omdl  v0.9.5
OpenSCAD Mechanical Design Library
archimedean.scad
Go to the documentation of this file.
1 //! Polyhedra data table: \c archimedean.
2 /***************************************************************************//**
3  \file
4  \author Roy Allen Sutton
5  \date 2017-2023
6 
7  \copyright
8 
9  This file is part of [omdl] (https://github.com/royasutton/omdl),
10  an OpenSCAD mechanical design library.
11 
12  The \em omdl is free software; you can redistribute it and/or modify
13  it under the terms of the [GNU Lesser General Public License]
14  (http://www.gnu.org/licenses/lgpl.html) as published by the Free
15  Software Foundation; either version 2.1 of the License, or (at
16  your option) any later version.
17 
18  The \em omdl is distributed in the hope that it will be useful,
19  but WITHOUT ANY WARRANTY; without even the implied warranty of
20  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
21  Lesser General Public License for more details.
22 
23  You should have received a copy of the GNU Lesser General Public
24  License along with the \em omdl; if not, write to the Free Software
25  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
26  02110-1301, USA; or see <http://www.gnu.org/licenses/>.
27 
28  \details
29 
30  This [omdl] formatted data table has been assembled using a script
31  that converts the polyhedra data obtained from [Anthony Thyssen]'s
32  [Studies into Polyhedra]. The vertices are tabulated in both their
33  original Cartesian as well as their converted spherical coordinate
34  form, which is convenient when scaling. The data originates from
35  one of three sources:
36 
37  \li Exact Mathematics as presented by [Anthony Thyssen],
38  \li the [Polyhedron Database] maintained by [Netlib], and
39  \li an [Encyclopedia of Polyhedra] by [George W. Hart].
40 
41  [omdl]: https://github.com/royasutton/omdl
42 
43  [Anthony Thyssen]: http://www.ict.griffith.edu.au/anthony/anthony.html
44  [Studies into Polyhedra]: http://www.ict.griffith.edu.au/anthony/graphics/polyhedra
45 
46  [George W. Hart]: http://www.georgehart.com
47  [Encyclopedia of Polyhedra]: http://www.georgehart.com/virtual-polyhedra/vp.html
48 
49  [Netlib]: http://www.netlib.org
50  [Polyhedron Database]: http://www.netlib.org/polyhedra
51 
52  \amu_pathid parent (++path_parent)
53  \amu_pathid group (++path)
54 
55  \ingroup \amu_eval(${group})
56 *******************************************************************************/
57 
58 //----------------------------------------------------------------------------//
59 /***************************************************************************//**
60  \addtogroup \amu_eval(${group})
61  @{
62  <br>
63  ### Archimedean ###
64  \amu_include (include/amu/includes_required.amu)
65 
66  \amu_eval
67  (
68  ++global
69  title="Examples"
70  stem=archimedean scope=db_dim size=qvga view=diag
71  )
72 
73  \amu_define object_stem (${stem}_${scope}_${size}_${view}_${shape})
74  \amu_make files_png (append=db_dim extension=png)
75  \amu_make files_stl (append=db_dim extension=stl)
76  \amu_word files_cnt (words="${files_png}" ++count)
77  \amu_seq cell_num (prefix="(" suffix=")" last="${files_cnt}" ++number)
78  \amu_eval object_prefix (shape="" ${object_stem})
79  \amu_filename cell_txt (files="${files_png}" separator="^" ++stem)
80  \amu_replace cell_id (text="${cell_txt}" search="${object_prefix}" replace="id: ")
81  \amu_replace cell_end (text="${cell_txt}" search="${object_prefix}")
82  \amu_replace cell_end (text="${cell_end}" search="_" replace="<br>")
83  \amu_combine cell_end (p="<center>" s="</center>" j="" f="^" t="^" ${cell_end})
84 
85  \htmlonly
86  \amu_image_table
87  (
88  type=html columns=4 image_width="200" cell_files="${files_png}"
89  table_caption="${title}" cell_captions="${cell_num}"
90  cell_titles="${cell_id}" cell_end="${cell_end}"
91  cell_urls="${files_stl}"
92  )
93  \endhtmlonly
94 
95  \amu_make eps_files (append=db_dim extension=png2eps)
96 
97  \latexonly
98  \amu_image_table
99  (
100  type=latex columns=4 image_width="1.25in" cell_files="${eps_files}"
101  table_caption="${title}" cell_captions="${cell_num}"
102  )
103  \endlatexonly
104 
105  \b Autostats
106 
107  \amu_scope scope (index=1)
108  \amu_file heading (file="${scope}.log" last=1 ++rmecho ++rmnl ++read ++quiet)
109  \amu_file texts (file="${scope}.log" first=2 ++rmecho ++rmnl ++read ++quiet)
110  \amu_word columns (tokenizer="^" words="${heading}" ++count)
111 
112  \amu_table table
113  (
114  columns=${columns} column_headings="${heading}" cell_texts="${texts}"
115  )
116 
117  \amu_if ( -w ${heading} )
118  { ${table} }
119  else
120  { \note Statistics table not available. To build and include, remove
121  \c db_autostat from \c scopes_exclude in library makefile.
122  For more information see \ref lb. }
123  endif
124 *******************************************************************************/
125 //----------------------------------------------------------------------------//
126 
127 //! <map> \c archimedean polyhedra data table columns definition.
128 //! \hideinitializer
129 dtc_polyhedra_archimedean =
130 [
131  ["id", "identifier"],
132  ["n", "name"],
133  ["o", "other name"],
134  ["g", "group"],
135  ["d", "data source"],
136  ["c", "cartesian vertices"],
137  ["s", "spherical vertices"],
138  ["f", "faces"],
139  ["e", "edges"]
140 ];
141 
142 //! <table> \c archimedean polyhedra data table rows.
143 //! \hideinitializer
144 dtr_polyhedra_archimedean =
145 [
146  [
147  "cuboctahedron",
148  "Cuboctahedron",
149  empty_str,
150  "archimedean",
151  "Exact Mathematics",
152  [
153  [ 1.00000000000, 0.00000000000, 1.00000000000],
154  [ 0.00000000000, 1.00000000000, 1.00000000000],
155  [-1.00000000000, 0.00000000000, 1.00000000000],
156  [ 0.00000000000, -1.00000000000, 1.00000000000],
157  [ 1.00000000000, 1.00000000000, 0.00000000000],
158  [-1.00000000000, 1.00000000000, 0.00000000000],
159  [-1.00000000000, -1.00000000000, 0.00000000000],
160  [ 1.00000000000, -1.00000000000, 0.00000000000],
161  [ 1.00000000000, 0.00000000000, -1.00000000000],
162  [ 0.00000000000, 1.00000000000, -1.00000000000],
163  [-1.00000000000, 0.00000000000, -1.00000000000],
164  [ 0.00000000000, -1.00000000000, -1.00000000000]
165  ],
166  [
167  [1.41421356237, 0.00000000000, 45.00000000000],
168  [1.41421356237, 89.99999999999, 45.00000000000],
169  [1.41421356237, 179.99999999999, 45.00000000000],
170  [1.41421356237, -89.99999999999, 45.00000000000],
171  [1.41421356237, 45.00000000000, 89.99999999999],
172  [1.41421356237, 134.99999999999, 89.99999999999],
173  [1.41421356237, -134.99999999999, 89.99999999999],
174  [1.41421356237, -45.00000000000, 89.99999999999],
175  [1.41421356237, 0.00000000000, 134.99999999999],
176  [1.41421356237, 89.99999999999, 134.99999999999],
177  [1.41421356237, 179.99999999999, 134.99999999999],
178  [1.41421356237, -89.99999999999, 134.99999999999]
179  ],
180  [
181  [3,2,1,0],
182  [0,4,8,7],
183  [1,5,9,4],
184  [2,6,10,5],
185  [3,7,11,6],
