omdl  v0.9.5
OpenSCAD Mechanical Design Library
archimedean_duals.scad
Go to the documentation of this file.
1 //! Polyhedra data table: \c archimedean_duals.
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 Duals ###
64  \amu_include (include/amu/includes_required.amu)
65 
66  \amu_eval
67  (
68  ++global
69  title="Examples"
70  stem=archimedean_duals 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_duals polyhedra data table columns definition.
128 //! \hideinitializer
129 dtc_polyhedra_archimedean_duals =
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_duals polyhedra data table rows.
143 //! \hideinitializer
144 dtr_polyhedra_archimedean_duals =
145 [
146  [
147  "disdyakis_dodecahedron",
148  "Disdyakis-Dodecahedron",
149  "Hexakis-Octahedron",
150  "archimedean_duals",
151  "Exact Mathematics",
152  [
153  [ 0.00000000000, 0.00000000000, 1.00000000000],
154  [ 0.70710678119, 0.00000000000, 0.70710678119],
155  [ 0.00000000000, 0.70710678119, 0.70710678119],
156  [-0.70710678119, 0.00000000000, 0.70710678119],
157  [ 0.00000000000, -0.70710678119, 0.70710678119],
158  [ 0.57735026919, 0.57735026919, 0.57735026919],
159  [-0.57735026919, 0.57735026919, 0.57735026919],
160  [-0.57735026919, -0.57735026919, 0.57735026919],
161  [ 0.57735026919, -0.57735026919, 0.57735026919],
162  [ 1.00000000000, 0.00000000000, 0.00000000000],
163  [ 0.70710678119, 0.70710678119, 0.00000000000],
164  [ 0.00000000000, 1.00000000000, 0.00000000000],
165  [-0.70710678119, 0.70710678119, 0.00000000000],
166  [-1.00000000000, 0.00000000000, 0.00000000000],
167  [-0.70710678119, -0.70710678119, 0.00000000000],
168  [ 0.00000000000, -1.00000000000, 0.00000000000],
169  [ 0.70710678119, -0.70710678119, 0.00000000000],
170  [ 0.57735026919, 0.57735026919, -0.57735026919],
171  [-0.57735026919, 0.57735026919, -0.57735026919],
172  [-0.57735026919, -0.57735026919, -0.57735026919],
173  [ 0.57735026919, -0.57735026919, -0.57735026919],
174  [ 0.70710678119, 0.00000000000, -0.70710678119],
175  [ 0.00000000000, 0.70710678119, -0.70710678119],
176  [-0.70710678119, 0.00000000000, -0.70710678119],
177  [ 0.00000000000, -0.70710678119, -0.70710678119],
178  [ 0.00000000000, 0.00000000000, -1.00000000000]
179  ],
180  [
181  [1.00000000000, 0.00000000000, 0.00000000000],
182  [1.00000000000, 0.00000000000, 45.00000000000],
183  [1.00000000000, 89.99999999999, 45.00000000000],
184  [1.00000000000, 179.99999999999, 45.00000000000],
185  [1.00000000000, -89.99999999999, 45.00000000000],
186  [1.00000000000, 45.00000000000, 54.73561031724],
187  [1.00000000000, 134.99999999999, 54.73561031724],
188  [1.00000000000, -134.99999999999, 54.73561031724],
189  [1.00000000000, -45.00000000000, 54.73561031724],
190  [1.00000000000, 0.00000000000, 89.99999999999],
191  [1.00000000000, 45.00000000000, 89.99999999999],
192  [1.00000000000, 89.99999999999, 89.99999999999],
193  [1.00000000000, 134.99999999999, 89.99999999999],
194  [1.00000000000, 179.99999999999, 89.99999999999],
195  [1.00000000000, -134.99999999999, 89.99999999999],
196  [1.00000000000, -89.99999999999, 89.99999999999],
197  [1.00000000000, -45.00000000000, 89.99999999999],
198  [1.00000000000, 45.00000000000, 125.26438968275],
199  [1.00000000000, 134.99999999999, 125.26438968275],
200  [1.00000000000, -134.99999999999, 125.26438968275],
201  [1.00000000000, -45.00000000000, 125.26438968275],
202  [1.00000000000, 0.00000000000, 134.99999999999],
203  [1.00000000000, 89.99999999999, 134.99999999999],
204  [1.00000000000, 179.99999999999, 134.99999999999],
205  [1.00000000000, -89.99999999999, 134.99999999999],
206  [1.00000000000, 0.00000000000, 179.99999999999]
207  ],
208  [
209  [6,3,13],
210  [3,6,0],
211  [1,5,9],
212  [5,1,0],
213  [6,2,0],
214  [2,5,0],
215  [2,6,11],
216  [5,2,11],
217  [23,18,13],
218  [18,23,25],
219  [12,6,13],
220  [18,12,13],
221  [6,12,11],
222  [12,18,11],
223  [17,21,9],
224  [21,17,25],
225  [5,10,9],
226  [10,17,9],
227  [10,5,11],
228  [17,10,11],
229  [22,18,25],
230  [17,22,25],
231  [18,22,11],
232  [22,17,11],
233  [7,3,0],
234  [3,7,13],
235  [4,7,0],
236  [7,4,15],
237  [7,14,13],
238  [14,7,15],
239  [23,19,25],
240  [19,14,15],
241  [19,23,13],
242  [14,19,13],
243  [1,8,0],
244  [8,4,0],
245  [8,1,9],
246  [16,8,9],
247  [8,16,15],
248  [4,8,15],
249  [19,24,25],
250  [24,19,15],
251  [21,20,9],
252  [20,16,9],
253  [20,21,25],
254  [24,20,25],
255  [16,20,15],
256  [20,24,15]
257  ],
258  [
259  [0,1],
260  [0,2],
261  [0,3],
262  [0,4],
263  [0,5],
264  [0,6],
265  [0,7],
266  [0,8],
267  [1,5],
268  [1,8],
269  [1,9],
270  [2,5],
271  [2,6],
272  [2,11],
273  [3,6],
274  [3,7],
275  [3,13],
276  [4,7],
277  [4,8],
278  [4,15],
279  [5,9],
280  [5,10],
281  [5,11],
282  [6,11],
283  [6,12],
284  [6,13],
285  [7,13],
286  [7,14],
287  [7,15],
288  [8,9],
289  [8,15],
290  [8,16],
291  [9,10],
292  [9,16],
293  [9,17],
294  [9,20],
295  [9,21],
296  [10,11],
297  [10,17],
298  [11,12],
299  [11,17],
300  [11,18],
301  [11,22],
302  [12,13],
303  [12,18],
304  [13,14],
305  [13,18],
306  [13,19],
307  [13,23],
308  [14,15],
309  [14,19],
310  [15,16],
311  [15,19],
312  [15,20],
313  [15,24],
314  [16,20],
315  [17,21],
316  [17,22],
317  [17,25],
318  [18,22],
319  [18,23],
