }, { 8, 18, 40 }, { 8, 20, 26 },
1995 { 8, 20, 40 }, { 8, 24, 30 }, { 8, 24, 40 }, { 8, 26, 30 },
1996 { 8, 26, 40 }, { 8, 30, 40 }, { 9, 11, 12 }, { 9, 11, 27 },
1997 { 9, 11, 31 }, { 9, 12, 29 }, { 9, 12, 31 }, { 9, 21, 23 },
1998 { 9, 21, 27 }, { 9, 21, 41 }, { 9, 23, 29 }, { 9, 23, 41 },
1999 { 9, 27, 31 }, { 9, 27, 41 }, { 9, 29, 31 }, { 9, 29, 41 },
2000 { 9, 31, 41 }, { 10, 11, 12 }, { 10, 11, 28 }, { 10, 11, 32 },
2001 { 10, 12, 30 }, { 10, 12, 32 }, { 10, 22, 24 }, { 10, 22, 28 },
2002 { 10, 22, 42 }, { 10, 24, 30 }, { 10, 24, 42 }, { 10, 28, 32 },
2003 { 10, 28, 42 }, { 10, 30, 32 }, { 10, 30, 42 }, { 10, 32, 42 },
2004 { 11, 12, 31 }, { 11, 12, 32 }, { 11, 25, 27 }, { 11, 25, 28 },
2005 { 11, 25, 43 }, { 11, 27, 31 }, { 11, 27, 43 }, { 11, 28, 32 },
2006 { 11, 28, 43 }, { 11, 31, 32 }, { 11, 31, 43 }, { 11, 32, 43 },
2007 { 12, 26, 29 }, { 12, 26, 30 }, { 12, 26, 44 }, { 12, 29, 31 },
2008 { 12, 29, 44 }, { 12, 30, 32 }, { 12, 30, 44 }, { 12, 31, 32 },
2009 { 12, 31, 44 }, { 12, 32, 44 }, { 13, 14, 33 }, { 13, 14, 34 },
2010 { 13, 14, 45 }, { 13, 15, 33 }, { 13, 15, 35 }, { 13, 15, 46 },
2011 { 13, 17, 34 }, { 13, 17, 35 }, { 13, 17, 48 }, { 13, 33, 45 },
2012 { 13, 33, 46 }, { 13, 34, 45 }, { 13, 34, 48 }, { 13, 35, 46 },
2013 { 13, 35, 48 }, { 13, 45, 46 }, { 13, 45, 48 }, { 13, 46, 48 },
2014 { 14, 16, 33 }, { 14, 16, 36 }, { 14, 16, 47 }, { 14, 18, 34 },
2015 { 14, 18, 36 }, { 14, 18, 49 }, { 14, 33, 45 }, { 14, 33, 47 },
2016 { 14, 34, 45 }, { 14, 34, 49 }, { 14, 36, 47 }, { 14, 36, 49 },
2017 { 14, 45, 47 }, { 14, 45, 49 }, { 14, 47, 49 }, { 15, 19, 33 },
2018 { 15, 19, 37 }, { 15, 19, 50 }, { 15, 21, 35 }, { 15, 21, 37 },
2019 { 15, 21, 54 }, { 15, 33, 46 }, { 15, 33, 50 }, { 15, 35, 46 },
2020 { 15, 35, 54 }, { 15, 37, 50 }, { 15, 37, 54 }, { 15, 46, 50 },
2021 { 15, 46, 54 }, { 15, 50, 54 }, { 16, 19, 33 }, { 16, 19, 38 },
2022 { 16, 19, 51 }, { 16, 22, 36 }, { 16, 22, 38 }, { 16, 22, 55 },
2023 { 16, 33, 47 }, { 16, 33, 51 }, { 16, 36, 47 }, { 16, 36, 55 },
2024 { 16, 38, 51 }, { 16, 38, 55 }, { 16, 47, 51 }, { 16, 47, 55 },
2025 { 16, 51, 55 }, { 17, 20, 34 }, { 17, 20, 39 }, { 17, 20, 52 },
2026 { 17, 23, 35 }, { 17, 23, 39 }, { 17, 23, 56 }, { 17, 34, 48 },
2027 { 17, 34, 52 }, { 17, 35, 48 }, { 17, 35, 56 }, { 17, 39, 52 },
2028 { 17, 39, 56 }, { 17, 48, 52 }, { 17, 48, 56 }, { 17, 52, 56 },
2029 { 18, 20, 34 }, { 18, 20, 40 }, { 18, 20, 53 }, { 18, 24, 36 },
2030 { 18, 24, 40 }, { 18, 24, 57 }, { 18, 34, 49 }, { 18, 34, 53 },
2031 { 18, 36, 49 }, { 18, 36, 57 }, { 18, 40, 53 }, { 18, 40, 57 },
2032 { 18, 49, 53 }, { 18, 49, 57 }, { 18, 53, 57 }, { 19, 25, 37 },
2033 { 19, 25, 38 }, { 19, 25, 58 }, { 19, 33, 50 }, { 19, 33, 51 },
2034 { 19, 37, 50 }, { 19, 37, 58 }, { 19, 38, 51 }, { 19, 38, 58 },
2035 { 19, 50, 51 }, { 19, 50, 58 }, { 19, 51, 58 }, { 20, 26, 39 },
2036 { 20, 26, 40 }, { 20, 26, 61 }, { 20, 34, 52 }, { 20, 34, 53 },
2037 { 20, 39, 52 }, { 20, 39, 61 }, { 20, 40, 53 }, { 20, 40, 61 },
2038 { 20, 52, 53 }, { 20, 52, 61 }, { 20, 53, 61 }, { 21, 23, 35 },
2039 { 21, 23, 41 }, { 21, 23, 59 }, { 21, 27, 37 }, { 21, 27, 41 },
2040 { 21, 27, 62 }, { 21, 35, 54 }, { 21, 35, 59 }, { 21, 37, 54 },
2041 { 21, 37, 62 }, { 21, 41, 59 }, { 21, 41, 62 }, { 21, 54, 59 },
2042 { 21, 54, 62 }, { 21, 59, 62 }, { 22, 24, 36 }, { 22, 24, 42 },
2043 { 22, 24, 60 }, { 22, 28, 38 }, { 22, 28, 42 }, { 22, 28, 63 },
2044 { 22, 36, 55 }, { 22, 36, 60 }, { 22, 38, 55 }, { 22, 38, 63 },
2045 { 22, 42, 60 }, { 22, 42, 63 }, { 22, 55, 60 }, { 22, 55, 63 },
2046 { 22, 60, 63 }, { 23, 29, 39 }, { 23, 29, 41 }, { 23, 29, 64 },
2047 { 23, 35, 56 }, { 23, 35, 59 }, { 23, 39, 56 }, { 23, 39, 64 },
2048 { 23, 41, 59 }, { 23, 41, 64 }, { 23, 56, 59 }, { 23, 56, 64 },
2049 { 23, 59, 64 }, { 24, 30, 40 }, { 24, 30, 42 }, { 24, 30, 65 },
2050 { 24, 36, 57 }, { 24, 36, 60 }, { 24, 40, 57 }, { 24, 40, 65 },
2051 { 24, 42, 60 }, { 24, 42, 65 }, { 24, 57, 60 }, { 24, 57, 65 },
2052 { 24, 60, 65 }, { 25, 27, 37 }, { 25, 27, 43 }, { 25, 27, 66 },
2053 { 25, 28, 38 }, { 25, 28, 43 }, { 25, 28, 67 }, { 25, 37, 58 },
2054 { 25, 37, 66 }, { 25, 38, 58 }, { 25, 38, 67 }, { 25, 43, 66 },
2055 { 25, 43, 67 }, { 25, 58, 66 }, { 25, 58, 67 }, { 25, 66, 67 },
2056 { 26, 29, 39 }, { 26, 29, 44 }, { 26, 29, 68 }, { 26, 30, 40 },
2057 { 26, 30, 44 }, { 26, 30, 69 }, { 26, 39, 61 }, { 26, 39, 68 },
2058 { 26, 40, 61 }, { 26, 40, 69 }, { 26, 44, 68 }, { 26, 44, 69 },