186  [8,9,10,11],
187  [0,1,4],
188  [1,2,5],
189  [2,3,6],
190  [3,0,7],
191  [4,9,8],
192  [5,10,9],
193  [6,11,10],
194  [7,8,11]
195  ],
196  [
197  [0,1],
198  [1,2],
199  [2,3],
200  [3,0],
201  [4,0],
202  [0,7],
203  [7,8],
204  [8,4],
205  [5,1],
206  [1,4],
207  [4,9],
208  [9,5],
209  [6,2],
210  [2,5],
211  [5,10],
212  [10,6],
213  [7,3],
214  [3,6],
215  [6,11],
216  [11,7],
217  [8,9],
218  [9,10],
219  [10,11],
220  [11,8]
221  ]
222  ],
223  [
224  "icosidodecahedron",
225  "Icosidodecahedron",
226  empty_str,
227  "archimedean",
228  "George W. Hart, 1997. george@li.net",
229  [
230  [ 0.00000000000, 0.00000000000, 1.05146200000],
231  [ 0.61803400000, 0.00000000000, 0.85065080000],
232  [ 0.27639320000, 0.55278640000, 0.85065080000],
233  [-0.61803400000, 0.00000000000, 0.85065080000],
234  [-0.27639320000, -0.55278640000, 0.85065080000],
235  [ 1.00000000000, 0.00000000000, 0.32491970000],
236  [ 0.72360680000, -0.55278640000, 0.52573110000],
237  [-0.17082040000, 0.89442720000, 0.52573110000],
238  [ 0.44721360000, 0.89442720000, 0.32491970000],
239  [-1.00000000000, 0.00000000000, 0.32491970000],
240  [-0.72360680000, 0.55278640000, 0.52573110000],
241  [ 0.17082040000, -0.89442720000, 0.52573110000],
242  [-0.44721360000, -0.89442720000, 0.32491970000],
243  [ 1.00000000000, 0.00000000000, -0.32491970000],
244  [ 0.89442720000, 0.55278640000, 0.00000000000],
245  [ 0.55278640000, -0.89442720000, 0.00000000000],
246  [-0.55278640000, 0.89442720000, 0.00000000000],
247  [ 0.44721360000, 0.89442720000, -0.32491970000],
248  [-1.00000000000, 0.00000000000, -0.32491970000],
249  [-0.89442720000, -0.55278640000, 0.00000000000],
250  [-0.44721360000, -0.89442720000, -0.32491970000],
251  [ 0.61803400000, 0.00000000000, -0.85065080000],
252  [ 0.72360680000, -0.55278640000, -0.52573110000],
253  [ 0.17082040000, -0.89442720000, -0.52573110000],
254  [-0.72360680000, 0.55278640000, -0.52573110000],
255  [-0.17082040000, 0.89442720000, -0.52573110000],
256  [ 0.27639320000, 0.55278640000, -0.85065080000],
257  [-0.61803400000, 0.00000000000, -0.85065080000],
258  [-0.27639320000, -0.55278640000, -0.85065080000],
259  [ 0.00000000000, 0.00000000000, -1.05146200000]
260  ],
261  [
262  [1.05146200000, 0.00000000000, 0.00000000000],
263  [1.05146222409, 0.00000000000, 36.00000076346],
264  [1.05146221452, 63.43494882292, 36.00000004571],
265  [1.05146222409, 179.99999999999, 36.00000076346],
266  [1.05146221452, -116.56505117707, 36.00000004571],
267  [1.05146222540, 0.00000000000, 71.99999980477],
268  [1.05146221736, -37.37736782970, 60.00000054620],
269  [1.05146222693, 100.81231727452, 60.00000084727],
270  [1.05146223497, 63.43494882292, 71.99999997421],
271  [1.05146222540, 179.99999999999, 71.99999980477],
272  [1.05146221736, 142.62263217029, 60.00000054620],
273  [1.05146222693, -79.18768272547, 60.00000084727],
274  [1.05146223497, -116.56505117707, 71.99999997421],
275  [1.05146222540, 0.00000000000, 108.00000019522],
276  [1.05146222953, 31.71747394503, 89.99999999999],
277  [1.05146222953, -58.28252605496, 89.99999999999],
278  [1.05146222953, 121.71747394503, 89.99999999999],
279  [1.05146223497, 63.43494882292, 108.00000002578],
280  [1.05146222540, 179.99999999999, 108.00000019522],
281  [1.05146222953, -148.28252605495, 89.99999999999],
282  [1.05146223497, -116.56505117707, 108.00000002578],
283  [1.05146222409, 0.00000000000, 143.99999923652],
284  [1.05146221736, -37.37736782970, 119.99999945379],
285  [1.05146222693, -79.18768272547, 119.99999915272],
286  [1.05146221736, 142.62263217029, 119.99999945379],
287  [1.05146222693, 100.81231727452, 119.99999915272],
288  [1.05146221452, 63.43494882292, 143.99999995428],
289  [1.05146222409, 179.99999999999, 143.99999923652],
290  [1.05146221452, -116.56505117707, 143.99999995428],
291  [1.05146200000, 0.00000000000, 179.99999999999]
292  ],
293  [
294  [2,1,0],
295  [4,3,0],
296  [5,6,1],
297  [7,8,2],
298  [9,10,3],
299  [11,12,4],
300  [14,13,5],
301  [15,11,6],
302  [10,16,7],
303  [17,14,8],
304  [19,18,9],
305  [20,19,12],
306  [21,22,13],
307  [22,23,15],
308  [24,25,16],
309  [25,26,17],
310  [27,24,18],
311  [23,28,20],
312  [26,29,21],
313  [28,29,27],
314  [3,10,7,2,0],
315  [1,6,11,4,0],
316  [2,8,14,5,1],
317  [4,12,19,9,3],
318  [13,22,15,6,5],
319  [16,25,17,8,7],
320  [18,24,16,10,9],
321  [15,23,20,12,11],
322  [14,17,26,21,13],
323  [19,20,28,27,18],
324  [29,28,23,22,21],
325  [27,29,26,25,24]
326  ],
327  [
328  [0,1],
329  [0,2],
330  [0,3],
331  [0,4],
332  [1,2],
333  [1,5],
334  [1,6],
335  [2,7],
336  [2,8],
337  [3,4],
338  [3,9],
339  [3,10],
340  [4,11],
341  [4,12],
342  [5,6],
343  [5,13],
344  [5,14],
345  [6,11],
346  [6,15],
347  [7,8],
348  [7,10],
349  [7,16],
350  [8,14],
351  [8,17],
352  [9,10],
353  [9,18],
354  [9,19],
355  [10,16],
356  [11,12],
357  [11,15],
358  [12,19],
359  [12,20],
360  [13,14],
361  [13,21],
362  [13,22],
363  [14,17],
364  [15,22],
365  [15,23],
366  [16,24],
367  [16,25],
368  [17,25],
369  [17,26],
370  [18,19],
371  [18,24],
372  [18,27],
373  [19,20],
374  [20,23],
375  [20,28],
376  [21,22],
377  [21,26],
378  [21,29],
379  [22,23],
380  [23,28],
381  [24,25],
382  [24,27],
383  [25,26],
384  [26,29],
385  [27,28],
386  [27,29],
387  [28,29]
388  ]
389  ],
390  [
391  "rhombicosidodecahedron",
392  "Rhombicosidodecahedron",
393  empty_str,
394  "archimedean",
395  "George W. Hart, 1997. george@li.net",
396  [
397  [ 0.00000000000, 0.00000000000, 1.02605400000],
398  [ 0.44783800000, 0.00000000000, 0.92316170000],
399  [-0.02363976000, 0.44721360000, 0.92316170000],
400  [-0.40507320000, 0.19098300000, 0.92316170000],
401  [-0.16933440000, -0.41458980000, 0.92316170000],
402  [ 0.42419820000, 0.44721360000, 0.82026960000],
403  [ 0.76738180000, 0.19098300000, 0.65378680000],
404  [ 0.55528270000, -0.41458980000, 0.75667880000],
405  [-0.23122410000, 0.75623060000, 0.65378680000],
406  [-0.57440760000, -0.22360680000, 0.82026960000],
407  [-0.61265760000, 0.50000000000, 0.65378680000],
408  [ 0.17384920000, -0.67082040000, 0.75667880000],
409  [-0.46696290000, -0.63819660000, 0.65378680000],
410  [ 0.49339300000, 0.75623060000, 0.48730390000],
411  [ 0.87482650000, -0.22360680000, 0.48730390000],
412  [ 0.83657650000, 0.50000000000, 0.32082100000],
413  [ 0.70549210000, -0.63819660000, 0.38441180000],
414  [ 0.08831973000, 0.94721360000, 0.38441180000],
415  [-0.54346280000, 0.80901700000, 0.32082100000],
416  [-0.88664630000, -0.17082040000, 0.48730390000],
417  [-0.91028610000, 0.27639320000, 0.38441180000],
418  [-0.12377940000, -0.89442720000, 0.48730390000],
419  [ 0.32405860000, -0.89442720000, 0.38441180000],
420  [-0.77920160000, -0.58541020000, 0.32082100000],
421  [ 0.62899220000, 0.80901700000, 0.05144604000],
422  [ 1.01042600000, -0.17082040000, 0.05144604000],
423  [ 0.98678590000, 0.27639320000, -0.05144604000],
424  [ 0.84109130000, -0.58541020000, -0.05144604000],
425  [-0.22391900000, 1.00000000000, 0.05144604000],
426  [ 0.22391900000, 1.00000000000, -0.05144604000],