320  [18,25],
321  [19,23],
322  [19,24],
323  [19,25],
324  [20,21],
325  [20,24],
326  [20,25],
327  [21,25],
328  [22,25],
329  [23,25],
330  [24,25]
331  ]
332  ],
333  [
334  "disdyakis_triacontahedron",
335  "Disdyakis-Triacontahedron",
336  "Hexakis-Icosahedron",
337  "archimedean_duals",
338  "George W. Hart, 1997. george@li.net",
339  [
340  [-0.50445781003, 0.85823482728, -0.16390828497],
341  [-0.36662979208, 0.81649657980, -0.50462268725],
342  [-0.93184127980, 0.48989796379, -0.30277358267],
343  [-0.59321945859, 0.81649657360, 0.19274866308],
344  [ 0.00000000000, 1.09544514122, 0.00000000000],
345  [-0.50445778133, 0.53041832127, -0.69432657505],
346  [-0.81622979173, 0.53041830040, 0.26520912954],
347  [ 0.00000001518, 0.85823486838, -0.53041833095],
348  [-0.59321946723, 0.19274867602, -0.81649654739],
349  [ 0.00000000000, 0.48989795293, -0.97979595711],
350  [-0.31177199523, 0.85823484751, 0.42911737364],
351  [-0.95984929502, 0.19274875966, 0.31187389294],
352  [-0.57590958810, 0.48989797384, 0.79267156652],
353  [ 0.36662981623, 0.81649662504, -0.50462266207],
354  [-0.81622981643, 0.00000002808, -0.59302572359],
355  [ 0.00000000558, 0.81649664218, 0.62374790189],
356  [-1.00891555440, 0.00000005159, -0.00000002191],
357  [ 0.50445781792, 0.85823483908, -0.16390823916],
358  [-0.31177210334, 0.00000001596, -0.95953570176],
359  [-0.95984928118, -0.19274864408, -0.31187392864],
360  [-0.57590955558, -0.48989798773, -0.79267154078],
361  [ 0.31177211852, 0.85823485242, 0.42911737081],
362  [-0.81622985171, 0.00000001860, 0.59302570450],
363  [-0.93184128858, -0.48989792546, 0.30277360378],
364  [ 0.50445777307, 0.53041826968, -0.69432655314],
365  [ 0.59321951559, 0.81649655588, 0.19274869309],
366  [ 0.93184128858, 0.48989792546, -0.30277360378],
367  [-0.00000002036, -0.19274873371, -1.00924525494],
368  [ 0.00000002470, 0.53041827232, 0.85823485312],
369  [ 0.57590955558, 0.48989798773, 0.79267154078],
370  [-0.59321949238, -0.19274868694, 0.81649654849],
371  [ 0.59321949238, 0.19274868694, -0.81649654849],
372  [ 0.31177214323, -0.00000007614, -0.95953585607],
373  [-0.81622981685, -0.53041833140, -0.26520912587],
374  [ 0.00000002036, 0.19274873371, 1.00924525494],
375  [-0.31177214323, 0.00000007614, 0.95953585607],
376  [ 0.81622981685, 0.53041833140, 0.26520912587],
377  [-0.00000002470, -0.53041827232, -0.85823485312],
378  [ 0.57590958810, -0.48989797384, -0.79267156652],
379  [-0.59321951559, -0.81649655588, -0.19274869309],
380  [-0.50445777307, -0.53041826968, 0.69432655314],
381  [-0.00000000000, -0.48989795293, 0.97979595711],
382  [ 0.81622985171, -0.00000001860, -0.59302570450],
383  [ 0.95984928118, 0.19274864408, 0.31187392864],
384  [-0.00000000558, -0.81649664218, -0.62374790189],
385  [-0.31177211852, -0.85823485242, -0.42911737081],
386  [ 0.31177210334, -0.00000001596, 0.95953570176],
387  [-0.36662981623, -0.81649662504, 0.50462266207],
388  [-0.50445781792, -0.85823483908, 0.16390823916],
389  [ 0.95984929502, -0.19274875966, -0.31187389294],
390  [ 1.00891555440, -0.00000005159, 0.00000002191],
391  [ 0.00000000000, -1.09544514122, 0.00000000000],
392  [ 0.59321946723, -0.19274867602, 0.81649654739],
393  [ 0.81622981643, -0.00000002808, 0.59302572359],
394  [ 0.93184127980, -0.48989796379, 0.30277358267],
395  [ 0.31177199523, -0.85823484751, -0.42911737364],
396  [-0.00000001518, -0.85823486838, 0.53041833095],
397  [ 0.81622979173, -0.53041830040, -0.26520912954],
398  [ 0.59321945859, -0.81649657360, -0.19274866308],
399  [ 0.50445778133, -0.53041832127, 0.69432657505],
400  [ 0.36662979208, -0.81649657980, 0.50462268725],
401  [ 0.50445781003, -0.85823482728, 0.16390828497]
402  ],
403  [
404  [1.00891556968, 120.44638608101, 99.34970439173],
405  [1.02748631414, 114.18141338542, 119.41445354663],
406  [1.09544512781, 152.26769800096, 106.04505691244],
407  [1.02748626651, 125.99999880122, 79.18768461129],
408  [1.09544514122, 89.99999999999, 89.99999999999],
409  [1.00891557700, 133.56299949458, 133.48707737940],
410  [1.00891552109, 146.98260050283, 74.75983830192],
411  [1.00891560357, 89.99999898680, 121.71747498907],
412  [1.02748625310, 162.00000114211, 142.62263196464],
413  [1.09544517063, 89.99999999999, 153.43495002171],
414  [1.00891553207, 109.96462504973, 64.82873988729],
415  [1.02748629119, 168.64536825352, 72.33019567813],
416  [1.09544515646, 139.61382144892, 43.64692674940],
417  [1.02748634634, 65.81858639072, 119.41445092243],
418  [1.00891556736, 179.99999802856, 126.00000226595],
419  [1.02748635602, 89.99999960836, 52.62263315940],
420  [1.00891555440, 179.99999707004, 90.00000124425],
421  [1.00891557622, 59.55361387162, 99.34970169408],
422  [1.00891556008, 179.99999706617, 161.99999705108],
423  [1.02748626742, -168.64537472596, 107.66980683355],
424  [1.09544512695, -139.61381905073, 136.35307291839],
425  [1.00891557314, 70.03536778427, 64.82874116074],
426  [1.00891558469, 179.99999869430, 53.99999978842],
427  [1.09544512397, -152.26770006971, 73.95494188062],
428  [1.00891553067, 46.43699819052, 133.48707816006],
429  [1.02748629097, 53.99999798965, 79.18768316812],
430  [1.09544512397, 27.73229993028, 106.04505811936],
431  [1.02748628164, -90.00000605311, 169.18768076305],