2059 { 26, 61, 68 }, { 26, 61, 69 }, { 26, 68, 69 }, { 27, 31, 41 },
2060 { 27, 31, 43 }, { 27, 31, 70 }, { 27, 37, 62 }, { 27, 37, 66 },
2061 { 27, 41, 62 }, { 27, 41, 70 }, { 27, 43, 66 }, { 27, 43, 70 },
2062 { 27, 62, 66 }, { 27, 62, 70 }, { 27, 66, 70 }, { 28, 32, 42 },
2063 { 28, 32, 43 }, { 28, 32, 71 }, { 28, 38, 63 }, { 28, 38, 67 },
2064 { 28, 42, 63 }, { 28, 42, 71 }, { 28, 43, 67 }, { 28, 43, 71 },
2065 { 28, 63, 67 }, { 28, 63, 71 }, { 28, 67, 71 }, { 29, 31, 41 },
2066 { 29, 31, 44 }, { 29, 31, 72 }, { 29, 39, 64 }, { 29, 39, 68 },
2067 { 29, 41, 64 }, { 29, 41, 72 }, { 29, 44, 68 }, { 29, 44, 72 },
2068 { 29, 64, 68 }, { 29, 64, 72 }, { 29, 68, 72 }, { 30, 32, 42 },
2069 { 30, 32, 44 }, { 30, 32, 73 }, { 30, 40, 65 }, { 30, 40, 69 },
2070 { 30, 42, 65 }, { 30, 42, 73 }, { 30, 44, 69 }, { 30, 44, 73 },
2071 { 30, 65, 69 }, { 30, 65, 73 }, { 30, 69, 73 }, { 31, 32, 43 },
2072 { 31, 32, 44 }, { 31, 32, 74 }, { 31, 41, 70 }, { 31, 41, 72 },
2073 { 31, 43, 70 }, { 31, 43, 74 }, { 31, 44, 72 }, { 31, 44, 74 },
2074 { 31, 70, 72 }, { 31, 70, 74 }, { 31, 72, 74 }, { 32, 42, 71 },
2075 { 32, 42, 73 }, { 32, 43, 71 }, { 32, 43, 74 }, { 32, 44, 73 },
2076 { 32, 44, 74 }, { 32, 71, 73 }, { 32, 71, 74 }, { 32, 73, 74 },
2077 { 33, 45, 46 }, { 33, 45, 47 }, { 33, 45, 75 }, { 33, 46, 50 },
2078 { 33, 46, 75 }, { 33, 47, 51 }, { 33, 47, 75 }, { 33, 50, 51 },
2079 { 33, 50, 75 }, { 33, 51, 75 }, { 34, 45, 48 }, { 34, 45, 49 },
2080 { 34, 45, 76 }, { 34, 48, 52 }, { 34, 48, 76 }, { 34, 49, 53 },
2081 { 34, 49, 76 }, { 34, 52, 53 }, { 34, 52, 76 }, { 34, 53, 76 },
2082 { 35, 46, 48 }, { 35, 46, 54 }, { 35, 46, 77 }, { 35, 48, 56 },
2083 { 35, 48, 77 }, { 35, 54, 59 }, { 35, 54, 77 }, { 35, 56, 59 },
2084 { 35, 56, 77 }, { 35, 59, 77 }, { 36, 47, 49 }, { 36, 47, 55 },
2085 { 36, 47, 78 }, { 36, 49, 57 }, { 36, 49, 78 }, { 36, 55, 60 },
2086 { 36, 55, 78 }, { 36, 57, 60 }, { 36, 57, 78 }, { 36, 60, 78 },
2087 { 37, 50, 54 }, { 37, 50, 58 }, { 37, 50, 79 }, { 37, 54, 62 },
2088 { 37, 54, 79 }, { 37, 58, 66 }, { 37, 58, 79 }, { 37, 62, 66 },
2089 { 37, 62, 79 }, { 37, 66, 79 }, { 38, 51, 55 }, { 38, 51, 58 },
2090 { 38, 51, 80 }, { 38, 55, 63 }, { 38, 55, 80 }, { 38, 58, 67 },
2091 { 38, 58, 80 }, { 38, 63, 67 }, { 38, 63, 80 }, { 38, 67, 80 },
2092 { 39, 52, 56 }, { 39, 52, 61 }, { 39, 52, 81 }, { 39, 56, 64 },
2093 { 39, 56, 81 }, { 39, 61, 68 }, { 39, 61, 81 }, { 39, 64, 68 },
2094 { 39, 64, 81 }, { 39, 68, 81 }, { 40, 53, 57 }, { 40, 53, 61 },
2095 { 40, 53, 82 }, { 40, 57, 65 }, { 40, 57, 82 }, { 40, 61, 69 },
2096 { 40, 61, 82 }, { 40, 65, 69 }, { 40, 65, 82 }, { 40, 69, 82 },
2097 { 41, 59, 62 }, { 41, 59, 64 }, { 41, 59, 83 }, { 41, 62, 70 },
2098 { 41, 62, 83 }, { 41, 64, 72 }, { 41, 64, 83 }, { 41, 70, 72 },
2099 { 41, 70, 83 }, { 41, 72, 83 }, { 42, 60, 63 }, { 42, 60, 65 },
2100 { 42, 60, 84 }, { 42, 63, 71 }, { 42, 63, 84 }, { 42, 65, 73 },
2101 { 42, 65, 84 }, { 42, 71, 73 }, { 42, 71, 84 }, { 42, 73, 84 },
2102 { 43, 66, 67 }, { 43, 66, 70 }, { 43, 66, 85 }, { 43, 67, 71 },
2103 { 43, 67, 85 }, { 43, 70, 74 }, { 43, 70, 85 }, { 43, 71, 74 },
2104 { 43, 71, 85 }, { 43, 74, 85 }, { 44, 68, 69 }, { 44, 68, 72 },
2105 { 44, 68, 86 }, { 44, 69, 73 }, { 44, 69, 86 }, { 44, 72, 74 },
2106 { 44, 72, 86 }, { 44, 73, 74 }, { 44, 73, 86 }, { 44, 74, 86 },
2107 { 45, 46, 48 }, { 45, 46, 75 }, { 45, 46, 87 }, { 45, 47, 49 },
2108 { 45, 47, 75 }, { 45, 47, 88 }, { 45, 48, 76 }, { 45, 48, 87 },
2109 { 45, 49, 76 }, { 45, 49, 88 }, { 45, 75, 87 }, { 45, 75, 88 },
2110 { 45, 76, 87 }, { 45, 76, 88 }, { 45, 87, 88 }, { 46, 48, 77 },
2111 { 46, 48, 87 }, { 46, 50, 54 }, { 46, 50, 75 }, { 46, 50, 89 },
2112 { 46, 54, 77 }, { 46, 54, 89 }, { 46, 75, 87 }, { 46, 75, 89 },
2113 { 46, 77, 87 }, { 46, 77, 89 }, { 46, 87, 89 }, { 47, 49, 78 },
2114 { 47, 49, 88 }, { 47, 51, 55 }, { 47, 51, 75 }, { 47, 51, 90 },
2115 { 47, 55, 78 }, { 47, 55, 90 }, { 47, 75, 88 }, { 47, 75, 90 },
2116 { 47, 78, 88 }, { 47, 78, 90 }, { 47, 88, 90 }, { 48, 52, 56 },
2117 { 48, 52, 76 }, { 48, 52, 91 }, { 48, 56, 77 }, { 48, 56, 91 },
2118 { 48, 76, 87 }, { 48, 76, 91 }, { 48, 77, 87 }, { 48, 77, 91 },
2119 { 48, 87, 91 }, { 49, 53, 57 }, { 49, 53, 76 }, { 49, 53, 92 },
2120 { 49, 57, 78 }, { 49, 57, 92 }, { 49, 76, 88 }, { 49, 76, 92 },
2121 { 49, 78, 88 }, { 49, 78, 92 }, { 49, 88, 92 }, { 50, 51, 58 },
2122 { 50, 51, 75 }, { 50, 51, 93 }, { 50, 54, 79 }, { 50, 54, 89 },
2123 { 50, 58, 79 }, { 50, 58, 93 }, { 50, 75, 89 }, { 50, 75, 93 },