427  [-0.84109130000, 0.58541020000, 0.05144604000],
428  [-0.98678590000, -0.27639320000, 0.05144604000],
429  [-1.01042600000, 0.17082040000, -0.05144604000],
430  [-0.22391900000, -1.00000000000, 0.05144604000],
431  [ 0.22391900000, -1.00000000000, -0.05144604000],
432  [-0.62899220000, -0.80901700000, -0.05144604000],
433  [ 0.77920160000, 0.58541020000, -0.32082100000],
434  [ 0.91028610000, -0.27639320000, -0.38441180000],
435  [ 0.88664630000, 0.17082040000, -0.48730390000],
436  [ 0.54346280000, -0.80901700000, -0.32082100000],
437  [-0.32405860000, 0.89442720000, -0.38441180000],
438  [ 0.12377940000, 0.89442720000, -0.48730390000],
439  [-0.70549210000, 0.63819660000, -0.38441180000],
440  [-0.83657650000, -0.50000000000, -0.32082100000],
441  [-0.87482650000, 0.22360680000, -0.48730390000],
442  [-0.08831973000, -0.94721360000, -0.38441180000],
443  [-0.49339300000, -0.75623060000, -0.48730390000],
444  [ 0.46696290000, 0.63819660000, -0.65378680000],
445  [ 0.61265760000, -0.50000000000, -0.65378680000],
446  [ 0.57440760000, 0.22360680000, -0.82026960000],
447  [ 0.23122410000, -0.75623060000, -0.65378680000],
448  [-0.17384920000, 0.67082040000, -0.75667880000],
449  [-0.55528270000, 0.41458980000, -0.75667880000],
450  [-0.76738180000, -0.19098300000, -0.65378680000],
451  [-0.42419820000, -0.44721360000, -0.82026960000],
452  [ 0.16933440000, 0.41458980000, -0.92316170000],
453  [ 0.40507320000, -0.19098300000, -0.92316170000],
454  [ 0.02363976000, -0.44721360000, -0.92316170000],
455  [-0.44783800000, 0.00000000000, -0.92316170000],
456  [ 0.00000000000, 0.00000000000, -1.02605400000]
457  ],
458  [
459  [1.02605400000, 0.00000000000, 0.00000000000],
460  [1.02605379907, 0.00000000000, 25.87863946032],
461  [1.02605378350, 93.02584502980, 25.87863766724],
462  [1.02605376467, 154.75716551729, 25.87863550033],
463  [1.02605378301, -112.21699072712, 25.87863761169],
464  [1.02605376740, 46.51292280560, 36.92323115163],
465  [1.02605385488, 13.97562138908, 50.41772025871],
466  [1.02605379272, -36.74606097804, 42.48407886988],
467  [1.02605384101, 107.00146913438, 50.41771961837],
468  [1.02605375523, -158.72990977078, 36.92323024763],
469  [1.02605385565, 140.78154683401, 50.41772029419],
470  [1.02605378015, -75.47092320856, 42.48407810369],
471  [1.02605381442, -126.19260960319, 50.41771839072],
472  [1.02605383084, 56.87807432731, 61.64519778692],
473  [1.02605384706, -14.33789625152, 61.64519827570],
474  [1.02605377753, 30.86566216850, 71.77950886770],
475  [1.02605381701, -42.13287071812, 67.99727322825],
476  [1.02605380498, 84.67305060271, 67.99727295686],
477  [1.02605381697, 123.89150656284, 71.77950959254],
478  [1.02605378091, -169.09506295665, 61.64519628217],
479  [1.02605380796, 163.10996149775, 67.99727302423],
480  [1.02605382262, -97.87909363115, 61.64519753931],
481  [1.02605381161, -70.08411643659, 67.99727310642],
482  [1.02605377527, -143.08264822785, 71.77950882609],
483  [1.02605379439, 52.13575161616, 87.12600115411],
484  [1.02605409485, -9.59556958271, 87.12600199642],
485  [1.02605375516, 15.64726159312, 92.87399895586],
486  [1.02605378623, -34.83840577676, 92.87399886876],
487  [1.02605380638, 102.62141758317, 87.12600118773],
488  [1.02605380638, 77.37858241682, 92.87399881226],
489  [1.02605378623, 145.16159422323, 87.12600113123],
490  [1.02605375516, -164.35273840687, 87.12600104413],
491  [1.02605409485, 170.40443041727, 92.87399800357],
492  [1.02605380638, -102.62141758317, 87.12600118773],
493  [1.02605380638, -77.37858241682, 92.87399881226],
494  [1.02605379439, -127.86424838383, 92.87399884588],
495  [1.02605377527, 36.91735177214, 108.22049117390],
496  [1.02605380796, -16.89003850224, 112.00272697576],
497  [1.02605378091, 10.90493704334, 118.35480371782],
498  [1.02605381697, -56.10849343714, 108.22049040744],
499  [1.02605381161, 109.91588356340, 112.00272689357],
500  [1.02605382262, 82.12090636884, 118.35480246068],
501  [1.02605381701, 137.86712928187, 112.00272677174],
502  [1.02605377753, -149.13433783149, 108.22049113229],
503  [1.02605384706, 165.66210374847, 118.35480172429],
504  [1.02605380498, -95.32694939728, 112.00272704313],
505  [1.02605383084, -123.12192567268, 118.35480221307],
506  [1.02605381442, 53.80739039680, 129.58228160927],
507  [1.02605385565, -39.21845316598, 129.58227970579],
508  [1.02605375523, 21.27009022921, 143.07676975236],
509  [1.02605384101, -72.99853086561, 129.58228038162],
510  [1.02605378015, 104.52907679143, 137.51592189630],
511  [1.02605379272, 143.25393902195, 137.51592113011],
512  [1.02605385488, -166.02437861090, 129.58227974128],
513  [1.02605376740, -133.48707719438, 143.07676884836],
514  [1.02605378301, 67.78300927287, 154.12136238830],
515  [1.02605376467, -25.24283448269, 154.12136449965],
516  [1.02605378350, -86.97415497019, 154.12136233275],
517  [1.02605379907, 179.99999999999, 154.12136053967],
518  [1.02605400000, 0.00000000000, 179.99999999999]
519  ],
520  [
521  [3,2,0],
522  [5,6,1],
523  [12,9,4],
524  [14,16,7],
525  [10,18,8],
526  [22,21,11],
527  [24,15,13],
528  [28,29,17],
529  [23,31,19],
530  [32,30,20],
531  [37,27,25],
532  [36,38,26],
533  [34,45,33],
534  [46,43,35],
535  [48,50,39],
536  [51,41,40],
537  [44,52,42],
538  [55,49,47],
539  [54,58,53],
540  [59,57,56],
541  [2,5,1,0],
542  [4,9,3,0],
543  [6,14,7,1],
544  [3,10,8,2],
545  [11,21,12,4],
546  [13,15,6,5],
547  [16,22,11,7],
548  [18,28,17,8],
549  [12,23,19,9],
550  [20,30,18,10],
551  [17,29,24,13],
552  [25,27,16,14],
553  [24,36,26,15],
554  [31,32,20,19],
555  [22,34,33,21],
556  [35,43,31,23],
557  [26,38,37,25],
558  [37,48,39,27],
559  [40,41,29,28],
560  [32,44,42,30],
561  [45,46,35,33],
562  [39,50,45,34],
563  [47,49,38,36],
564  [42,52,51,40],
565  [51,55,47,41],
566  [46,54,53,43],
567  [53,58,52,44],
568  [56,57,50,48],
569  [55,59,56,49],
570  [57,59,58,54],
571  [1,7,11,4,0],
572  [8,17,13,5,2],
573  [9,19,20,10,3],
574  [15,26,25,14,6],
575  [21,33,35,23,12],
576  [27,39,34,22,16],
577  [30,42,40,28,18],
578  [29,41,47,36,24],
579  [43,53,44,32,31],
580  [38,49,56,48,37],
581  [50,57,54,46,45],
582  [52,58,59,55,51]
583  ],
584  [
585  [0,1],
586  [0,2],
587  [0,3],
588  [0,4],
589  [1,5],
590  [1,6],
591  [1,7],
592  [2,3],
593  [2,5],
594  [2,8],
595  [3,9],
596  [3,10],
597  [4,9],
598  [4,11],
599  [4,12],
600  [5,6],
601  [5,13],
602  [6,14],
603  [6,15],
604  [7,11],
605  [7,14],
606  [7,16],
607  [8,10],
608  [8,17],
609  [8,18],
610  [9,12],
611  [9,19],
612  [10,18],
613  [10,20],
614  [11,21],
615  [11,22],
616  [12,21],
617  [12,23],
618  [13,15],
619  [13,17],
620  [13,24],
621  [14,16],
622  [14,25],
623  [15,24],
624  [15,26],
625  [16,22],
626  [16,27],
627  [17,28],
628  [17,29],
629  [18,28],
630  [18,30],
631  [19,20],
632  [19,23],
633  [19,31],
634  [20,30],
635  [20,32],
636  [21,22],
637  [21,33],
638  [22,34],
639  [23,31],
640  [23,35],
641  [24,29],
642  [24,36],
643  [25,26],
644  [25,27],
645  [25,37],
646  [26,36],
647  [26,38],
648  [27,37],
649  [27,39],
650  [28,29],
651  [28,40],
652  [29,41],
653  [30,32],