432  [1.00891555976, 89.99999733187, 31.71747261228],
433  [1.09544512695, 40.38618094925, 43.64692708160],
434  [1.02748627054, -162.00000090189, 37.37736920747],
435  [1.02748627054, 17.99999909809, 142.62263079252],
436  [1.00891571917, -0.00001399184, 161.99999760451],
437  [1.00891555675, -146.98259977856, 105.24016093031],
438  [1.02748628164, 89.99999394687, 10.81231923693],
439  [1.00891571917, 179.99998600815, 18.00000239548],
440  [1.00891555675, 33.01740022143, 74.75983906968],
441  [1.00891555976, -90.00000266812, 148.28252738771],
442  [1.09544515646, -40.38617855106, 136.35307325059],
443  [1.02748629097, -126.00000201034, 100.81231683187],
444  [1.00891553067, -133.56300180947, 46.51292183993],
445  [1.09544517063, -89.99999999999, 26.56504997828],
446  [1.00891558469, -0.00000130569, 126.00000021157],
447  [1.02748626742, 11.35462527402, 72.33019316644],
448  [1.02748635602, -90.00000039163, 127.37736684059],
449  [1.00891557314, -109.96463221572, 115.17125883925],
450  [1.00891556008, -0.00000293381, 18.00000294891],
451  [1.02748634634, -114.18141360927, 60.58554907756],
452  [1.00891557622, -120.44638612836, 80.65029830591],
453  [1.02748629119, -11.35463174646, 107.66980432186],
454  [1.00891555440, -0.00000292995, 89.99999875574],
455  [1.09544514122, -89.99999999999, 89.99999999999],
456  [1.02748625310, -17.99999885788, 37.37736803535],
457  [1.00891556736, -0.00000197142, 53.99999773404],
458  [1.09544512781, -27.73230199903, 73.95494308754],
459  [1.00891553207, -70.03537495026, 115.17126011270],
460  [1.00891560357, -90.00000101319, 58.28252501092],
461  [1.00891552109, -33.01739949716, 105.24016169807],
462  [1.02748626651, -54.00000119877, 100.81231538870],
463  [1.00891557700, -46.43700050541, 46.51292262059],
464  [1.02748631414, -65.81858661456, 60.58554645336],
465  [1.00891556968, -59.55361391898, 80.65029560825]
466  ],
467  [
468  [1,0,2],
469  [0,3,2],
470  [1,4,0],
471  [2,5,1],
472  [4,3,0],
473  [6,2,3],
474  [7,4,1],
475  [8,5,2],
476  [9,1,5],
477  [4,10,3],
478  [6,11,2],
479  [3,12,6],
480  [7,13,4],
481  [1,9,7],
482  [8,9,5],
483  [2,14,8],
484  [15,10,4],
485  [12,3,10],
486  [12,11,6],
487  [16,2,11],
488  [9,13,7],
489  [17,4,13],
490  [18,9,8],
491  [19,14,2],
492  [20,8,14],
493  [15,12,10],
494  [4,21,15],
495  [12,22,11],
496  [16,19,2],
497  [11,23,16],
498  [9,24,13],
499  [17,25,4],
500  [13,26,17],
501  [18,27,9],
502  [8,20,18],
503  [19,20,14],
504  [28,12,15],
505  [25,21,4],
506  [29,15,21],
507  [30,22,12],
508  [23,11,22],
509  [23,19,16],
510  [31,24,9],
511  [26,13,24],
512  [26,25,17],
513  [20,27,18],
514  [32,9,27],
515  [33,20,19],
516  [28,34,12],
517  [15,29,28],
518  [25,29,21],
519  [30,23,22],
520  [12,35,30],
521  [23,33,19],
522  [31,26,24],
523  [9,32,31],
524  [26,36,25],
525  [20,37,27],
526  [27,38,32],
527  [33,39,20],
528  [29,34,28],
529  [35,12,34],
530  [36,29,25],
531  [40,23,30],
532  [41,30,35],
533  [39,33,23],
534  [42,26,31],
535  [38,31,32],
536  [43,36,26],
537  [44,37,20],
538  [38,27,37],
539  [45,20,39],
540  [29,46,34],
541  [34,41,35],
542  [36,43,29],
543  [40,47,23],
544  [30,41,40],
545  [23,48,39],
546  [42,49,26],
547  [31,38,42],
548  [26,50,43],
549  [44,38,37],
550  [20,45,44],
551  [39,51,45],
552  [52,46,29],
553  [41,34,46],
554  [53,29,43],
555  [41,47,40],
556  [48,23,47],
557  [51,39,48],
558  [38,49,42],
559  [50,26,49],
560  [54,43,50],
561  [55,38,44],
562  [51,44,45],
563  [52,41,46],
564  [29,53,52],
565  [43,54,53],
566  [41,56,47],
567  [47,51,48],
568  [38,57,49],
569  [49,54,50],
570  [55,58,38],
571  [44,51,55],
572  [59,41,52],
573  [54,52,53],
574  [60,56,41],
575  [51,47,56],
576  [58,57,38],
577  [54,49,57],
578  [51,58,55],
579  [59,60,41],
580  [52,54,59],
581  [60,51,56],
582  [58,54,57],
583  [51,61,58],
584  [54,60,59],
585  [61,51,60],
586  [61,54,58],
587  [54,61,60]
588  ],
589  [
590  [0,1],
591  [0,2],
592  [0,3],
593  [0,4],
594  [1,2],
595  [1,4],
596  [1,5],
597  [1,7],
598  [1,9],
599  [2,3],
600  [2,5],
601  [2,6],
602  [2,8],
603  [2,11],
604  [2,14],
605  [2,16],
606  [2,19],
607  [3,4],
608  [3,6],
609  [3,10],
610  [3,12],
611  [4,7],
612  [4,10],
613  [4,13],
614  [4,15],
615  [4,17],
616  [4,21],
617  [4,25],
618  [5,8],
619  [5,9],
620  [6,11],
621  [6,12],
622  [7,9],
623  [7,13],
624  [8,9],
625  [8,14],
626  [8,18],
627  [8,20],
628  [9,13],
629  [9,18],
630  [9,24],
631  [9,27],
632  [9,31],
633  [9,32],
634  [10,12],
635  [10,15],
636  [11,12],
637  [11,16],
638  [11,22],
639  [11,23],
640  [12,15],
641  [12,22],
642  [12,28],
643  [12,30],
644  [12,34],
645  [12,35],
646  [13,17],
647  [13,24],
648  [13,26],
649  [14,19],
650  [14,20],
651  [15,21],
652  [15,28],
653  [15,29],
654  [16,19],
655  [16,23],
656  [17,25],
657  [17,26],
658  [18,20],
659  [18,27],
660  [19,20],
661  [19,23],
662  [19,33],
663  [20,27],
664  [20,33],
665  [20,37],
666  [20,39],
667  [20,44],
668  [20,45],
669  [21,25],
670  [21,29],
671  [22,23],
672  [22,30],
673  [23,30],
674  [23,33],
675  [23,39],
676  [23,40],
677  [23,47],
678  [23,48],
679  [24,26],
680  [24,31],
681  [25,26],
682  [25,29],
683  [25,36],
684  [26,31],
685  [26,36],
686  [26,42],
687  [26,43],
688  [26,49],
689  [26,50],
690  [27,32],
691  [27,37],