2124 { 50, 79, 89 }, { 50, 79, 93 }, { 50, 89, 93 }, { 51, 55, 80 },
2125 { 51, 55, 90 }, { 51, 58, 80 }, { 51, 58, 93 }, { 51, 75, 90 },
2126 { 51, 75, 93 }, { 51, 80, 90 }, { 51, 80, 93 }, { 51, 90, 93 },
2127 { 52, 53, 61 }, { 52, 53, 76 }, { 52, 53, 94 }, { 52, 56, 81 },
2128 { 52, 56, 91 }, { 52, 61, 81 }, { 52, 61, 94 }, { 52, 76, 91 },
2129 { 52, 76, 94 }, { 52, 81, 91 }, { 52, 81, 94 }, { 52, 91, 94 },
2130 { 53, 57, 82 }, { 53, 57, 92 }, { 53, 61, 82 }, { 53, 61, 94 },
2131 { 53, 76, 92 }, { 53, 76, 94 }, { 53, 82, 92 }, { 53, 82, 94 },
2132 { 53, 92, 94 }, { 54, 59, 62 }, { 54, 59, 77 }, { 54, 59, 95 },
2133 { 54, 62, 79 }, { 54, 62, 95 }, { 54, 77, 89 }, { 54, 77, 95 },
2134 { 54, 79, 89 }, { 54, 79, 95 }, { 54, 89, 95 }, { 55, 60, 63 },
2135 { 55, 60, 78 }, { 55, 60, 96 }, { 55, 63, 80 }, { 55, 63, 96 },
2136 { 55, 78, 90 }, { 55, 78, 96 }, { 55, 80, 90 }, { 55, 80, 96 },
2137 { 55, 90, 96 }, { 56, 59, 64 }, { 56, 59, 77 }, { 56, 59, 97 },
2138 { 56, 64, 81 }, { 56, 64, 97 }, { 56, 77, 91 }, { 56, 77, 97 },
2139 { 56, 81, 91 }, { 56, 81, 97 }, { 56, 91, 97 }, { 57, 60, 65 },
2140 { 57, 60, 78 }, { 57, 60, 98 }, { 57, 65, 82 }, { 57, 65, 98 },
2141 { 57, 78, 92 }, { 57, 78, 98 }, { 57, 82, 92 }, { 57, 82, 98 },
2142 { 57, 92, 98 }, { 58, 66, 67 }, { 58, 66, 79 }, { 58, 66, 99 },
2143 { 58, 67, 80 }, { 58, 67, 99 }, { 58, 79, 93 }, { 58, 79, 99 },
2144 { 58, 80, 93 }, { 58, 80, 99 }, { 58, 93, 99 }, { 59, 62, 83 },
2145 { 59, 62, 95 }, { 59, 64, 83 }, { 59, 64, 97 }, { 59, 77, 95 },
2146 { 59, 77, 97 }, { 59, 83, 95 }, { 59, 83, 97 }, { 59, 95, 97 },
2147 { 60, 63, 84 }, { 60, 63, 96 }, { 60, 65, 84 }, { 60, 65, 98 },
2148 { 60, 78, 96 }, { 60, 78, 98 }, { 60, 84, 96 }, { 60, 84, 98 },
2149 { 60, 96, 98 }, { 61, 68, 69 }, { 61, 68, 81 }, { 61, 68, 100 },
2150 { 61, 69, 82 }, { 61, 69, 100 }, { 61, 81, 94 }, { 61, 81, 100 },
2151 { 61, 82, 94 }, { 61, 82, 100 }, { 61, 94, 100 }, { 62, 66, 70 },
2152 { 62, 66, 79 }, { 62, 66, 101 }, { 62, 70, 83 }, { 62, 70, 101 },
2153 { 62, 79, 95 }, { 62, 79, 101 }, { 62, 83, 95 }, { 62, 83, 101 },
2154 { 62, 95, 101 }, { 63, 67, 71 }, { 63, 67, 80 }, { 63, 67, 102 },
2155 { 63, 71, 84 }, { 63, 71, 102 }, { 63, 80, 96 }, { 63, 80, 102 },
2156 { 63, 84, 96 }, { 63, 84, 102 }, { 63, 96, 102 }, { 64, 68, 72 },
2157 { 64, 68, 81 }, { 64, 68, 103 }, { 64, 72, 83 }, { 64, 72, 103 },
2158 { 64, 81, 97 }, { 64, 81, 103 }, { 64, 83, 97 }, { 64, 83, 103 },
2159 { 64, 97, 103 }, { 65, 69, 73 }, { 65, 69, 82 }, { 65, 69, 104 },
2160 { 65, 73, 84 }, { 65, 73, 104 }, { 65, 82, 98 }, { 65, 82, 104 },
2161 { 65, 84, 98 }, { 65, 84, 104 }, { 65, 98, 104 }, { 66, 67, 85 },
2162 { 66, 67, 99 }, { 66, 70, 85 }, { 66, 70, 101 }, { 66, 79, 99 },
2163 { 66, 79, 101 }, { 66, 85, 99 }, { 66, 85, 101 }, { 66, 99, 101 },
2164 { 67, 71, 85 }, { 67, 71, 102 }, { 67, 80, 99 }, { 67, 80, 102 },
2165 { 67, 85, 99 }, { 67, 85, 102 }, { 67, 99, 102 }, { 68, 69, 86 },
2166 { 68, 69, 100 }, { 68, 72, 86 }, { 68, 72, 103 }, { 68, 81, 100 },
2167 { 68, 81, 103 }, { 68, 86, 100 }, { 68, 86, 103 }, { 68, 100, 103 },
2168 { 69, 73, 86 }, { 69, 73, 104 }, { 69, 82, 100 }, { 69, 82, 104 },
2169 { 69, 86, 100 }, { 69, 86, 104 }, { 69, 100, 104 }, { 70, 72, 74 },
2170 { 70, 72, 83 }, { 70, 72, 105 }, { 70, 74, 85 }, { 70, 74, 105 },
2171 { 70, 83, 101 }, { 70, 83, 105 }, { 70, 85, 101 }, { 70, 85, 105 },
2172 { 70, 101, 105 }, { 71, 73, 74 }, { 71, 73, 84 }, { 71, 73, 106 },
2173 { 71, 74, 85 }, { 71, 74, 106 }, { 71, 84, 102 }, { 71, 84, 106 },
2174 { 71, 85, 102 }, { 71, 85, 106 }, { 71, 102, 106 }, { 72, 74, 86 },
2175 { 72, 74, 105 }, { 72, 83, 103 }, { 72, 83, 105 }, { 72, 86, 103 },
2176 { 72, 86, 105 }, { 72, 103, 105 }, { 73, 74, 86 }, { 73, 74, 106 },
2177 { 73, 84, 104 }, { 73, 84, 106 }, { 73, 86, 104 }, { 73, 86, 106 },
2178 { 73, 104, 106 }, { 74, 85, 105 }, { 74, 85, 106 }, { 74, 86, 105 },
2179 { 74, 86, 106 }, { 74, 105, 106 }, { 75, 87, 88 }, { 75, 87, 89 },
2180 { 75, 87, 107 }, { 75, 88, 90 }, { 75, 88, 107 }, { 75, 89, 93 },
2181 { 75, 89, 107 }, { 75, 90, 93 }, { 75, 90, 107 }, { 75, 93, 107 },
2182 { 76, 87, 88 }, { 76, 87, 91 }, { 76, 87, 108 }, { 76, 88, 92 },
2183 { 76, 88, 108 }, { 76, 91, 94 }, { 76, 91, 108 }, { 76, 92, 94 },
2184 { 76, 92, 108 }, { 76, 94, 108 }, { 77, 87, 89 }, { 77, 87, 91 },
2185 { 77, 87, 109 }, { 77, 89, 95 }, { 77, 89, 109 }, { 77, 91, 97 },
2186 { 77, 91, 109 }, { 77, 95, 97 }, { 77, 95, 109 }, { 77, 97, 109 },