654  [30,42],
655  [31,32],
656  [31,43],
657  [32,44],
658  [33,34],
659  [33,35],
660  [33,45],
661  [34,39],
662  [34,45],
663  [35,43],
664  [35,46],
665  [36,38],
666  [36,47],
667  [37,38],
668  [37,48],
669  [38,49],
670  [39,48],
671  [39,50],
672  [40,41],
673  [40,42],
674  [40,51],
675  [41,47],
676  [41,51],
677  [42,44],
678  [42,52],
679  [43,46],
680  [43,53],
681  [44,52],
682  [44,53],
683  [45,46],
684  [45,50],
685  [46,54],
686  [47,49],
687  [47,55],
688  [48,50],
689  [48,56],
690  [49,55],
691  [49,56],
692  [50,57],
693  [51,52],
694  [51,55],
695  [52,58],
696  [53,54],
697  [53,58],
698  [54,57],
699  [54,58],
700  [55,59],
701  [56,57],
702  [56,59],
703  [57,59],
704  [58,59]
705  ]
706  ],
707  [
708  "rhombicuboctahedron",
709  "Rhombicuboctahedron",
710  empty_str,
711  "archimedean",
712  "George W. Hart, 1997. george@li.net",
713  [
714  [-0.38268328143, 0.92387933161, 0.38268275114],
715  [-0.38268343592, 0.92387933161, -0.38268395285],
716  [-0.92387956713, 0.38268363700, 0.38268319358],
717  [-0.38268348346, 0.38268394530, 0.92387928288],
718  [ 0.38268342775, 0.92387976304, 0.38268292984],
719  [-0.92387954291, 0.38268320557, -0.38268368911],
720  [-0.38268347397, 0.38268302193, -0.92388015529],
721  [ 0.38268345196, 0.92387933161, -0.38268395285],
722  [-0.92387953022, -0.38268325141, 0.38268356327],
723  [ 0.38268340442, 0.38268394530, 0.92387928288],
724  [-0.38268343288, -0.38268297614, 0.92387974597],
725  [ 0.92387952807, 0.38268362957, 0.38268319029],
726  [-0.92387952807, -0.38268362957, -0.38268319029],
727  [ 0.38268343288, 0.38268297614, -0.92387974597],
728  [-0.38268340442, -0.38268394530, -0.92387928288],
729  [ 0.92387953022, 0.38268325141, -0.38268356327],
730  [-0.38268345196, -0.92387933161, 0.38268395285],
731  [ 0.38268347397, -0.38268302193, 0.92388015529],
732  [ 0.92387954291, -0.38268320557, 0.38268368911],
733  [-0.38268342775, -0.92387976304, -0.38268292984],
734  [ 0.38268348346, -0.38268394530, -0.92387928288],
735  [ 0.92387956713, -0.38268363700, -0.38268319358],
736  [ 0.38268343592, -0.92387933161, 0.38268395285],
737  [ 0.38268328143, -0.92387933161, -0.38268275114]
738  ],
739  [
740  [1.07072200000, 112.49999641510, 69.05900891887],
741  [1.07072248472, 112.50000459306, 110.94105000815],
742  [1.07072248843, 157.49998992667, 69.05899357100],
743  [1.07072245696, 134.99996542698, 30.36121857159],
744  [1.07072248843, 67.50000529880, 69.05900868190],
745  [1.07072249045, 157.50001223320, 110.94103477982],
746  [1.07072287631, 135.00003384006, 149.63883548151],
747  [1.07072249045, 67.49999455764, 110.94104989073],
748  [1.07072245090, -157.50000952836, 69.05897162082],
749  [1.07072242871, 45.00004049049, 30.36121599080],
750  [1.07072249208, -135.00003419220, 30.36117275276],
751  [1.07072245090, 22.50001053653, 69.05899299087],
752  [1.07072245090, -157.49998946346, 110.94100700912],
753  [1.07072249208, 44.99996580779, 149.63882724723],
754  [1.07072242871, -134.99995950950, 149.63878400919],
755  [1.07072245090, 22.49999047163, 110.94102837917],
756  [1.07072249045, -112.50000544234, 69.05895010926],
757  [1.07072287631, -44.99996615993, 30.36116451848],
758  [1.07072249045, -22.49998776678, 69.05896522017],
759  [1.07072248843, -112.49999470119, 110.94099131809],
760  [1.07072245696, -45.00003457301, 149.63878142840],
761  [1.07072248843, -22.50001007332, 110.94100642899],
762  [1.07072248472, -67.49999540692, 69.05894999184],
763  [1.07072200000, -67.50000358489, 110.94099108112]
764  ],
765  [
766  [2,5,1,0],
767  [3,0,4,9],
768  [0,1,7,4],
769  [7,1,6,13],
770  [12,5,2,8],
771  [2,3,10,8],
772  [10,3,9,17],
773  [4,7,15,11],
774  [6,5,12,14],
775  [20,13,6,14],
776  [19,12,8,16],
777  [11,18,17,9],
778  [22,16,10,17],
779  [11,15,21,18],
780  [13,20,21,15],
781  [20,14,19,23],
782  [19,16,22,23],
783  [21,23,22,18],
784  [0,3,2],
785  [1,5,6],
786  [4,11,9],
787  [7,13,15],
788  [10,16,8],
789  [14,12,19],
790  [18,22,17],
791  [21,20,23]
792  ],
793  [
794  [0,1],
795  [0,2],
796  [0,3],
797  [0,4],
798  [1,5],
799  [1,6],
800  [1,7],
801  [2,3],
802  [2,5],
803  [2,8],
804  [3,9],
805  [3,10],
806  [4,7],
807  [4,9],
808  [4,11],
809  [5,6],
810  [5,12],
811  [6,13],
812  [6,14],
813  [7,13],
814  [7,15],
815  [8,10],
816  [8,12],
817  [8,16],
818  [9,11],
819  [9,17],
820  [10,16],
821  [10,17],
822  [11,15],
823  [11,18],
824  [12,14],
825  [12,19],
826  [13,15],
827  [13,20],
828  [14,19],
829  [14,20],
830  [15,21],
831  [16,19],
832  [16,22],
833  [17,18],
834  [17,22],
835  [18,21],
836  [18,22],
837  [19,23],
838  [20,21],
839  [20,23],
840  [21,23],
841  [22,23]
842  ]
843  ],
844  [
845  "snub_cuboctahedron",
846  "Snub Cuboctahedron",
847  empty_str,
848  "archimedean",
849  "George W. Hart, 1997. george@li.net",
850  [
851  [-0.27080486838, 0.91612592153, -0.49808755020],
852  [ 0.49808752302, 0.91612592153, -0.27080485082],
853  [ 0.27080461020, 0.49808762370, -0.91612594227],
854  [-0.49808776095, 0.27080472331, -0.91612586036],
855  [-0.91612603041, 0.49808754905, -0.27080459790],
856  [-0.49808755600, 0.91612592153, 0.27080487431],
857  [ 0.27080483540, 0.91612592153, 0.49808757369],
858  [ 0.91612638185, 0.49808776091, 0.27080461106],
859  [ 0.91612582460, 0.27080477644, -0.49808782776],
860  [ 0.49808737939, -0.27080467879, -0.91612587453],
861  [-0.27080496579, -0.49808761926, -0.91612588047],
862  [-0.91612638116, -0.27080488360, -0.49808748945],
863  [-0.91612582693, 0.27080476883, 0.49808776457],
864  [-0.27080454048, 0.49808753367, 0.91612582796],
865  [ 0.49808778376, 0.27080473693, 0.91612584341],
866  [ 0.91612599837, -0.27080473304, 0.49808741445],
867  [ 0.91612591445, -0.49808759505, -0.27080488342],
868  [ 0.27080470991, -0.91612597736, -0.49808767275],
869  [-0.49808763898, -0.91612596752, -0.27080463049],
870  [-0.91612587282, -0.49808764658, 0.27080495527],
871  [-0.49808740806, -0.27080480939, 0.91612601632],
872  [ 0.27080490915, -0.49808763944, 0.91612593107],
873  [ 0.49808769710, -0.91612596056, 0.27080465324],
874  [-0.27080465180, -0.91612595072, 0.49808769550]
875  ],
876  [
877  [1.07736400000, 106.46756696343, 117.53695200801],
878  [1.07736398302, 61.46756400888, 104.55792985199],
879  [1.07736398673, 61.46757444337, 148.24869417527],
880  [1.07736400896, 151.46757102596, 148.24868398663],
881  [1.07736402407, 151.46756561016, 104.55791538808],
882  [1.07736400417, 118.53243758301, 75.44206914970],
883  [1.07736400257, 73.53243493329, 62.46304665467],
884  [1.07736442417, 28.53243539300, 75.44208941452],
885  [1.07736402279, 16.46756332351, 117.53696802255],
886  [1.07736383341, -28.53244343978, 148.24870050408],
887  [1.07736402150, -118.53245734220, 148.24868494079],
888  [1.07736436659, -163.53243997559, 117.53693819966],
889  [1.07736399364, 163.53243715351, 62.46303495878],
890  [1.07736383038, 118.53242371225, 31.75130394128],
891  [1.07736400852, 28.53242908251, 31.75131768838],
892  [1.07736396857, -16.46755787311, 62.46305526226],
893  [1.07736401850, -28.53243965349, 104.55793115311],