692  [27,38],
693  [28,29],
694  [28,34],
695  [29,34],
696  [29,36],
697  [29,43],
698  [29,46],
699  [29,52],
700  [29,53],
701  [30,35],
702  [30,40],
703  [30,41],
704  [31,32],
705  [31,38],
706  [31,42],
707  [32,38],
708  [33,39],
709  [34,35],
710  [34,41],
711  [34,46],
712  [35,41],
713  [36,43],
714  [37,38],
715  [37,44],
716  [38,42],
717  [38,44],
718  [38,49],
719  [38,55],
720  [38,57],
721  [38,58],
722  [39,45],
723  [39,48],
724  [39,51],
725  [40,41],
726  [40,47],
727  [41,46],
728  [41,47],
729  [41,52],
730  [41,56],
731  [41,59],
732  [41,60],
733  [42,49],
734  [43,50],
735  [43,53],
736  [43,54],
737  [44,45],
738  [44,51],
739  [44,55],
740  [45,51],
741  [46,52],
742  [47,48],
743  [47,51],
744  [47,56],
745  [48,51],
746  [49,50],
747  [49,54],
748  [49,57],
749  [50,54],
750  [51,55],
751  [51,56],
752  [51,58],
753  [51,60],
754  [51,61],
755  [52,53],
756  [52,54],
757  [52,59],
758  [53,54],
759  [54,57],
760  [54,58],
761  [54,59],
762  [54,60],
763  [54,61],
764  [55,58],
765  [56,60],
766  [57,58],
767  [58,61],
768  [59,60],
769  [60,61]
770  ]
771  ],
772  [
773  "kite_hexecontahedron",
774  "Kite Hexecontahedron",
775  empty_str,
776  "archimedean_duals",
777  "George W. Hart, 1997. george@li.net",
778  [
779  [ 0.31751071895, 0.00000000340, 0.97719758819],
780  [ 0.00000001127, 0.18926497122, 0.99100426972],
781  [-0.31751074542, -0.00000003162, 0.97719756131],
782  [ 0.00000000000, -0.47140450895, 0.94280907941],
783  [ 0.51374312445, -0.54018153041, 0.70710681970],
784  [ 0.58249766001, -0.18926493753, 0.80173929639],
785  [ 0.55416926303, 0.47140450330, 0.76274852191],
786  [-0.00000005975, 0.54018152913, 0.87403204499],
787  [-0.55416932145, 0.47140454384, 0.76274848242],
788  [-0.58249771487, -0.18926492629, 0.80173925260],
789  [-0.51374316338, -0.54018151801, 0.70710678126],
790  [ 0.83125389314, -0.00000002527, 0.60394129932],
791  [ 0.89666469792, -0.47140454470, 0.29134409404],
792  [-0.00000004010, -0.87403202745, 0.54018149056],
793  [ 0.36000332522, -0.80173921652, 0.49550210795],
794  [ 0.31751075905, 0.87403203813, 0.43701599790],
795  [-0.00000006329, 0.80173927623, 0.61247427683],
796  [-0.83125394207, 0.00000000773, 0.60394123806],
797  [-0.31751078833, 0.87403205872, 0.43701597508],
798  [-0.36000339413, -0.80173930908, 0.49550207363],
799  [-0.89666468978, -0.47140453296, 0.29134402622],
800  [ 0.94250097679, 0.18926497873, 0.30623723192],
801  [ 0.83125388233, 0.54018152140, 0.27009080693],
802  [ 0.51374313409, -0.87403206340, 0.16692530143],
803  [ 1.02748628783, -0.00000001240, 0.00000003844],
804  [ 0.00000000000, -1.05409255675, 0.00000000000],
805  [ 0.58249766471, 0.80173926315, 0.18926500599],
806  [ 0.00000000000, 1.05409255675, 0.00000000000],
807  [-0.83125378687, 0.54018144318, 0.27009073756],
808  [-0.94250106167, 0.18926498020, 0.30623715984],
809  [-0.58249771017, 0.80173927439, 0.18926496219],
810  [-0.51374315374, -0.87403205100, 0.16692526298],
811  [-1.02748628783, 0.00000001240, -0.00000003844],
812  [ 0.89666468978, 0.47140453296, -0.29134402622],
813  [ 0.58249771017, -0.80173927439, -0.18926496219],
814  [ 0.83125378687, -0.54018144318, -0.27009073756],
815  [ 0.94250106167, -0.18926498020, -0.30623715984],
816  [ 0.31751078833, -0.87403205872, -0.43701597508],
817  [ 0.51374315374, 0.87403205100, -0.16692526298],
818  [-0.51374313409, 0.87403206340, -0.16692530143],
819  [-0.89666469792, 0.47140454470, -0.29134409404],
820  [-0.83125388233, -0.54018152140, -0.27009080693],
821  [-0.58249766471, -0.80173926315, -0.18926500599],
822  [-0.31751075905, -0.87403203813, -0.43701599790],
823  [-0.94250097679, -0.18926497873, -0.30623723192],
824  [ 0.83125394207, -0.00000000773, -0.60394123806],
825  [ 0.55416932145, -0.47140454384, -0.76274848242],
826  [ 0.00000006329, -0.80173927623, -0.61247427683],
827  [ 0.36000339413, 0.80173930908, -0.49550207363],
828  [ 0.00000004010, 0.87403202745, -0.54018149056],
829  [ 0.51374316338, 0.54018151801, -0.70710678126],
830  [-0.36000332522, 0.80173921652, -0.49550210795],
831  [-0.83125389314, 0.00000002527, -0.60394129932],
832  [-0.51374312445, 0.54018153041, -0.70710681970],
833  [-0.55416926303, -0.47140450330, -0.76274852191],
834  [ 0.58249771487, 0.18926492629, -0.80173925260],
835  [ 0.00000005975, -0.54018152913, -0.87403204499],
836  [ 0.31751074542, 0.00000003162, -0.97719756131],
837  [ 0.00000000000, 0.47140450895, -0.94280907941],
838  [-0.58249766001, 0.18926493753, -0.80173929639],
839  [-0.31751071895, -0.00000000340, -0.97719758819],
840  [-0.00000001127, -0.18926497122, -0.99100426972]
841  ],
842  [
843  [1.02748634200, 0.00000061320, 17.99999869722],
844  [1.00891560199, 89.99999658970, 10.81231680724],
845  [1.02748632463, -179.99999429390, 18.00000056439],
846  [1.05409258193, -89.99999999999, 26.56504968170],
847  [1.02748632019, -46.43700162957, 46.51292053460],
848  [1.00891557619, -17.99999775680, 37.37736611922],
849  [1.05409254124, 40.38617586423, 43.64692761206],
850  [1.02748630166, 90.00000633706, 31.71747526862],
851  [1.05409256151, 139.61382468489, 43.64693187669],
852  [1.00891557095, -162.00000482901, 37.37736982663],
853  [1.02748630668, -133.56300119541, 46.51292277440],
854  [1.02748631518, -0.00000174191, 54.00000025335],