2187 { 78, 88, 90 }, { 78, 88, 92 }, { 78, 88, 110 }, { 78, 90, 96 },
2188 { 78, 90, 110 }, { 78, 92, 98 }, { 78, 92, 110 }, { 78, 96, 98 },
2189 { 78, 96, 110 }, { 78, 98, 110 }, { 79, 89, 93 }, { 79, 89, 95 },
2190 { 79, 89, 111 }, { 79, 93, 99 }, { 79, 93, 111 }, { 79, 95, 101 },
2191 { 79, 95, 111 }, { 79, 99, 101 }, { 79, 99, 111 }, { 79, 101, 111 },
2192 { 80, 90, 93 }, { 80, 90, 96 }, { 80, 90, 112 }, { 80, 93, 99 },
2193 { 80, 93, 112 }, { 80, 96, 102 }, { 80, 96, 112 }, { 80, 99, 102 },
2194 { 80, 99, 112 }, { 80, 102, 112 }, { 81, 91, 94 }, { 81, 91, 97 },
2195 { 81, 91, 113 }, { 81, 94, 100 }, { 81, 94, 113 }, { 81, 97, 103 },
2196 { 81, 97, 113 }, { 81, 100, 103 }, { 81, 100, 113 }, { 81, 103, 113 },
2197 { 82, 92, 94 }, { 82, 92, 98 }, { 82, 92, 114 }, { 82, 94, 100 },
2198 { 82, 94, 114 }, { 82, 98, 104 }, { 82, 98, 114 }, { 82, 100, 104 },
2199 { 82, 100, 114 }, { 82, 104, 114 }, { 83, 95, 97 }, { 83, 95, 101 },
2200 { 83, 95, 115 }, { 83, 97, 103 }, { 83, 97, 115 }, { 83, 101, 105 },
2201 { 83, 101, 115 }, { 83, 103, 105 }, { 83, 103, 115 }, { 83, 105, 115 },
2202 { 84, 96, 98 }, { 84, 96, 102 }, { 84, 96, 116 }, { 84, 98, 104 },
2203 { 84, 98, 116 }, { 84, 102, 106 }, { 84, 102, 116 }, { 84, 104, 106 },
2204 { 84, 104, 116 }, { 84, 106, 116 }, { 85, 99, 101 }, { 85, 99, 102 },
2205 { 85, 99, 117 }, { 85, 101, 105 }, { 85, 101, 117 }, { 85, 102, 106 },
2206 { 85, 102, 117 }, { 85, 105, 106 }, { 85, 105, 117 }, { 85, 106, 117 },
2207 { 86, 100, 103 }, { 86, 100, 104 }, { 86, 100, 118 }, { 86, 103, 105 },
2208 { 86, 103, 118 }, { 86, 104, 106 }, { 86, 104, 118 }, { 86, 105, 106 },
2209 { 86, 105, 118 }, { 86, 106, 118 }, { 87, 88, 107 }, { 87, 88, 108 },
2210 { 87, 89, 107 }, { 87, 89, 109 }, { 87, 91, 108 }, { 87, 91, 109 },
2211 { 87, 107, 108 }, { 87, 107, 109 }, { 87, 108, 109 }, { 88, 90, 107 },
2212 { 88, 90, 110 }, { 88, 92, 108 }, { 88, 92, 110 }, { 88, 107, 108 },
2213 { 88, 107, 110 }, { 88, 108, 110 }, { 89, 93, 107 }, { 89, 93, 111 },
2214 { 89, 95, 109 }, { 89, 95, 111 }, { 89, 107, 109 }, { 89, 107, 111 },
2215 { 89, 109, 111 }, { 90, 93, 107 }, { 90, 93, 112 }, { 90, 96, 110 },
2216 { 90, 96, 112 }, { 90, 107, 110 }, { 90, 107, 112 }, { 90, 110, 112 },
2217 { 91, 94, 108 }, { 91, 94, 113 }, { 91, 97, 109 }, { 91, 97, 113 },
2218 { 91, 108, 109 }, { 91, 108, 113 }, { 91, 109, 113 }, { 92, 94, 108 },
2219 { 92, 94, 114 }, { 92, 98, 110 }, { 92, 98, 114 }, { 92, 108, 110 },
2220 { 92, 108, 114 }, { 92, 110, 114 }, { 93, 99, 111 }, { 93, 99, 112 },
2221 { 93, 107, 111 }, { 93, 107, 112 }, { 93, 111, 112 }, { 94, 100, 113 },
2222 { 94, 100, 114 }, { 94, 108, 113 }, { 94, 108, 114 }, { 94, 113, 114 },
2223 { 95, 97, 109 }, { 95, 97, 115 }, { 95, 101, 111 }, { 95, 101, 115 },
2224 { 95, 109, 111 }, { 95, 109, 115 }, { 95, 111, 115 }, { 96, 98, 110 },
2225 { 96, 98, 116 }, { 96, 102, 112 }, { 96, 102, 116 }, { 96, 110, 112 },
2226 { 96, 110, 116 }, { 96, 112, 116 }, { 97, 103, 113 }, { 97, 103, 115 },
2227 { 97, 109, 113 }, { 97, 109, 115 }, { 97, 113, 115 }, { 98, 104, 114 },
2228 { 98, 104, 116 }, { 98, 110, 114 }, { 98, 110, 116 }, { 98, 114, 116 },
2229 { 99, 101, 111 }, { 99, 101, 117 }, { 99, 102, 112 }, { 99, 102, 117 },
2230 { 99, 111, 112 }, { 99, 111, 117 }, { 99, 112, 117 }, { 100, 103, 113 },
2231 { 100, 103, 118 }, { 100, 104, 114 }, { 100, 104, 118 }, { 100, 113, 114 },
2232 { 100, 113, 118 }, { 100, 114, 118 }, { 101, 105, 115 }, { 101, 105, 117 },
2233 { 101, 111, 115 }, { 101, 111, 117 }, { 101, 115, 117 }, { 102, 106, 116 },
2234 { 102, 106, 117 }, { 102, 112, 116 }, { 102, 112, 117 }, { 102, 116, 117 },
2235 { 103, 105, 115 }, { 103, 105, 118 }, { 103, 113, 115 }, { 103, 113, 118 },
2236 { 103, 115, 118 }, { 104, 106, 116 }, { 104, 106, 118 }, { 104, 114, 116 },
2237 { 104, 114, 118 }, { 104, 116, 118 }, { 105, 106, 117 }, { 105, 106, 118 },
2238 { 105, 115, 117 }, { 105, 115, 118 }, { 105, 117, 118 }, { 106, 116, 117 },
2239 { 106, 116, 118 }, { 106, 117, 118 }, { 107, 108, 109 }, { 107, 108, 110 },
2240 { 107, 108, 119 }, { 107, 109, 111 }, { 107, 109, 119 }, { 107, 110, 112 },
2241 { 107, 110, 119 }, { 107, 111, 112 }, { 107, 111, 119 }, { 107, 112, 119 },
2242 { 108, 109, 113 }, { 108, 109, 119 }, { 108, 110, 114 }, { 108, 110, 119 },
2243 { 108, 113, 114 }, { 108, 113, 119 }, { 108, 114, 119 }, { 109, 111, 115 },
2244 { 109, 111, 119 }, { 109, 113, 115 }, { 109, 113, 119 }, { 109, 115, 119 },