894  [1.07736406430, -73.53244309997, 117.53695757482],
895  [1.07736402036, -118.53244038155, 104.55791723032],
896  [1.07736402498, -151.46755676624, 75.44206498868],
897  [1.07736400007, -151.46754634816, 31.75129948809],
898  [1.07736405962, -61.46754866063, 31.75131322146],
899  [1.07736404703, -61.46755663058, 75.44208188813],
900  [1.07736403756, -106.46755401042, 62.46304031944]
901  ],
902  [
903  [1,6,5,0],
904  [3,10,9,2],
905  [12,19,11,4],
906  [8,16,15,7],
907  [14,21,20,13],
908  [18,23,22,17],
909  [2,1,0],
910  [3,2,0],
911  [4,3,0],
912  [5,4,0],
913  [7,6,1],
914  [8,7,1],
915  [2,8,1],
916  [9,8,2],
917  [11,10,3],
918  [4,11,3],
919  [5,12,4],
920  [13,12,5],
921  [6,13,5],
922  [14,13,6],
923  [7,14,6],
924  [15,14,7],
925  [9,16,8],
926  [17,16,9],
927  [10,17,9],
928  [18,17,10],
929  [11,18,10],
930  [19,18,11],
931  [20,19,12],
932  [13,20,12],
933  [15,21,14],
934  [22,21,15],
935  [16,22,15],
936  [17,22,16],
937  [19,23,18],
938  [20,23,19],
939  [21,23,20],
940  [22,23,21]
941  ],
942  [
943  [0,1],
944  [0,2],
945  [0,3],
946  [0,4],
947  [0,5],
948  [1,2],
949  [1,6],
950  [1,7],
951  [1,8],
952  [2,3],
953  [2,8],
954  [2,9],
955  [3,4],
956  [3,10],
957  [3,11],
958  [4,5],
959  [4,11],
960  [4,12],
961  [5,6],
962  [5,12],
963  [5,13],
964  [6,7],
965  [6,13],
966  [6,14],
967  [7,8],
968  [7,14],
969  [7,15],
970  [8,9],
971  [8,16],
972  [9,10],
973  [9,16],
974  [9,17],
975  [10,11],
976  [10,17],
977  [10,18],
978  [11,18],
979  [11,19],
980  [12,13],
981  [12,19],
982  [12,20],
983  [13,14],
984  [13,20],
985  [14,15],
986  [14,21],
987  [15,16],
988  [15,21],
989  [15,22],
990  [16,17],
991  [16,22],
992  [17,18],
993  [17,22],
994  [18,19],
995  [18,23],
996  [19,20],
997  [19,23],
998  [20,21],
999  [20,23],
1000  [21,22],
1001  [21,23],
1002  [22,23]
1003  ]
1004  ],
1005  [
1006  "snub_icosidodecahedron",
1007  "Snub Icosidodecahedron",
1008  "Snub Dodecahedron",
1009  "archimedean",
1010  "George W. Hart, 1997. george@li.net",
1011  [
1012  [ 0.00000000000, 0.00000000000, 1.02803100000],
1013  [ 0.46385690000, 0.00000000000, 0.91743420000],
1014  [ 0.21874360000, 0.40904090000, 0.91743420000],
1015  [-0.25754860000, 0.38578740000, 0.91743420000],
1016  [-0.46165090000, -0.04518499000, 0.91743420000],
1017  [-0.17785800000, -0.42840370000, 0.91743420000],
1018  [ 0.57267820000, -0.42840370000, 0.73848410000],
1019  [ 0.82594010000, -0.04518499000, 0.61043420000],
1020  [ 0.64379550000, 0.38578740000, 0.70252700000],
1021  [ 0.34964800000, 0.74964330000, 0.61043420000],
1022  [-0.42100900000, 0.71201840000, 0.61043420000],
1023  [-0.67831390000, 0.32123960000, 0.70252700000],
1024  [-0.60315360000, -0.44666580000, 0.70252700000],
1025  [-0.27496120000, -0.78013790000, 0.61043420000],
1026  [ 0.17607660000, -0.69317170000, 0.73848410000],
1027  [ 0.52081380000, -0.78013790000, 0.42069780000],
1028  [ 0.85525180000, -0.44666580000, 0.35479980000],
1029  [ 1.01294000000, -0.03548596000, 0.17187760000],
1030  [ 0.71822390000, 0.66184200000, 0.32088680000],
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1380  ]
1381  ],
1382  [
1383  "truncated_cube",
1384  "Truncated Cube",
1385  empty_str,
1386  "archimedean",
1387  "George W. Hart, 1997. george@li.net",
1388  [
1389  [-0.29289338102, 0.70710695251, -0.70710688668],
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1397  [-0.70710699991, 0.29289339044, 0.70710719193],
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1413  ],
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1438  [1.04201100000, -67.49999368986, 47.26579436069]
1439  ],
1440  [
1441  [2,6,11,15,9,4,1,0],
1442  [3,7,12,16,10,5,2,0],
1443  [4,8,14,19,13,7,3,1],
1444  [10,17,21,22,18,11,6,5],
1445  [9,15,18,22,23,20,14,8],
1446  [13,19,20,23,21,17,16,12],
1447  [1,3,0],
1448  [5,6,2],
1449  [9,8,4],
1450  [13,12,7],
1451  [16,17,10],
1452  [18,15,11],
1453  [20,19,14],
1454  [23,22,21]
1455  ],
1456  [
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1470  [7,12],
1471  [7,13],
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1473  [8,14],
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1475  [10,16],
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1481  [13,19],
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1486  [17,21],
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1488  [19,20],
1489  [20,23],
1490  [21,22],
1491  [21,23],
1492  [22,23]
1493  ]
1494  ],
1495  [
1496  "truncated_cuboctahedron",
1497  "Truncated Cuboctahedron",
1498  "Great Rhombicuboctahedron",
1499  "archimedean",
1500  "George W. Hart, 1997. george@li.net",
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1502  [ 0.00000000000, 0.00000000000, 1.02411700000],
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1709  "George W. Hart, 1997. george@li.net",
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1905  [20,29],
1906  [21,30],
1907  [21,31],
1908  [22,23],
1909  [22,31],
1910  [23,32],
1911  [24,25],
1912  [24,33],
1913  [26,29],
1914  [27,34],
1915  [27,35],
1916  [28,36],
1917  [28,37],
1918  [29,38],
1919  [30,31],
1920  [30,39],
1921  [32,40],
1922  [32,41],
1923  [33,42],
1924  [33,43],
1925  [34,35],
1926  [34,44],
1927  [35,36],
1928  [36,37],
1929  [37,45],
1930  [38,46],
1931  [38,47],
1932  [39,48],
1933  [39,49],
1934  [40,41],
1935  [40,50],
1936  [41,42],
1937  [42,43],
1938  [43,51],
1939  [44,52],
1940  [44,53],
1941  [45,51],
1942  [45,54],
1943  [46,47],
1944  [46,52],
1945  [47,48],
1946  [48,49],
1947  [49,55],
1948  [50,55],
1949  [50,56],
1950  [51,54],
1951  [52,53],
1952  [53,57],
1953  [54,58],
1954  [55,56],
1955  [56,59],
1956  [57,58],
1957  [57,59],
1958  [58,59]
1959  ]
1960  ],
1961  [
1962  "truncated_icosahedron",
1963  "Truncated Icosahedron",
1964  "Soccer Ball",
1965  "archimedean",
1966  "George W. Hart, 1997. george@li.net",
1967  [
1968  [ 0.00000000000, 0.00000000000, 1.02100000000],
1969  [ 0.40354820000, 0.00000000000, 0.93786430000],
1970  [-0.22746440000, 0.33333330000, 0.93786430000],
1971  [-0.14712260000, -0.37577400000, 0.93786430000],
1972  [ 0.57963200000, 0.33333330000, 0.77159330000],
1973  [ 0.50583210000, -0.37577400000, 0.80334830000],
1974  [-0.60205140000, 0.29089270000, 0.77159330000],
1975  [-0.05138057000, 0.66666670000, 0.77159330000],
1976  [ 0.16549880000, -0.60801510000, 0.80334830000],
1977  [-0.52170960000, -0.41821470000, 0.77159330000],
1978  [ 0.85799980000, 0.29089270000, 0.47080620000],
1979  [ 0.35216760000, 0.66666670000, 0.68845780000],
1980  [ 0.78419990000, -0.41821470000, 0.50256120000],
1981  [-0.65747500000, 0.59799620000, 0.50256120000],
1982  [-0.74917400000, -0.08488134000, 0.68845780000],
1983  [-0.31714180000, 0.83023730000, 0.50256120000],
1984  [ 0.10353330000, -0.88269690000, 0.50256120000],
1985  [-0.58367510000, -0.69289640000, 0.47080620000],
1986  [ 0.80257610000, 0.59799620000, 0.20177410000],
1987  [ 0.96028370000, -0.08488134000, 0.33629020000],
1988  [ 0.48995470000, 0.83023730000, 0.33629020000],
1989  [ 0.72223430000, -0.69289640000, 0.20177410000],