855  [1.05409259858, -27.73230224166, 73.95493917425],
856  [1.02748626646, -90.00000262866, 58.28252604708],
857  [1.00891550908, -65.81858650511, 60.58554777641],
858  [1.02748628614, 70.03536918416, 64.82873918611],
859  [1.00891555981, 90.00000452307, 52.62263321232],
860  [1.02748631876, 179.99999946728, 54.00000462068],
861  [1.02748630300, 109.96463207855, 64.82874103382],
862  [1.00891559036, -114.18141512172, 60.58555261657],
863  [1.05409256766, -152.26769813128, 73.95494252661],
864  [1.00891553940, 11.35462944224, 72.33018751495],
865  [1.02748631959, 33.01739826504, 74.75983516356],
866  [1.02748630742, -59.55361679393, 80.65029465008],
867  [1.02748628783, -0.00000069174, 89.99999785636],
868  [1.05409255675, -89.99999999999, 89.99999999999],
869  [1.00891556533, 54.00000029669, 79.18768078490],
870  [1.05409255675, 89.99999999999, 89.99999999999],
871  [1.02748618300, 146.98260251978, 74.75983709775],
872  [1.00891559709, 168.64537146750, 72.33019285450],
873  [1.00891559229, 126.00000144763, 79.18768360925],
874  [1.02748630045, -120.44638451846, 80.65029675853],
875  [1.02748628783, 179.99999930825, 90.00000214363],
876  [1.05409256766, 27.73230186871, 106.04505747338],
877  [1.00891559229, -53.99999855235, 100.81231639074],
878  [1.02748618300, -33.01739748021, 105.24016290224],
879  [1.00891559709, -11.35462853249, 107.66980714549],
880  [1.02748630300, -70.03536792144, 115.17125896617],
881  [1.02748630045, 59.55361548153, 99.34970324145],
882  [1.02748630742, 120.44638320606, 99.34970534991],
883  [1.05409259858, 152.26769775832, 106.04506082573],
884  [1.02748631959, -146.98260173495, 105.24016483643],
885  [1.00891556533, -125.99999970329, 100.81231921509],
886  [1.02748628614, -109.96463081583, 115.17126081388],
887  [1.00891553940, -168.64537055775, 107.66981248504],
888  [1.02748631876, -0.00000053271, 125.99999537931],
889  [1.05409256151, -40.38617531509, 136.35306812330],
890  [1.00891555981, -89.99999547692, 127.37736678767],
891  [1.00891559036, 65.81858487826, 119.41444738341],
892  [1.02748626646, 89.99999737133, 121.71747395291],
893  [1.02748630668, 46.43699880458, 133.48707722559],
894  [1.00891550908, 114.18141349487, 119.41445222357],
895  [1.02748631518, 179.99999825808, 125.99999974664],
896  [1.02748632019, 133.56299837042, 133.48707946539],
897  [1.05409254124, -139.61382413575, 136.35307238793],
898  [1.00891557095, 17.99999517097, 142.62263017336],
899  [1.02748630166, -89.99999366293, 148.28252473137],
900  [1.02748632463, 0.00000570609, 161.99999943560],
901  [1.05409258193, 89.99999999999, 153.43495031828],
902  [1.00891557619, 162.00000224318, 142.62263388077],
903  [1.02748634200, -179.99999938679, 162.00000130277],
904  [1.00891560199, -90.00000341028, 169.18768319275]
905  ],
906  [
907  [2,1,0,3],
908  [0,5,4,3],
909  [1,7,6,0],
910  [2,8,7,1],
911  [3,10,9,2],
912  [6,11,5,0],
913  [11,12,4,5],
914  [14,13,3,4],
915  [16,15,6,7],
916  [9,17,8,2],
917  [18,16,7,8],
918  [13,19,10,3],
919  [20,17,9,10],
920  [6,22,21,11],
921  [12,23,14,4],
922  [11,21,24,12],
923  [14,23,25,13],
924  [15,26,22,6],
925  [16,18,27,15],
926  [17,29,28,8],
927  [8,28,30,18],
928  [19,31,20,10],
929  [13,25,31,19],
930  [20,32,29,17],
931  [33,24,21,22],
932  [35,34,23,12],
933  [36,35,12,24],
934  [34,37,25,23],
935  [27,38,26,15],
936  [38,33,22,26],
937  [30,39,27,18],
938  [32,40,28,29],
939  [40,39,30,28],
940  [42,41,20,31],
941  [43,42,31,25],
942  [41,44,32,20],
943  [33,45,36,24],
944  [35,46,37,34],
945  [36,45,46,35],
946  [37,47,43,25],
947  [27,49,48,38],
948  [38,48,50,33],
949  [39,51,49,27],
950  [32,44,52,40],
951  [40,53,51,39],
952  [42,43,54,41],
953  [41,54,52,44],
954  [50,55,45,33],
955  [56,47,37,46],
956  [55,57,46,45],
957  [56,54,43,47],
958  [58,50,48,49],
959  [53,58,49,51],
960  [59,53,40,52],
961  [60,59,52,54],
962  [50,58,57,55],
963  [46,57,61,56],
964  [56,61,60,54],
965  [53,59,60,58],
966  [60,61,57,58]
967  ],
968  [
969  [0,1],
970  [0,3],
971  [0,5],
972  [0,6],
973  [1,2],
974  [1,7],
975  [2,3],
976  [2,8],
977  [2,9],
978  [3,4],
979  [3,10],
980  [3,13],
981  [4,5],
982  [4,12],
983  [4,14],
984  [5,11],
985  [6,7],
986  [6,11],
987  [6,15],
988  [6,22],
989  [7,8],
990  [7,16],
991  [8,17],
992  [8,18],
993  [8,28],
994  [9,10],
995  [9,17],
996  [10,19],
997  [10,20],
998  [11,12],
999  [11,21],
1000  [12,23],
1001  [12,24],
1002  [12,35],
1003  [13,14],
1004  [13,19],
1005  [13,25],
1006  [14,23],
1007  [15,16],
1008  [15,26],
1009  [15,27],
1010  [16,18],
1011  [17,20],
1012  [17,29],
1013  [18,27],
1014  [18,30],
1015  [19,31],
1016  [20,31],
1017  [20,32],
1018  [20,41],
1019  [21,22],
1020  [21,24],
1021  [22,26],
1022  [22,33],
1023  [23,25],
1024  [23,34],
1025  [24,33],
1026  [24,36],
1027  [25,31],
1028  [25,37],
1029  [25,43],
1030  [26,38],
1031  [27,38],
1032  [27,39],
1033  [27,49],
1034  [28,29],
1035  [28,30],
1036  [28,40],
1037  [29,32],
1038  [30,39],
1039  [31,42],
1040  [32,40],
1041  [32,44],
1042  [33,38],
1043  [33,45],
1044  [33,50],
1045  [34,35],
1046  [34,37],
1047  [35,36],
1048  [35,46],
1049  [36,45],
1050  [37,46],
1051  [37,47],
1052  [38,48],
1053  [39,40],
1054  [39,51],
1055  [40,52],
1056  [40,53],
1057  [41,42],
1058  [41,44],