2245 { 110, 112, 116 }, { 110, 112, 119 }, { 110, 114, 116 }, { 110, 114, 119 },
2246 { 110, 116, 119 }, { 111, 112, 117 }, { 111, 112, 119 }, { 111, 115, 117 },
2247 { 111, 115, 119 }, { 111, 117, 119 }, { 112, 116, 117 }, { 112, 116, 119 },
2248 { 112, 117, 119 }, { 113, 114, 118 }, { 113, 114, 119 }, { 113, 115, 118 },
2249 { 113, 115, 119 }, { 113, 118, 119 }, { 114, 116, 118 }, { 114, 116, 119 },
2250 { 114, 118, 119 }, { 115, 117, 118 }, { 115, 117, 119 }, { 115, 118, 119 },
2251 { 116, 117, 118 }, { 116, 117, 119 }, { 116, 118, 119 }, { 117, 118, 119 }
2256 /* Add a rotation around the wx-plane to the matrix m. */
2257 static void rotatewx(float m[4][4], float phi)
2275 /* Add a rotation around the wy-plane to the matrix m. */
2276 static void rotatewy(float m[4][4], float phi)
2294 /* Add a rotation around the wz-plane to the matrix m. */
2295 static void rotatewz(float m[4][4], float phi)
2313 /* Add a rotation around the xy-plane to the matrix m. */
2314 static void rotatexy(float m[4][4], float phi)
2332 /* Add a rotation around the xz-plane to the matrix m. */
2333 static void rotatexz(float m[4][4], float phi)
2351 /* Add a rotation around the yz-plane to the matrix m. */
2352 static void rotateyz(float m[4][4], float phi)
2370 /* Compute the rotation matrix m from the rotation angles. */
2371 static void rotateall(float al, float be, float de, float ze, float et,
2372 float th, float m[4][4])
2388 /* Multiply two rotation matrices: o=m*n. */
2389 static void mult_rotmat(float m[4][4], float n[4][4], float o[4][4])
2399 o[i][j] += m[i][k]*n[k][j];
2405 /* Compute a 4D rotation matrix from two unit quaternions. */
2406 static void quats_to_rotmat(float p[4], float q[4], float m[4][4])
2408 double al, be, de, ze, et, th;
2409 double r00, r01, r02, r12, r22;
2411 r00 = 1.0-2.0*(p[1]*p[1]+p[2]*p[2]);
2412 r01 = 2.0*(p[0]*p[1]+p[2]*p[3]);
2413 r02 = 2.0*(p[2]*p[0]-p[1]*p[3]);
2414 r12 = 2.0*(p[1]*p[2]+p[0]*p[3]);
2415 r22 = 1.0-2.0*(p[1]*p[1]+p[0]*p[0]);
2417 al = atan2(-r12,r22)*180.0/M_PI;
2418 be = atan2(r02,sqrt(r00*r00+r01*r01))*180.0/M_PI;
2419 de = atan2(-r01,r00)*180.0/M_PI;
2421 r00 = 1.0-2.0*(q[1]*q[1]+q[2]*q[2]);
2422 r01 = 2.0*(q[0]*q[1]+q[2]*q[3]);
2423 r02 = 2.0*(q[2]*q[0]-q[1]*q[3]);
2424 r12 = 2.0*(q[1]*q[2]+q[0]*q[3]);
2425 r22 = 1.0-2.0*(q[1]*q[1]+q[0]*q[0]);
2427 et = atan2(-r12,r22)*180.0/M_PI;
2428 th = atan2(r02,sqrt(r00*r00+r01*r01))*180.0/M_PI;
2429 ze = atan2(-r01,r00)*180.0/M_PI;
2431 rotateall(al,be,de,ze,et,-th,m);
2435 /* Compute the normal vector of a plane based on three points in the plane. */
2436 static void normal(const float *p, const float *q, const float *r,
2439 float u[3], v[3], t;
2447 n[0] = u[1]*v[2]-u[2]*v[1];
2448 n[1] = u[2]*v[0]-u[0]*v[2];
2449 n[2] = u[0]*v[1]-u[1]*v[0];
2450 t = sqrt(n[0]*n[0]+n[1]*n[1]+n[2]*n[2]);
2457 /* Project an array of vertices from 4d to 3d. */
2458 static void project(ModeInfo *mi, const float vert[][4], float v[][4], int num)
2460 float s, q1[4], q2[4], r1[4][4], r2[4][4], m[4][4];
2462 polytopesstruct *pp = &poly[MI_SCREEN(mi)];
2464 rotateall(pp->alpha,pp->beta,pp->delta,pp->zeta,pp->eta,pp->theta,r1);
2466 gltrackball_get_quaternion(pp->trackballs[0],q1);
2467 gltrackball_get_quaternion(pp->trackballs[1],q2);
2468 quats_to_rotmat(q1,q2,r2);
2470 mult_rotmat(r2,r1,m);
2472 /* Project the vertices from 4d to 3d. */
2473 for (i=0; i<num; i++)
2479 s += m[j][k]*vert[i][k];
2480 v[i][j] = s+offset4d[j];
2482 if (projection_4d == DISP_4D_ORTHOGRAPHIC)
2495 /* Move the projected vertices along the z-axis so that they become visible
2497 for (i=0; i<num; i++)
2500 v[i][j] += offset3d[j];
2505 /* Draw a single polytope. */
2506 static void draw(ModeInfo *mi,
2508 const int edge[][2], int num_edge,
2509 const int face[], int num_face,
2511 float edge_color[][4],
2512 float face_color[][4],
2513 float face_color_trans[][4])
2517 GLfloat red[4] = { 1.0, 0.0, 0.0, 1.0 };
2518 GLfloat red_trans[4] = { 1.0, 0.0, 0.0, 1.0 };
2520 mi->polygon_count = 0;
2521 if (display_mode == DISP_WIREFRAME)
2523 if (color_mode == COLORS_SINGLE)
2526 for (i=0; i<num_edge; i++)
2528 if (color_mode == COLORS_DEPTH)
2529 glColor4fv(edge_color[i]);
2530 glVertex4fv(v[edge[i][0]]);
2531 glVertex4fv(v[edge[i][1]]);
2534 mi->polygon_count = num_edge;
2538 if (color_mode == COLORS_SINGLE)
2540 red_trans[3] = face_color_trans[0][3]/2.0;
2541 if (display_mode == DISP_TRANSPARENT)
2542 glMaterialfv(GL_FRONT_AND_BACK,GL_AMBIENT_AND_DIFFUSE,red_trans);