1990  [-0.86002130000, 0.52932580000, 0.15039350000],
1991  [-0.95172030000, -0.15355180000, 0.33629020000],
1992  [-0.17935480000, 0.99380800000, 0.15039350000],
1993  [ 0.38190100000, -0.92513750000, 0.20177410000],
1994  [-0.27105370000, -0.92513750000, 0.33629020000],
1995  [-0.84943630000, -0.52932580000, 0.20177410000],
1996  [ 0.84943630000, 0.52932580000, -0.20177410000],
1997  [ 1.00714400000, -0.15355180000, -0.06725804000],
1998  [ 0.22419350000, 0.99380800000, 0.06725804000],
1999  [ 0.86002130000, -0.52932580000, -0.15039350000],
2000  [-0.72223430000, 0.69289640000, -0.20177410000],
2001  [-1.00714400000, 0.15355180000, 0.06725804000],
2002  [-0.38190100000, 0.92513750000, -0.20177410000],
2003  [ 0.17935480000, -0.99380800000, -0.15039350000],
2004  [-0.22419350000, -0.99380800000, -0.06725804000],
2005  [-0.80257610000, -0.59799620000, -0.20177410000],
2006  [ 0.58367510000, 0.69289640000, -0.47080620000],
2007  [ 0.95172030000, 0.15355180000, -0.33629020000],
2008  [ 0.27105370000, 0.92513750000, -0.33629020000],
2009  [ 0.65747500000, -0.59799620000, -0.50256120000],
2010  [-0.78419990000, 0.41821470000, -0.50256120000],
2011  [-0.96028370000, 0.08488134000, -0.33629020000],
2012  [-0.10353330000, 0.88269690000, -0.50256120000],
2013  [ 0.31714180000, -0.83023730000, -0.50256120000],
2014  [-0.48995470000, -0.83023730000, -0.33629020000],
2015  [-0.85799980000, -0.29089270000, -0.47080620000],
2016  [ 0.52170960000, 0.41821470000, -0.77159330000],
2017  [ 0.74917400000, 0.08488134000, -0.68845780000],
2018  [ 0.60205140000, -0.29089270000, -0.77159330000],
2019  [-0.50583210000, 0.37577400000, -0.80334830000],
2020  [-0.16549880000, 0.60801510000, -0.80334830000],
2021  [ 0.05138057000, -0.66666670000, -0.77159330000],
2022  [-0.35216760000, -0.66666670000, -0.68845780000],
2023  [-0.57963200000, -0.33333330000, -0.77159330000],
2024  [ 0.14712260000, 0.37577400000, -0.93786430000],
2025  [ 0.22746440000, -0.33333330000, -0.93786430000],
2026  [-0.40354820000, 0.00000000000, -0.93786430000],
2027  [ 0.00000000000, 0.00000000000, -1.02100000000]
2028  ],
2029  [
2030  [1.02100000000, 0.00000000000, 0.00000000000],
2031  [1.02099980163, 0.00000000000, 23.28144638293],
2032  [1.02099979793, 124.30936434470, 23.28144589964],
2033  [1.02099980594, -111.38127902894, 23.28144694392],
2034  [1.02099978693, 29.90223722693, 40.91139210327],
2035  [1.02099985484, -36.60802452007, 38.11020697864],
2036  [1.02099983926, 154.21159674586, 40.91139549154],
2037  [1.02099983960, 94.40712229420, 40.91139551397],
2038  [1.02099985590, -74.77325938912, 38.11020705442],
2039  [1.02099983479, -141.28351568403, 40.91139520210],
2040  [1.02099985195, 18.72850168715, 62.54042349524],
2041  [1.02099982848, 62.15468446190, 47.60036644159],
2042  [1.02099989138, -28.07105081702, 60.51310082742],
2043  [1.02099979950, 137.71239836034, 60.51309791186],
2044  [1.02099983670, -173.53595915020, 47.60036686260],
2045  [1.02099983123, 110.90632399834, 60.51309891853],
2046  [1.02099986348, -83.31022869146, 60.51309994199],
2047  [1.02099976565, -130.10977924110, 62.54042097858],
2048  [1.02099982318, 36.68964578432, 78.60194693065],
2049  [1.02099986532, -5.05135680674, 70.76925197952],
2050  [1.02099984377, 59.45352419280, 70.76925155768],
2051  [1.02099980052, -43.81233790609, 78.60194667427],
2052  [1.02099982558, 148.38853924145, 81.52949732417],
2053  [1.02099989389, -170.83480568164, 70.76925253889],
2054  [1.02099984818, 100.23018223788, 81.52949751303],
2055  [1.02099978214, -67.56894045029, 78.60194646638],
2056  [1.02099980451, -106.32992359903, 70.76925078909],
2057  [1.02099981280, -148.07092378406, 78.60194681318],
2058  [1.02099981280, 31.92907621593, 101.39805318680],
2059  [1.02099991967, -8.66870768157, 93.77707609267],
2060  [1.02099985811, 77.28742557611, 86.22292367924],
2061  [1.02099982558, -31.61146075854, 98.47050267582],
2062  [1.02099980052, 136.18766209390, 101.39805332572],
2063  [1.02099991967, 171.33129231842, 86.22292390732],
2064  [1.02099978214, 112.43105954969, 101.39805353360],
2065  [1.02099984818, -79.76981776211, 98.47050248695],
2066  [1.02099985811, -102.71257442388, 93.77707632074],
2067  [1.02099982318, -143.31035421567, 101.39805306934],
2068  [1.02099976565, 49.89022075889, 117.45957902141],
2069  [1.02099989389, 9.16519431835, 109.23074746110],
2070  [1.02099980451, 73.67007640096, 109.23074921090],
2071  [1.02099979950, -42.28760163965, 119.48690208813],
2072  [1.02099989138, 151.92894918297, 119.48689917256],
2073  [1.02099986532, 174.94864319325, 109.23074802047],
2074  [1.02099986348, 96.68977130853, 119.48690005800],
2075  [1.02099983123, -69.09367600165, 119.48690108146],
2076  [1.02099984377, -120.54647580719, 109.23074844231],
2077  [1.02099985195, -161.27149831284, 117.45957650474],
2078  [1.02099983479, 38.71648431595, 139.08860479789],
2079  [1.02099983670, 6.46404084979, 132.39963313738],
2080  [1.02099983926, -25.78840325413, 139.08860450844],
2081  [1.02099985484, 143.39197547992, 141.88979302135],
2082  [1.02099985590, 105.22674061087, 141.88979294557],
2083  [1.02099983960, -85.59287770579, 139.08860448602],
2084  [1.02099982848, -117.84531553809, 132.39963355840],
2085  [1.02099978693, -150.09776277306, 139.08860789672],
2086  [1.02099980594, 68.61872097105, 156.71855305607],
2087  [1.02099979793, -55.69063565529, 156.71855410035],
2088  [1.02099980163, 179.99999999999, 156.71855361706],
2089  [1.02100000000, 0.00000000000, 179.99999999999]
2090  ],
2091  [
2092  [1,5,8,3,0],
2093  [6,13,15,7,2],
2094  [11,20,18,10,4],
2095  [17,27,23,14,9],
2096  [19,29,31,21,12],
2097  [25,35,36,26,16],
2098  [33,43,42,32,22],
2099  [34,44,40,30,24],
2100  [38,48,49,39,28],
2101  [46,54,55,47,37],
2102  [50,57,53,45,41],
2103  [58,59,56,52,51],
2104  [2,7,11,4,1,0],
2105  [3,9,14,6,2,0],
2106  [4,10,19,12,5,1],
2107  [8,16,26,17,9,3],
2108  [12,21,25,16,8,5],
2109  [14,23,33,22,13,6],
2110  [15,24,30,20,11,7],
2111  [18,28,39,29,19,10],
2112  [22,32,34,24,15,13],
2113  [26,36,46,37,27,17],
2114  [20,30,40,38,28,18],
2115  [31,41,45,35,25,21],
2116  [27,37,47,43,33,23],
2117  [39,49,50,41,31,29],
2118  [42,51,52,44,34,32],
2119  [45,53,54,46,36,35],
2120  [40,44,52,56,48,38],
2121  [43,47,55,58,51,42],
2122  [56,59,57,50,49,48],
2123  [57,59,58,55,54,53]
2124  ],
2125  [
2126  [0,1],
2127  [0,2],
2128  [0,3],
2129  [1,4],
2130  [1,5],
2131  [2,6],
2132  [2,7],
2133  [3,8],
2134  [3,9],
2135  [4,10],
2136  [4,11],
2137  [5,8],
2138  [5,12],
2139  [6,13],
2140  [6,14],
2141  [7,11],
2142  [7,15],
2143  [8,16],
2144  [9,14],
2145  [9,17],
2146  [10,18],
2147  [10,19],
2148  [11,20],
2149  [12,19],
2150  [12,21],
2151  [13,15],
2152  [13,22],
2153  [14,23],
2154  [15,24],
2155  [16,25],
2156  [16,26],
2157  [17,26],
2158  [17,27],
2159  [18,20],
2160  [18,28],
2161  [19,29],
2162  [20,30],
2163  [21,25],
2164  [21,31],
2165  [22,32],
2166  [22,33],
2167  [23,27],
2168  [23,33],
2169  [24,30],
2170  [24,34],
2171  [25,35],
2172  [26,36],
2173  [27,37],
2174  [28,38],
2175  [28,39],
2176  [29,31],
2177  [29,39],
2178  [30,40],