1059  [41,54],
1060  [42,43],
1061  [43,47],
1062  [43,54],
1063  [44,52],
1064  [45,46],
1065  [45,55],
1066  [46,56],
1067  [46,57],
1068  [47,56],
1069  [48,49],
1070  [48,50],
1071  [49,51],
1072  [49,58],
1073  [50,55],
1074  [50,58],
1075  [51,53],
1076  [52,54],
1077  [52,59],
1078  [53,58],
1079  [53,59],
1080  [54,56],
1081  [54,60],
1082  [55,57],
1083  [56,61],
1084  [57,58],
1085  [57,61],
1086  [58,60],
1087  [59,60],
1088  [60,61]
1089  ]
1090  ],
1091  [
1092  "kite_icositetrahedron",
1093  "Kite Icositetrahedron",
1094  empty_str,
1095  "archimedean_duals",
1096  "Exact Mathematics",
1097  [
1098  [ 0.00000000000, 0.70710678119, 0.70710678119],
1099  [-0.54691816068, 0.54691816068, 0.54691816068],
1100  [-0.70710678119, 0.00000000000, 0.70710678119],
1101  [ 0.00000000000, 0.00000000000, 1.00000000000],
1102  [ 0.70710678119, 0.00000000000, 0.70710678119],
1103  [ 0.54691816068, 0.54691816068, 0.54691816068],
1104  [ 0.00000000000, 1.00000000000, 0.00000000000],
1105  [-0.70710678119, 0.70710678119, 0.00000000000],
1106  [-1.00000000000, 0.00000000000, 0.00000000000],
1107  [-0.54691816068, -0.54691816068, 0.54691816068],
1108  [ 0.00000000000, -0.70710678119, 0.70710678119],
1109  [ 0.70710678119, 0.70710678119, 0.00000000000],
1110  [ 1.00000000000, 0.00000000000, 0.00000000000],
1111  [ 0.54691816068, -0.54691816068, 0.54691816068],
1112  [ 0.00000000000, 0.70710678119, -0.70710678119],
1113  [-0.54691816068, 0.54691816068, -0.54691816068],
1114  [-0.70710678119, -0.70710678119, 0.00000000000],
1115  [-0.70710678119, 0.00000000000, -0.70710678119],
1116  [ 0.00000000000, -1.00000000000, 0.00000000000],
1117  [ 0.54691816068, 0.54691816068, -0.54691816068],
1118  [ 0.70710678119, -0.70710678119, 0.00000000000],
1119  [ 0.70710678119, 0.00000000000, -0.70710678119],
1120  [ 0.00000000000, 0.00000000000, -1.00000000000],
1121  [-0.54691816068, -0.54691816068, -0.54691816068],
1122  [ 0.00000000000, -0.70710678119, -0.70710678119],
1123  [ 0.54691816068, -0.54691816068, -0.54691816068]
1124  ],
1125  [
1126  [1.00000000000, 89.99999999999, 45.00000000000],
1127  [0.94729004188, 134.99999999999, 54.73561031724],
1128  [1.00000000000, 179.99999999999, 45.00000000000],
1129  [1.00000000000, 0.00000000000, 0.00000000000],
1130  [1.00000000000, 0.00000000000, 45.00000000000],
1131  [0.94729004188, 45.00000000000, 54.73561031724],
1132  [1.00000000000, 89.99999999999, 89.99999999999],
1133  [1.00000000000, 134.99999999999, 89.99999999999],
1134  [1.00000000000, 179.99999999999, 89.99999999999],
1135  [0.94729004188, -134.99999999999, 54.73561031724],
1136  [1.00000000000, -89.99999999999, 45.00000000000],
1137  [1.00000000000, 45.00000000000, 89.99999999999],
1138  [1.00000000000, 0.00000000000, 89.99999999999],
1139  [0.94729004188, -45.00000000000, 54.73561031724],
1140  [1.00000000000, 89.99999999999, 134.99999999999],
1141  [0.94729004188, 134.99999999999, 125.26438968275],
1142  [1.00000000000, -134.99999999999, 89.99999999999],
1143  [1.00000000000, 179.99999999999, 134.99999999999],
1144  [1.00000000000, -89.99999999999, 89.99999999999],
1145  [0.94729004188, 45.00000000000, 125.26438968275],
1146  [1.00000000000, -45.00000000000, 89.99999999999],
1147  [1.00000000000, 0.00000000000, 134.99999999999],
1148  [1.00000000000, 0.00000000000, 179.99999999999],
1149  [0.94729004188, -134.99999999999, 125.26438968275],
1150  [1.00000000000, -89.99999999999, 134.99999999999],
1151  [0.94729004188, -45.00000000000, 125.26438968275]
1152  ],
1153  [
1154  [2,1,0,3],
1155  [0,5,4,3],
1156  [1,7,6,0],
1157  [2,8,7,1],
1158  [3,10,9,2],
1159  [6,11,5,0],
1160  [11,12,4,5],
1161  [13,10,3,4],
1162  [15,14,6,7],
1163  [9,16,8,2],
1164  [17,15,7,8],
1165  [18,16,9,10],
1166  [6,14,19,11],
1167  [12,20,13,4],
1168  [11,19,21,12],
1169  [13,20,18,10],
1170  [15,17,22,14],
1171  [16,23,17,8],
1172  [18,24,23,16],
1173  [22,21,19,14],
1174  [21,25,20,12],
1175  [25,24,18,20],
1176  [23,24,22,17],
1177  [22,24,25,21]
1178  ],
1179  [
1180  [0,1],
1181  [0,3],
1182  [0,5],
1183  [0,6],
1184  [1,2],
1185  [1,7],
1186  [2,3],
1187  [2,8],
1188  [2,9],
1189  [3,4],
1190  [3,10],
1191  [4,5],
1192  [4,12],
1193  [4,13],
1194  [5,11],
1195  [6,7],
1196  [6,11],
1197  [6,14],
1198  [7,8],
1199  [7,15],
1200  [8,16],
1201  [8,17],
1202  [9,10],
1203  [9,16],
1204  [10,13],
1205  [10,18],
1206  [11,12],
1207  [11,19],
1208  [12,20],
1209  [12,21],
1210  [13,20],
1211  [14,15],
1212  [14,19],
1213  [14,22],
1214  [15,17],
1215  [16,18],
1216  [16,23],
1217  [17,22],
1218  [17,23],
1219  [18,20],
1220  [18,24],
1221  [19,21],
1222  [20,25],
1223  [21,22],
1224  [21,25],
1225  [22,24],
1226  [23,24],
1227  [24,25]
1228  ]
1229  ],
1230  [
1231  "pentagonal_hexecontahedron",
1232  "Pentagonal Hexecontahedron",
1233  empty_str,
1234  "archimedean_duals",
1235  "George W. Hart, 1997. george@li.net",
1236  [
1237  [ 0.43929670799, 0.80229243417, 0.42738850835],
1238  [ 0.17873728116, 0.89900927828, 0.42326233269],
1239  [ 0.00000006746, 0.80229240544, 0.61289686773],
1240  [ 0.09198324699, 0.61435695625, 0.79587706028],
1241  [ 0.55655387022, 0.47343303562, 0.76603073261],
1242  [ 0.83268557636, 0.43710531793, 0.36727273995],
1243  [ 0.78534839615, 0.61435687832, 0.15845831941],