2544 glMaterialfv(GL_FRONT_AND_BACK,GL_AMBIENT_AND_DIFFUSE,red);
2546 for (i=0; i<num_face; i++)
2548 glBegin(GL_POLYGON);
2549 if (color_mode == COLORS_DEPTH)
2551 if (display_mode == DISP_TRANSPARENT)
2552 glMaterialfv(GL_FRONT_AND_BACK,GL_AMBIENT_AND_DIFFUSE,
2553 face_color_trans[i]);
2555 glMaterialfv(GL_FRONT_AND_BACK,GL_AMBIENT_AND_DIFFUSE,
2558 normal(v[face[i*vert_per_face]],v[face[i*vert_per_face+1]],
2559 v[face[i*vert_per_face+2]],n);
2561 for (j=0; j<vert_per_face; j++)
2562 glVertex4fv(v[face[i*vert_per_face+j]]);
2565 mi->polygon_count = num_face;
2570 /* Draw a 5-cell {3,3,3} projected into 3d. */
2571 static void cell_5(ModeInfo *mi)
2573 polytopesstruct *hp = &poly[MI_SCREEN(mi)];
2574 float v[NUM_VERT_5][4];
2576 project(mi,vert_5,v,NUM_VERT_5);
2577 draw(mi,v,edge_5,NUM_EDGE_5,(int *)face_5,NUM_FACE_5,
2578 VERT_PER_FACE_5,hp->edge_color_5,hp->face_color_5,
2579 hp->face_color_trans_5);
2583 /* Draw a 8-cell {4,3,3} projected into 3d. */
2584 static void cell_8(ModeInfo *mi)
2586 polytopesstruct *hp = &poly[MI_SCREEN(mi)];
2587 float v[NUM_VERT_8][4];
2589 project(mi,vert_8,v,NUM_VERT_8);
2590 draw(mi,v,edge_8,NUM_EDGE_8,(int *)face_8,NUM_FACE_8,
2591 VERT_PER_FACE_8,hp->edge_color_8,hp->face_color_8,
2592 hp->face_color_trans_8);
2596 /* Draw a 16-cell {3,3,4} projected into 3d. */
2597 static void cell_16(ModeInfo *mi)
2599 polytopesstruct *hp = &poly[MI_SCREEN(mi)];
2600 float v[NUM_VERT_16][4];
2602 project(mi,vert_16,v,NUM_VERT_16);
2603 draw(mi,v,edge_16,NUM_EDGE_16,(int *)face_16,NUM_FACE_16,
2604 VERT_PER_FACE_16,hp->edge_color_16,hp->face_color_16,
2605 hp->face_color_trans_16);
2609 /* Draw a 24-cell {3,4,3} projected into 3d. */
2610 static void cell_24(ModeInfo *mi)
2612 polytopesstruct *hp = &poly[MI_SCREEN(mi)];
2613 float v[NUM_VERT_24][4];
2615 project(mi,vert_24,v,NUM_VERT_24);
2616 draw(mi,v,edge_24,NUM_EDGE_24,(int *)face_24,NUM_FACE_24,
2617 VERT_PER_FACE_24,hp->edge_color_24,hp->face_color_24,
2618 hp->face_color_trans_24);
2622 /* Draw a 120-cell {5,3,3} projected into 3d. */
2623 static void cell_120(ModeInfo *mi)
2625 polytopesstruct *hp = &poly[MI_SCREEN(mi)];
2626 float v[NUM_VERT_120][4];
2628 project(mi,vert_120,v,NUM_VERT_120);
2629 draw(mi,v,edge_120,NUM_EDGE_120,(int *)face_120,NUM_FACE_120,
2630 VERT_PER_FACE_120,hp->edge_color_120,hp->face_color_120,
2631 hp->face_color_trans_120);
2635 /* Draw a 600-cell {3,3,5} projected into 3d. */
2636 static void cell_600(ModeInfo *mi)
2638 polytopesstruct *hp = &poly[MI_SCREEN(mi)];
2639 float v[NUM_VERT_600][4];
2641 project(mi,vert_600,v,NUM_VERT_600);
2642 draw(mi,v,edge_600,NUM_EDGE_600,(int *)face_600,NUM_FACE_600,
2643 VERT_PER_FACE_600,hp->edge_color_600,hp->face_color_600,
2644 hp->face_color_trans_600);
2648 /* Compute a color based on the w-depth of a point. */
2649 static void color(float depth, float alpha, float min, float max,
2655 d = (depth-min)/(max-min);
2699 /* Set the colors of a single polytope's edges and faces. */
2700 static void colors(const float vert[][4],
2701 const int edge[][2], int num_edge,
2702 const int face[], int num_face,
2704 float edge_color[][4],
2705 float face_color[][4],
2706 float face_color_trans[][4],
2708 float min_edge_depth, float max_edge_depth,
2709 float min_face_depth, float max_face_depth)
2714 for (i=0; i<num_edge; i++)
2716 depth = (vert[edge[i][0]][3]+vert[edge[i][1]][3])/2.0;
2717 color(depth,1.0,min_edge_depth,max_edge_depth,edge_color[i]);
2719 for (i=0; i<num_face; i++)
2722 for (j=0; j<vert_per_face; j++)
2723 depth += vert[face[i*vert_per_face+j]][3];
2724 depth /= vert_per_face;
2725 color(depth,1.0,min_face_depth,max_face_depth,face_color[i]);
2726 color(depth,alpha,min_face_depth,max_face_depth,face_color_trans[i]);
2731 /* Set the colors of the polytopes' edges and faces. */
2732 static void set_colors(ModeInfo *mi)
2734 polytopesstruct *hp = &poly[MI_SCREEN(mi)];
2736 colors(vert_5,edge_5,NUM_EDGE_5,(int *)face_5,NUM_FACE_5,
2737 VERT_PER_FACE_5,hp->edge_color_5,hp->face_color_5,
2738 hp->face_color_trans_5,0.5,MIN_EDGE_DEPTH_5,
2739 MAX_EDGE_DEPTH_5,MIN_FACE_DEPTH_5,MAX_FACE_DEPTH_5);
2742 colors(vert_8,edge_8,NUM_EDGE_8,(int *)face_8,NUM_FACE_8,
2743 VERT_PER_FACE_8,hp->edge_color_8,hp->face_color_8,
2744 hp->face_color_trans_8,0.4,MIN_EDGE_DEPTH_8,
2745 MAX_EDGE_DEPTH_8,MIN_FACE_DEPTH_8,MAX_FACE_DEPTH_8);
2748 colors(vert_16,edge_16,NUM_EDGE_16,(int *)face_16,NUM_FACE_16,
2749 VERT_PER_FACE_16,hp->edge_color_16,hp->face_color_16,