2179  [31,41],
2180  [32,34],
2181  [32,42],
2182  [33,43],
2183  [34,44],
2184  [35,36],
2185  [35,45],
2186  [36,46],
2187  [37,46],
2188  [37,47],
2189  [38,40],
2190  [38,48],
2191  [39,49],
2192  [40,44],
2193  [41,45],
2194  [41,50],
2195  [42,43],
2196  [42,51],
2197  [43,47],
2198  [44,52],
2199  [45,53],
2200  [46,54],
2201  [47,55],
2202  [48,49],
2203  [48,56],
2204  [49,50],
2205  [50,57],
2206  [51,52],
2207  [51,58],
2208  [52,56],
2209  [53,54],
2210  [53,57],
2211  [54,55],
2212  [55,58],
2213  [56,59],
2214  [57,59],
2215  [58,59]
2216  ]
2217  ],
2218  [
2219  "truncated_icosidodecahedron",
2220  "Truncated Icosidodecahedron",
2221  "Great Rhombicosidodecahedron",
2222  "archimedean",
2223  "George W. Hart, 1997. george@li.net",
2224  [
2225  [ 0.00000000000, 0.00000000000, 1.00875900000],
2226  [ 0.26299220000, 0.00000000000, 0.97387400000],
2227  [-0.00462747000, 0.26295150000, 0.97387400000],
2228  [-0.22113630000, -0.14235030000, 0.97387400000],
2229  [ 0.25836470000, 0.26295150000, 0.93898860000],
2230  [ 0.46738610000, -0.14235030000, 0.88254290000],
2231  [-0.23039130000, 0.38355260000, 0.90410330000],
2232  [-0.31595020000, -0.37267800000, 0.88254290000],
2233  [-0.44690010000, -0.02174919000, 0.90410330000],
2234  [ 0.45813120000, 0.38355260000, 0.81277220000],
2235  [ 0.53511040000, -0.37267800000, 0.76965150000],
2236  [ 0.66715260000, -0.02174919000, 0.75632650000],
2237  [-0.33269260000, 0.57868930000, 0.75632650000],
2238  [-0.45152760000, 0.24120230000, 0.86921790000],
2239  [-0.54171400000, -0.25207690000, 0.81277220000],
2240  [-0.24822600000, -0.60300570000, 0.76965150000],
2241  [ 0.51836800000, 0.57868930000, 0.64343510000],
2242  [ 0.66252520000, 0.24120230000, 0.72144120000],
2243  [ 0.73487680000, -0.25207690000, 0.64343510000],
2244  [ 0.44029650000, -0.60300570000, 0.67832050000],
2245  [-0.55382890000, 0.43633900000, 0.72144120000],
2246  [-0.27245570000, 0.77382610000, 0.58698940000],
2247  [-0.69975360000, -0.36180340000, 0.63011010000],
2248  [-0.04383203000, -0.74535600000, 0.67832050000],
2249  [-0.40626560000, -0.71273220000, 0.58698940000],
2250  [ 0.72276200000, 0.43633900000, 0.55210400000],
2251  [ 0.41606670000, 0.77382610000, 0.49565830000],
2252  [ 0.83982940000, -0.36180340000, 0.42588760000],
2253  [ 0.21916010000, -0.74535600000, 0.64343510000],
2254  [ 0.54524910000, -0.71273220000, 0.46077300000],
2255  [-0.71472840000, 0.48912540000, 0.51721870000],
2256  [-0.07268925000, 0.89442720000, 0.46077300000],
2257  [-0.43335530000, 0.82661250000, 0.38276690000],
2258  [-0.86065310000, -0.30901700000, 0.42588760000],
2259  [-0.63202940000, -0.59213110000, 0.51721870000],
2260  [-0.20187160000, -0.85508250000, 0.49565830000],
2261  [ 0.82485460000, 0.48912540000, 0.31299620000],
2262  [ 0.19030290000, 0.89442720000, 0.42588760000],
2263  [ 0.51815940000, 0.82661250000, 0.25655050000],
2264  [ 0.94192210000, -0.30901700000, 0.18677980000],
2265  [ 0.74501560000, -0.59213110000, 0.33455660000],
2266  [ 0.32411270000, -0.85508250000, 0.42588760000],
2267  [-0.87276790000, 0.37939890000, 0.33455660000],
2268  [-0.65449160000, 0.68426210000, 0.34788160000],
2269  [-0.23358880000, 0.94721360000, 0.25655050000],
2270  [-0.79292890000, -0.53934470000, 0.31299620000],
2271  [-0.96295440000, -0.11388030000, 0.27811090000],
2272  [-0.09691900000, -0.96480910000, 0.27811090000],
2273  [ 0.92980720000, 0.37939890000, 0.09544872000],
2274  [ 0.72255330000, 0.68426210000, 0.16521940000],
2275  [ 0.29239560000, 0.94721360000, 0.18677980000],
2276  [ 0.84710820000, -0.53934470000, 0.09544872000],
2277  [ 1.00215900000, -0.11388030000, 0.01744268000],
2278  [ 0.16607320000, -0.96480910000, 0.24322550000],
2279  [-0.81253110000, 0.57453560000, 0.16521940000],
2280  [-0.96758180000, 0.14907120000, 0.24322550000],
2281  [-0.13149610000, 1.00000000000, 0.01744268000],
2282  [-0.82750590000, -0.57453560000, 0.05232804000],
2283  [-0.99753150000, -0.14907120000, 0.01744268000],
2284  [-0.13149610000, -1.00000000000, 0.01744268000],
2285  [ 0.82750590000, 0.57453560000, -0.05232804000],
2286  [ 0.99753150000, 0.14907120000, -0.01744268000],
2287  [ 0.13149610000, 1.00000000000, -0.01744268000],
2288  [ 0.81253110000, -0.57453560000, -0.16521940000],
2289  [ 0.96758180000, -0.14907120000, -0.24322550000],
2290  [ 0.13149610000, -1.00000000000, -0.01744268000],
2291  [-0.84710820000, 0.53934470000, -0.09544872000],
2292  [-1.00215900000, 0.11388030000, -0.01744268000],
2293  [-0.16607320000, 0.96480910000, -0.24322550000],
2294  [-0.72255330000, -0.68426210000, -0.16521940000],
2295  [-0.92980720000, -0.37939890000, -0.09544872000],
2296  [-0.29239560000, -0.94721360000, -0.18677980000],
2297  [ 0.79292890000, 0.53934470000, -0.31299620000],
2298  [ 0.96295440000, 0.11388030000, -0.27811090000],
2299  [ 0.09691900000, 0.96480910000, -0.27811090000],
2300  [ 0.65449160000, -0.68426210000, -0.34788160000],
2301  [ 0.87276790000, -0.37939890000, -0.33455660000],
2302  [ 0.23358880000, -0.94721360000, -0.25655050000],
2303  [-0.74501560000, 0.59213110000, -0.33455660000],
2304  [-0.94192210000, 0.30901700000, -0.18677980000],
2305  [-0.32411270000, 0.85508250000, -0.42588760000],
2306  [-0.82485460000, -0.48912540000, -0.31299620000],
2307  [-0.51815940000, -0.82661250000, -0.25655050000],
2308  [-0.19030290000, -0.89442720000, -0.42588760000],
2309  [ 0.63202940000, 0.59213110000, -0.51721870000],
2310  [ 0.86065310000, 0.30901700000, -0.42588760000],
2311  [ 0.20187160000, 0.85508250000, -0.49565830000],
2312  [ 0.71472840000, -0.48912540000, -0.51721870000],
2313  [ 0.43335530000, -0.82661250000, -0.38276690000],
2314  [ 0.07268925000, -0.89442720000, -0.46077300000],
2315  [-0.83982940000, 0.36180340000, -0.42588760000],
2316  [-0.54524910000, 0.71273220000, -0.46077300000],
2317  [-0.21916010000, 0.74535600000, -0.64343510000],
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2713  ]
2714  ],
2715  [
2716  "truncated_octahedron",
2717  "Truncated Octahedron",
2718  empty_str,
2719  "archimedean",
2720  "Exact Mathematics",
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2761  [2.23606797750, -89.99999999999, 63.43494882292],
2762  [2.23606797750, 0.00000000000, 153.43494882291],
2763  [2.23606797750, -63.43494882292, 89.99999999999],
2764  [2.23606797750, 179.99999999999, 63.43494882292],
2765  [2.23606797750, 153.43494882291, 89.99999999999],
2766  [2.23606797750, -89.99999999999, 153.43494882291],
2767  [2.23606797750, -89.99999999999, 116.56505117707],
2768  [2.23606797750, 179.99999999999, 153.43494882291],
2769  [2.23606797750, -116.56505117707, 89.99999999999],
2770  [2.23606797750, 179.99999999999, 116.56505117707],
2771  [2.23606797750, -153.43494882291, 89.99999999999]
2772  ],
2773  [
2774  [7,3,1,9],
2775  [12,7,9,17,22,20],
2776  [1,0,8,16,17,9],
2777  [11,4,5,10],
2778  [16,23,22,17],
2779  [14,10,5,3,7,12],
2780  [4,2,0,1,3,5],
2781  [21,13,15,19],
2782  [19,18,20,22,23,21],
2783  [14,18,19,15,11,10],
2784  [18,14,12,20],
2785  [23,16,8,6,13,21],
2786  [15,13,6,2,4,11],
2787  [2,6,8,0]