1244  [ 0.58289950583, 0.80229240479, 0.18939554729],
1245  [ 0.45777926592, 0.89900921799, -0.03919402468],
1246  [ 0.00000000000, 1.05862833462, 0.00000000000],
1247  [-0.34731349305, 0.89900920644, 0.30078448134],
1248  [-0.27072042988, 0.80229239831, 0.54986633993],
1249  [-0.55655390763, 0.47343299202, 0.76603069967],
1250  [-0.09198320445, 0.43710533357, 0.90542460472],
1251  [-0.00000000905, 0.18939553536, 0.99168792345],
1252  [ 0.27072047218, 0.13301931890, 0.96349980145],
1253  [ 0.72849974112, 0.02347183286, 0.69860779465],
1254  [ 0.88953432998, -0.02347180069, 0.47696269454],
1255  [ 0.94315123980, 0.18939555441, 0.30644845257],
1256  [ 0.99999995431, 0.13301930039, 0.04026735447],
1257  [ 0.90052309976, 0.47343299404, -0.29259778957],
1258  [ 0.54222076745, 0.80229236680, -0.28572569731],
1259  [ 0.36025169895, 0.80229232718, -0.49584397047],
1260  [ 0.10418585254, 0.89900925391, -0.44748557905],
1261  [-0.39338880734, 0.89900926034, -0.23736733525],
1262  [-0.60661117016, 0.80229234172, -0.08755242503],
1263  [-0.58289952357, 0.80229238174, 0.18939556276],
1264  [-0.72849968218, 0.61435691219, 0.33342076992],
1265  [-0.43929667370, 0.02347185555, 0.90872605286],
1266  [-0.17873725271, -0.02347183451, 0.99338701856],
1267  [ 0.00000000000, -0.47343302627, 0.94686604800],
1268  [ 0.34731355256, -0.13301926608, 0.93861320249],
1269  [ 0.58289957938, -0.18939547759, 0.80229235215],
1270  [ 0.60661117307, -0.43710532795, 0.67843750503],
1271  [ 0.90052307979, -0.47343299009, 0.29259766155],
1272  [ 1.00000000613, -0.13301932365, -0.04026744817],
1273  [ 0.94315122404, -0.18939551904, -0.30644845487],
1274  [ 0.88953427761, 0.02347182633, -0.47696271173],
1275  [ 0.60661113829, 0.43710534604, -0.67843753884],
1276  [ 0.39338883185, 0.61435691555, -0.69794444237],
1277  [-0.00000000000, 0.47343302627, -0.94686604800],
1278  [-0.10418589186, 0.80229239808, -0.60397673362],
1279  [-0.36025172233, 0.80229235166, -0.49584395247],
1280  [-0.54222076190, 0.61435692629, -0.58981173439],
1281  [-0.90052307979, 0.47343299009, -0.29259766155],
1282  [-0.88953425296, 0.43710534217, 0.19231037033],
1283  [-0.94315122404, 0.18939551904, 0.30644845487],
1284  [-0.83268557958, 0.13301930581, 0.55520827313],
1285  [-0.78534838748, -0.13301932941, 0.62036224592],
1286  [-0.58289954342, -0.18939549734, 0.80229240317],
1287  [-0.45777918898, -0.43710533504, 0.78657024882],
1288  [ 0.39338883830, -0.61435689801, 0.69794443237],
1289  [ 0.36025172233, -0.80229235166, 0.49584395247],
1290  [ 0.54222077033, -0.80229238127, 0.28572568684],
1291  [ 0.78534844264, -0.61435690293, -0.15845837472],
1292  [ 0.83268558591, -0.43710535473, -0.36727280108],
1293  [ 0.55655390763, -0.47343299202, -0.76603069967],
1294  [ 0.72849968132, -0.02347183893, -0.69860782530],
1295  [ 0.58289954342, 0.18939549734, -0.80229240317],
1296  [ 0.34731352396, 0.13301929849, -0.93861321900],
1297  [-0.45777923893, 0.43710532911, -0.78657017807],
1298  [-0.58289957938, 0.18939547759, -0.80229235215],
1299  [-0.78534846448, 0.13301931721, -0.62036222178],
1300  [-1.00000002178, 0.02347182189, -0.13698420147],
1301  [-0.99999996499, -0.02347187224, 0.13698423280],
1302  [-0.90052309976, -0.47343299404, 0.29259778957],
1303  [-0.54222076798, -0.61435688975, 0.58981176357],
1304  [-0.36025169895, -0.80229232718, 0.49584397047],
1305  [-0.10418586666, -0.80229236670, 0.60397677120],
1306  [ 0.10418587795, -0.89900928430, 0.44748555213],
1307  [ 0.00000000000, -1.05862833462, 0.00000000000],
1308  [ 0.45777927425, -0.89900929770, 0.03919397554],
1309  [ 0.58289952357, -0.80229238174, -0.18939556276],
1310  [ 0.43929671969, -0.80229240424, -0.42738845533],
1311  [ 0.27072040245, -0.13301931953, -0.96349985242],
1312  [ 0.00000000905, -0.18939553536, -0.99168792345],
1313  [-0.17873726905, 0.02347175806, -0.99338697109],
1314  [-0.43929673700, -0.02347181154, -0.90872603996],
1315  [-0.55655387022, -0.47343303562, -0.76603073261],
1316  [-0.83268560661, -0.13301934937, -0.55520826741],
1317  [-0.94315123980, -0.18939555441, -0.30644845257],
1318  [-0.88953435441, -0.43710535369, -0.19231035386],
1319  [-0.60661114910, -0.80229238188, 0.08755244013],
1320  [-0.39338879086, -0.89900920621, 0.23736724631],
1321  [ 0.17873722735, -0.89900926813, -0.42326229632],
1322  [-0.00000006746, -0.80229240544, -0.61289686773],
1323  [ 0.09198318282, -0.61435689475, -0.79587709948],
1324  [-0.09198319903, -0.43710532147, -0.90542450316],
1325  [-0.72849973616, -0.61435691761, -0.33342072744],
1326  [-0.58289950583, -0.80229240479, -0.18939554729],
1327  [-0.34731357412, -0.89900923918, -0.30078446839],
1328  [-0.27072048765, -0.80229245067, -0.54986636865]
1329  ],
1330  [
1331  [1.00961165041, 61.29700936664, 64.95564737476],
1332  [1.00961165821, 78.75532043858, 65.21383893442],
1333  [1.00961164528, 89.99999518238, 52.62263150736],
1334  [1.00961164935, 81.48476761966, 37.97305536118],
1335  [1.05862842064, 40.38617971112, 43.64692623462],
1336  [1.00961160530, 27.69652703195, 68.66770858220],
1337  [1.00961156703, 38.03511385344, 80.97010500411],
1338  [1.00961161345, 54.00000215711, 79.18768264039],
1339  [1.00961160943, 63.01461466555, 92.22483241518],
1340  [1.05862833462, 89.99999999999, 89.99999999999],