2750 hp->face_color_trans_16,0.25,MIN_EDGE_DEPTH_16,
2751 MAX_EDGE_DEPTH_16,MIN_FACE_DEPTH_16,MAX_FACE_DEPTH_16);
2754 colors(vert_24,edge_24,NUM_EDGE_24,(int *)face_24,NUM_FACE_24,
2755 VERT_PER_FACE_24,hp->edge_color_24,hp->face_color_24,
2756 hp->face_color_trans_24,0.25,MIN_EDGE_DEPTH_24,
2757 MAX_EDGE_DEPTH_24,MIN_FACE_DEPTH_24,MAX_FACE_DEPTH_24);
2760 colors(vert_120,edge_120,NUM_EDGE_120,(int *)face_120,NUM_FACE_120,
2761 VERT_PER_FACE_120,hp->edge_color_120,hp->face_color_120,
2762 hp->face_color_trans_120,0.15,MIN_EDGE_DEPTH_120,
2763 MAX_EDGE_DEPTH_120,MIN_FACE_DEPTH_120,MAX_FACE_DEPTH_120);
2766 colors(vert_600,edge_600,NUM_EDGE_600,(int *)face_600,NUM_FACE_600,
2767 VERT_PER_FACE_600,hp->edge_color_600,hp->face_color_600,
2768 hp->face_color_trans_600,0.06,MIN_EDGE_DEPTH_600,
2769 MAX_EDGE_DEPTH_600,MIN_FACE_DEPTH_600,MAX_FACE_DEPTH_600);
2773 static void init(ModeInfo *mi)
2775 polytopesstruct *pp = &poly[MI_SCREEN(mi)];
2791 /* Redisplay the polytopes. */
2792 static void display_polytopes(ModeInfo *mi)
2794 polytopesstruct *pp = &poly[MI_SCREEN(mi)];
2796 if (!pp->button_pressed)
2798 pp->alpha += speed_wx * pp->speed_scale;
2799 if (pp->alpha >= 360.0)
2801 pp->beta += speed_wy * pp->speed_scale;
2802 if (pp->beta >= 360.0)
2804 pp->delta += speed_wz * pp->speed_scale;
2805 if (pp->delta >= 360.0)
2807 pp->zeta += speed_xy * pp->speed_scale;
2808 if (pp->zeta >= 360.0)
2810 pp->eta += speed_xz * pp->speed_scale;
2811 if (pp->eta >= 360.0)
2813 pp->theta += speed_yz * pp->speed_scale;
2814 if (pp->theta >= 360.0)
2818 glMatrixMode(GL_PROJECTION);
2820 if (projection_3d == DISP_3D_ORTHOGRAPHIC)
2822 if (pp->aspect >= 1.0)
2823 glOrtho(-pp->aspect,pp->aspect,-1.0,1.0,0.1,100.0);
2825 glOrtho(-1.0,1.0,-1.0/pp->aspect,1.0/pp->aspect,0.1,100.0);
2829 gluPerspective(60.0,pp->aspect,0.1,100.0);
2832 glMatrixMode(GL_MODELVIEW);
2837 if (polytope == POLYTOPE_RANDOM)
2838 pp->poly = random() % (POLYTOPE_LAST_CELL+1);
2840 pp->poly = polytope;
2842 if (++pp->tick > 1000)
2845 if (pp->poly == POLYTOPE_5_CELL)
2847 else if (pp->poly == POLYTOPE_8_CELL)
2849 else if (pp->poly == POLYTOPE_16_CELL)
2851 else if (pp->poly == POLYTOPE_24_CELL)
2853 else if (pp->poly == POLYTOPE_120_CELL)
2855 else if (pp->poly == POLYTOPE_600_CELL)
2862 ENTRYPOINT void reshape_polytopes(ModeInfo *mi, int width, int height)
2864 polytopesstruct *pp = &poly[MI_SCREEN(mi)];
2866 pp->WindW = (GLint)width;
2867 pp->WindH = (GLint)height;
2868 glViewport(0,0,width,height);
2869 pp->aspect = (GLfloat)width/(GLfloat)height;
2873 ENTRYPOINT Bool polytopes_handle_event(ModeInfo *mi, XEvent *event)
2875 polytopesstruct *pp = &poly[MI_SCREEN(mi)];
2879 if (event->xany.type == KeyPress || event->xany.type == KeyRelease)
2880 XLookupString (&event->xkey, &c, 1, &sym, 0);
2882 if (event->xany.type == ButtonPress &&
2883 event->xbutton.button == Button1)
2885 pp->button_pressed = True;
2886 gltrackball_start(pp->trackballs[pp->current_trackball],
2887 event->xbutton.x, event->xbutton.y,
2888 MI_WIDTH(mi), MI_HEIGHT(mi));
2891 else if (event->xany.type == ButtonRelease &&
2892 event->xbutton.button == Button1)
2894 pp->button_pressed = False;
2897 else if (event->xany.type == KeyPress)
2899 if (sym == XK_Shift_L || sym == XK_Shift_R)
2901 pp->current_trackball = 1;
2902 if (pp->button_pressed)
2903 gltrackball_start(pp->trackballs[pp->current_trackball],
2904 event->xbutton.x, event->xbutton.y,
2905 MI_WIDTH(mi), MI_HEIGHT(mi));
2909 else if (event->xany.type == KeyRelease)
2911 if (sym == XK_Shift_L || sym == XK_Shift_R)
2913 pp->current_trackball = 0;
2914 if (pp->button_pressed)
2915 gltrackball_start(pp->trackballs[pp->current_trackball],
2916 event->xbutton.x, event->xbutton.y,
2917 MI_WIDTH(mi), MI_HEIGHT(mi));
2921 else if (event->xany.type == MotionNotify && pp->button_pressed)
2923 gltrackball_track(pp->trackballs[pp->current_trackball],
2924 event->xmotion.x, event->xmotion.y,
2925 MI_WIDTH(mi), MI_HEIGHT(mi));
2934 *-----------------------------------------------------------------------------
2935 *-----------------------------------------------------------------------------
2937 *-----------------------------------------------------------------------------
2938 *-----------------------------------------------------------------------------
2942 *-----------------------------------------------------------------------------
2943 * Initialize polytopes. Called each time the window changes.