2788  ],
2789  [
2790  [0,1],
2791  [0,2],
2792  [0,8],
2793  [1,3],
2794  [1,9],
2795  [2,4],
2796  [2,6],
2797  [3,5],
2798  [3,7],
2799  [4,5],
2800  [4,11],
2801  [5,10],
2802  [6,8],
2803  [6,13],
2804  [7,9],
2805  [7,12],
2806  [8,16],
2807  [9,17],
2808  [10,11],
2809  [10,14],
2810  [11,15],
2811  [12,14],
2812  [12,20],
2813  [13,15],
2814  [13,21],
2815  [14,18],
2816  [15,19],
2817  [16,17],
2818  [16,23],
2819  [17,22],
2820  [18,19],
2821  [18,20],
2822  [19,21],
2823  [20,22],
2824  [21,23],
2825  [22,23]
2826  ]
2827  ],
2828  [
2829  "truncated_tetrahedron",
2830  "Truncated Tetrahedron",
2831  empty_str,
2832  "archimedean",
2833  "Exact Mathematics",
2834  [
2835  [ 1.00000000000, 1.00000000000, -3.00000000000],
2836  [ 3.00000000000, 1.00000000000, -1.00000000000],
2837  [ 1.00000000000, 3.00000000000, -1.00000000000],
2838  [-1.00000000000, 1.00000000000, 3.00000000000],
2839  [-3.00000000000, 1.00000000000, 1.00000000000],
2840  [-1.00000000000, 3.00000000000, 1.00000000000],
2841  [ 1.00000000000, -1.00000000000, 3.00000000000],
2842  [ 3.00000000000, -1.00000000000, 1.00000000000],
2843  [ 1.00000000000, -3.00000000000, 1.00000000000],
2844  [-1.00000000000, -1.00000000000, -3.00000000000],
2845  [-3.00000000000, -1.00000000000, -1.00000000000],
2846  [-1.00000000000, -3.00000000000, -1.00000000000]
2847  ],
2848  [
2849  [3.31662479036, 45.00000000000, 154.76059817931],
2850  [3.31662479036, 18.43494882292, 107.54840061379],
2851  [3.31662479036, 71.56505117707, 107.54840061379],
2852  [3.31662479036, 134.99999999999, 25.23940182068],
2853  [3.31662479036, 161.56505117707, 72.45159938620],
2854  [3.31662479036, 108.43494882291, 72.45159938620],
2855  [3.31662479036, -45.00000000000, 25.23940182068],
2856  [3.31662479036, -18.43494882292, 72.45159938620],
2857  [3.31662479036, -71.56505117707, 72.45159938620],
2858  [3.31662479036, -134.99999999999, 154.76059817931],
2859  [3.31662479036, -161.56505117707, 107.54840061379],
2860  [3.31662479036, -108.43494882291, 107.54840061379]
2861  ],
2862  [
2863  [0,1,2],
2864  [3,4,5],
2865  [6,7,8],
2866  [9,10,11],
2867  [0,2,5,4,10,9],
2868  [5,2,1,7,6,3],
2869  [4,3,6,8,11,10],
2870  [1,0,9,11,8,7]
2871  ],
2872  [
2873  [0,1],
2874  [0,2],
2875  [0,9],
2876  [1,2],
2877  [1,7],
2878  [2,5],
2879  [3,4],
2880  [3,5],
2881  [3,6],
2882  [4,5],
2883  [4,10],
2884  [6,7],
2885  [6,8],
2886  [7,8],
2887  [8,11],
2888  [9,10],
2889  [9,11],
2890  [10,11]
2891  ]
2892  ]
2893 ];
2894 
2895 //! @}
2896 
2897 //----------------------------------------------------------------------------//
2898 // openscad-amu auxiliary scripts
2899 //----------------------------------------------------------------------------//
2900 
2901 /*
2902 BEGIN_SCOPE db;
2903 BEGIN_SCOPE autostat;
2904  BEGIN_OPENSCAD;
2905  include <omdl-base.scad>;
2906  include <database/geometry/polyhedra/archimedean.scad>;
2907 
2908  fs = "^";
2909 
2910  tc = dtc_polyhedra_archimedean;
2911  tr = dtr_polyhedra_archimedean;
2912 
2913  ids = table_get_row_ids(tr);
2914 
2915  echo
2916  (
2917  str
2918  (
2919  "no.", fs, "id", fs, "other name", fs,
2920  "vertices", fs, "faces", fs, "edges",
2921 
2922  fs, "face-verticies",
2923  fs, "face-angles",
2924  fs, "edge-lengths",
2925  fs, "edge-angles"
2926  )
2927  );
2928 
2929  for ( id = ids )
2930  {
2931  i = first(find(id, ids, c=1))+1;
2932 
2933  n = table_get_value(tr, tc, id, "n");
2934  o = table_get_value(tr, tc, id, "o");
2935  g = table_get_value(tr, tc, id, "g");
2936  d = table_get_value(tr, tc, id, "d");
2937 
2938  c = table_get_value(tr, tc, id, "c");
2939  s = table_get_value(tr, tc, id, "s");
2940  f = table_get_value(tr, tc, id, "f");
2941  e = table_get_value(tr, tc, id, "e");
2942 
2943  fo = is_empty(o) ? "-" : o;
2944 
2945  echo
2946  (
2947  str
2948  (
2949  i, fs, id, fs, fo, fs,
2950  len(c), fs, len(f), fs, len(e),
2951 
2952  fs, histogram(sort_q(polytope_face_vertex_counts(f)), m=9),
2953  fs, histogram(sort_q(round_d(polytope_face_angles(c, f), d=1)), m=9),
2954  fs, histogram(sort_q(round_s(polytope_edge_lengths(c, e), d=3)), m=9),
2955  fs, histogram(sort_q(round_d(polytope_edge_angles(c, f), d=1)), m=9),
2956 
2957  fs
2958  )
2959  );
2960  }
2961  END_OPENSCAD;
2962 
2963  BEGIN_MFSCRIPT;
2964  include --path "${INCLUDE_PATH}" {var_init,var_gen_term}.mfs;
2965  include --path "${INCLUDE_PATH}" scr_make_mf.mfs;
2966  END_MFSCRIPT;
2967 END_SCOPE;
2968 END_SCOPE;
2969 */
2970 
2971 /*
2972 BEGIN_SCOPE db;
2973 BEGIN_SCOPE dim;
2974  BEGIN_OPENSCAD;
2975  include <omdl-base.scad>;
2976  include <units/coordinate.scad>;
2977  include <tools/align.scad>;
2978  include <tools/polytope.scad>;
2979  include <database/geometry/polyhedra/archimedean.scad>;
2980 
2981  config = 0;
2982 
2983  tc = dtc_polyhedra_archimedean;
2984  tr = dtr_polyhedra_archimedean;
2985 
2986  id = "default";
2987  sr = 100;
2988 
2989  pv = table_get_value(tr, tc, id, "c");
2990  pf = table_get_value(tr, tc, id, "f");
2991  pe = table_get_value(tr, tc, id, "e");
2992 
2993  sv = coordinate_scale3d_csc(pv, sr);
2994 
2995  if (config == 0) // png preview
2996  {
2997  $fn = 25;
2998 
2999  %polyhedron(sv, pf);
3000 
3001  polytope_frame(sv, pf, pe)
3002  {
3003  circle(r = sr / 25);
3004  color("lightblue")
3005  sphere(r = sr / 25 * (1 + 1/2));
3006  }
3007  }
3008 
3009  if (config == 1) // stl model
3010  {
3011  polyhedron(sv, pf);
3012  }
3013  END_OPENSCAD;
3014 
3015  BEGIN_MFSCRIPT;
3016  include --path "${INCLUDE_PATH}" {var_init,var_gen_png2eps}.mfs;
3017 
3018  views name "views" views "diag";
3019  defines name "ids" define "id"
3020  strings
3021  "
3022  cuboctahedron
3023  icosidodecahedron
3024  rhombicosidodecahedron
3025  rhombicuboctahedron
3026  snub_cuboctahedron
3027  snub_icosidodecahedron
3028  truncated_cube
3029  truncated_cuboctahedron
3030  truncated_dodecahedron
3031  truncated_icosahedron
3032  truncated_icosidodecahedron
3033  truncated_octahedron
3034  truncated_tetrahedron
3035  ";
3036  variables add_opts_combine "views ids";
3037  variables add_opts "-D config=0 --viewall --autocenter --view=axes";
3038 
3039  include --path "${INCLUDE_PATH}" scr_make_mf_begin.mfs;
3040  include --path "${INCLUDE_PATH}" scr_make_mf_add_ext.mfs;
3041 
3042  include --path "${INCLUDE_PATH}" var_gen_stl.mfs;
3043  variables add_opts_combine "ids";
3044  variables add_opts "-D config=1";
3045 
3046  include --path "${INCLUDE_PATH}" scr_make_mf_add_ext.mfs;
3047  include --path "${INCLUDE_PATH}" scr_make_mf_end.mfs;
3048  END_MFSCRIPT;
3049 END_SCOPE;
3050 END_SCOPE;
3051 */
3052 
3053 //----------------------------------------------------------------------------//
3054 // end of file
3055 //----------------------------------------------------------------------------//
empty_str
empty_str
<string> A string with no characters (the empty string).
Definition: constants.scad:301
dtr_polyhedra_archimedean
dtr_polyhedra_archimedean
Definition: archimedean.scad:212
dtc_polyhedra_archimedean
dtc_polyhedra_archimedean
Definition: archimedean.scad:197