2944 *-----------------------------------------------------------------------------
2947 ENTRYPOINT void init_polytopes(ModeInfo *mi)
2949 polytopesstruct *pp;
2953 poly = (polytopesstruct *)calloc(MI_NUM_SCREENS(mi),
2954 sizeof(polytopesstruct));
2958 pp = &poly[MI_SCREEN(mi)];
2960 pp->trackballs[0] = gltrackball_init(True);
2961 pp->trackballs[1] = gltrackball_init(True);
2962 pp->current_trackball = 0;
2963 pp->button_pressed = False;
2965 /* Set the display mode. */
2966 if (!strcasecmp(mode,"wireframe") || !strcasecmp(mode,"0"))
2968 display_mode = DISP_WIREFRAME;
2970 else if (!strcasecmp(mode,"surface") || !strcasecmp(mode,"1"))
2972 display_mode = DISP_SURFACE;
2974 else if (!strcasecmp(mode,"transparent") || !strcasecmp(mode,"2"))
2976 display_mode = DISP_TRANSPARENT;
2980 display_mode = DISP_TRANSPARENT;
2983 /* Set the Klein bottle. */
2984 if (!strcasecmp(poly_str,"random") || !strcasecmp(poly_str,"-1"))
2986 polytope = POLYTOPE_RANDOM;
2988 else if (!strcasecmp(poly_str,"5-cell") || !strcasecmp(poly_str,"0"))
2990 polytope = POLYTOPE_5_CELL;
2992 else if (!strcasecmp(poly_str,"8-cell") || !strcasecmp(poly_str,"1"))
2994 polytope = POLYTOPE_8_CELL;
2996 else if (!strcasecmp(poly_str,"16-cell") || !strcasecmp(poly_str,"2"))
2998 polytope = POLYTOPE_16_CELL;
3000 else if (!strcasecmp(poly_str,"24-cell") || !strcasecmp(poly_str,"3"))
3002 polytope = POLYTOPE_24_CELL;
3004 else if (!strcasecmp(poly_str,"120-cell") || !strcasecmp(poly_str,"4"))
3006 polytope = POLYTOPE_120_CELL;
3008 else if (!strcasecmp(poly_str,"600-cell") || !strcasecmp(poly_str,"5"))
3010 polytope = POLYTOPE_600_CELL;
3014 polytope = POLYTOPE_RANDOM;
3017 /* Set the color mode. */
3018 if (!strcasecmp(color_str,"single") || !strcasecmp(color_str,"0"))
3020 color_mode = COLORS_SINGLE;
3022 else if (!strcasecmp(color_str,"depth") || !strcasecmp(color_str,"1"))
3024 color_mode = COLORS_DEPTH;
3028 color_mode = COLORS_DEPTH;
3031 /* Set the 3d projection mode. */
3032 if (!strcasecmp(proj_3d,"perspective") || !strcasecmp(proj_3d,"0"))
3034 projection_3d = DISP_3D_PERSPECTIVE;
3036 else if (!strcasecmp(proj_3d,"orthographic") || !strcasecmp(proj_3d,"1"))
3038 projection_3d = DISP_3D_ORTHOGRAPHIC;
3042 projection_3d = DISP_3D_PERSPECTIVE;
3045 /* Set the 4d projection mode. */
3046 if (!strcasecmp(proj_4d,"perspective") || !strcasecmp(proj_4d,"0"))
3048 projection_4d = DISP_4D_PERSPECTIVE;
3050 else if (!strcasecmp(proj_4d,"orthographic") || !strcasecmp(proj_4d,"1"))
3052 projection_4d = DISP_4D_ORTHOGRAPHIC;
3056 projection_4d = DISP_4D_PERSPECTIVE;
3059 /* make multiple screens rotate at slightly different rates. */
3060 pp->speed_scale = 0.9 + frand(0.3);
3062 if ((pp->glx_context = init_GL(mi)) != NULL)
3064 reshape_polytopes(mi,MI_WIDTH(mi),MI_HEIGHT(mi));
3065 glDrawBuffer(GL_BACK);
3075 *-----------------------------------------------------------------------------
3076 * Called by the mainline code periodically to update the display.
3077 *-----------------------------------------------------------------------------
3079 ENTRYPOINT void draw_polytopes(ModeInfo *mi)
3081 static const GLfloat light_ambient[] = { 0.0, 0.0, 0.0, 1.0 };
3082 static const GLfloat light_diffuse[] = { 1.0, 1.0, 1.0, 1.0 };
3083 static const GLfloat light_specular[] = { 0.0, 0.0, 0.0, 1.0 };
3084 static const GLfloat light_position[] = { 0.0, 0.0, 1.0, 0.0 };
3085 static const GLfloat mat_specular[] = { 1.0, 1.0, 1.0, 1.0 };
3087 Display *display = MI_DISPLAY(mi);
3088 Window window = MI_WINDOW(mi);
3089 polytopesstruct *hp;
3093 hp = &poly[MI_SCREEN(mi)];
3095 MI_IS_DRAWN(mi) = True;
3096 if (!hp->glx_context)
3099 glXMakeCurrent(display,window,*(hp->glx_context));
3102 glMatrixMode(GL_PROJECTION);
3104 if (projection_3d == DISP_3D_PERSPECTIVE)
3105 gluPerspective(60.0,1.0,0.1,100.0);
3107 glOrtho(-1.0,1.0,-1.0,1.0,0.1,100.0);;
3108 glMatrixMode(GL_MODELVIEW);
3111 if (display_mode == DISP_WIREFRAME)
3113 glDisable(GL_DEPTH_TEST);
3114 glDisable(GL_LIGHTING);
3115 glDisable(GL_LIGHT0);
3116 glDisable(GL_BLEND);
3118 else if (display_mode == DISP_SURFACE)
3120 glEnable(GL_DEPTH_TEST);
3121 glDepthFunc(GL_LESS);
3122 glLightModeli(GL_LIGHT_MODEL_TWO_SIDE,GL_TRUE);
3123 glEnable(GL_LIGHTING);
3124 glEnable(GL_LIGHT0);
3125 glLightfv(GL_LIGHT0,GL_AMBIENT,light_ambient);
3126 glLightfv(GL_LIGHT0,GL_DIFFUSE,light_diffuse);
3127 glLightfv(GL_LIGHT0,GL_SPECULAR,light_specular);
3128 glLightfv(GL_LIGHT0,GL_POSITION,light_position);
3129 glMaterialfv(GL_FRONT_AND_BACK,GL_SPECULAR,mat_specular);
3130 glMaterialf(GL_FRONT_AND_BACK,GL_SHININESS,0.0);
3131 glDepthMask(GL_TRUE);
3132 glDisable(GL_BLEND);
3134 else if (display_mode == DISP_TRANSPARENT)
3136 glDisable(GL_DEPTH_TEST);
3137 glLightModeli(GL_LIGHT_MODEL_TWO_SIDE,GL_TRUE);
3138 glEnable(GL_LIGHTING);
3139 glEnable(GL_LIGHT0);
3140 glLightfv(GL_LIGHT0,GL_AMBIENT,light_ambient);
3141 glLightfv(GL_LIGHT0,GL_DIFFUSE,light_diffuse);
3142 glLightfv(GL_LIGHT0,GL_SPECULAR,light_specular);
3143 glLightfv(GL_LIGHT0,GL_POSITION,light_position);
3144 glMaterialfv(GL_FRONT_AND_BACK,GL_SPECULAR,mat_specular);
3145 glMaterialf(GL_FRONT_AND_BACK,GL_SHININESS,0.0);
3146 glDepthMask(GL_FALSE);
3148 glBlendFunc(GL_SRC_ALPHA,GL_ONE);
3152 glDisable(GL_DEPTH_TEST);
3153 glDisable(GL_LIGHTING);
3154 glDisable(GL_LIGHT0);
3155 glDisable(GL_BLEND);
3159 glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT);
3162 display_polytopes(mi);
3169 glXSwapBuffers(display,window);
3174 *-----------------------------------------------------------------------------
3175 * The display is being taken away from us. Free up malloc'ed
3176 * memory and X resources that we've alloc'ed. Only called
3177 * once, we must zap everything for every screen.
3178 *-----------------------------------------------------------------------------
3181 ENTRYPOINT void release_polytopes(ModeInfo *mi)
3187 for (screen = 0; screen < MI_NUM_SCREENS(mi); screen++)
3189 polytopesstruct *hp = &poly[screen];
3191 if (hp->glx_context)
3192 hp->glx_context = (GLXContext *)NULL;
3194 (void) free((void *)poly);
3195 poly = (polytopesstruct *)NULL;
3201 ENTRYPOINT void change_polytopes(ModeInfo *mi)
3203 polytopesstruct *hp = &poly[MI_SCREEN(mi)];
3205 if (!hp->glx_context)
3208 glXMakeCurrent(MI_DISPLAY(mi),MI_WINDOW(mi),*(hp->glx_context));
3211 #endif /* !STANDALONE */
3213 XSCREENSAVER_MODULE ("Polytopes", polytopes)
projects / xscreensaver / blob