1341  [1.00961156884, 111.12300154166, 72.66722413539],
1342  [1.00961162599, 108.64612441404, 57.00051168206],
1343  [1.05862839697, 139.61382479374, 43.64692747453],
1344  [1.00961165671, 101.88376642571, 26.25879685072],
1345  [1.00961161162, 90.00000273800, 10.81231669055],
1346  [1.00961159891, 26.16733309536, 17.38334950437],
1347  [1.00961163350, 1.84539790457, 46.21478062238],
1348  [1.00961163901, -1.51149099804, 61.80837455707],
1349  [1.00961160416, 11.35462917564, 72.33019088823],
1350  [1.00961156032, 7.57696450584, 87.71420844474],
1351  [1.05862841427, 27.73230061580, 106.04506232512],
1352  [1.00961159690, 55.94762390722, 106.43966824196],
1353  [1.00961156288, 65.81858581692, 119.41445314553],
1354  [1.00961164511, 83.38950178162, 116.30985956258],
1355  [1.00961163611, 113.63324281828, 103.59796355553],
1356  [1.00961157901, 127.09283218079, 94.97487673704],
1357  [1.00961160827, 125.99999945497, 79.18768169041],
1358  [1.00961161459, 139.85846120224, 70.71625820493],
1359  [1.00961157614, 176.94156416301, 25.83208386624],
1360  [1.00961165859, -172.51870851491, 10.28563969853],
1361  [1.05862842547, -89.99999999999, 26.56505128698],
1362  [1.00961159504, -20.95657736121, 21.61539826705],
1363  [1.00961160101, -17.99999318234, 37.37737018516],
1364  [1.00961162397, -35.77535984455, 47.78003400382],
1365  [1.05862836014, -27.73230094227, 73.95494404152],
1366  [1.00961161845, -7.57696542715, 92.28579674494],
1367  [1.00961158350, -11.35462729490, 107.66980962215],
1368  [1.00961160159, 1.51149273733, 118.19162768828],
1369  [1.00961163362, 35.77536252738, 132.21996809013],
1370  [1.00961162698, 57.36749971808, 133.73309750916],
1371  [1.05862842547, 89.99999999999, 153.43494871301],
1372  [1.00961165149, 97.39903800635, 126.74300584502],
1373  [1.00961158184, 114.18141491933, 119.41445136596],
1374  [1.00961164293, 131.43106472543, 125.74625690728],
1375  [1.05862836014, 152.26769905772, 106.04505595846],
1376  [1.00961158169, 153.83110989949, 79.01922788456],
1377  [1.00961158350, 168.64537270509, 72.33019037784],
1378  [1.00961162667, 170.92383868216, 56.63829530939],
1379  [1.00961158267, -170.38669518854, 52.08757182343],
1380  [1.00961162449, -162.00000402271, 37.37736716018],
1381  [1.00961161647, -136.32342652086, 38.82339809945],
1382  [1.00961161191, -57.36749854869, 46.26690245765],
1383  [1.00961158184, -65.81858508066, 60.58554863403],
1384  [1.00961160698, -55.94762424524, 73.56033254647],
1385  [1.00961162684, -38.03511332103, 99.02989763480],
1386  [1.00961165134, -27.69652874662, 111.33229412132],
1387  [1.05862839697, -40.38617520625, 136.35307252546],
1388  [1.00961161170, -1.84539853322, 133.78522297221],
1389  [1.00961162449, 17.99999597728, 142.62263283981],
1390  [1.00961160482, 20.95658360002, 158.38460287550],
1391  [1.00961158143, 136.32343003141, 141.17659796717],
1392  [1.00961160101, 162.00000681764, 142.62262981482],
1393  [1.00961162614, 170.38669697882, 127.91242451979],
1394  [1.00961162901, 178.65541058453, 97.79794829998],
1395  [1.00961157818, -178.65540762511, 82.20204951025],
1396  [1.05862841427, -152.26769938418, 73.95493767487],
1397  [1.00961164101, -131.43106673516, 54.25374097365],
1398  [1.00961156288, -114.18141418307, 60.58554685446],
1399  [1.00961164644, -97.39903652278, 53.25699127882],
1400  [1.00961166286, -83.38950040503, 63.69014264007],
1401  [1.05862833462, -89.99999999999, 89.99999999999],
1402  [1.00961168228, -63.01461629797, 87.77517053656],
1403  [1.00961160827, -54.00000054502, 100.81231830958],
1404  [1.00961160928, -61.29700782356, 115.04435039503],
1405  [1.00961162894, -26.16733904394, 162.61665473392],
1406  [1.00961161162, -89.99999726198, 169.18768330944],
1407  [1.00961161300, 172.51873328176, 169.71435947143],
1408  [1.00961159105, -176.94157032627, 154.16791270602],
1409  [1.05862842064, -139.61382028887, 136.35307376537],
1410  [1.00961165156, -170.92383604873, 123.36170337156],
1411  [1.00961160416, -168.64537082435, 107.66980911176],
1412  [1.00961167292, -153.83111188827, 100.98077015886],
1413  [1.00961159958, -127.09282984347, 85.02512250434],
1414  [1.00961156058, -113.63324320390, 76.40204060059],
1415  [1.00961162439, -78.75532361358, 114.78615967833],
1416  [1.00961164528, -90.00000481761, 127.37736849262],
1417  [1.00961163698, -81.48477263339, 142.02694915345],
1418  [1.00961155990, -101.88376606561, 153.74120125915],
1419  [1.00961164280, -139.85846304551, 109.28373868058],
1420  [1.00961161345, -125.99999784287, 100.81231735960],
1421  [1.00961162203, -111.12300533565, 107.33277415240],
1422  [1.00961169873, -108.64612698520, 122.99948758071]
1423  ],
1424  [
1425  [3,2,1,0,4],
1426  [7,6,5,4,0],
1427  [9,8,7,0,1],
1428  [11,10,9,1,2],
1429  [13,12,11,2,3],
1430  [15,14,13,3,4],
1431  [18,17,16,4,5],
1432  [20,19,18,5,6],
1433  [8,21,20,6,7],
1434  [23,22,21,8,9],
1435  [26,25,24,9,10],
1436  [12,27,26,10,11],
1437  [14,29,28,12,13],
1438  [31,30,29,14,15],
1439  [16,32,31,15,4],
1440  [34,33,32,16,17],
1441  [19,35,34,17,18],
1442  [37,36,35,19,20],
1443  [22,39,38,20,21],
1444  [41,40,39,22,23],
1445  [24,42,41,23,9],
1446  [44,43,42,24,25],
1447  [27,45,44,25,26],
1448  [47,46,45,27,12],
1449  [49,48,47,12,28],
1450  [30,50,49,28,29],
1451  [32,33,51,30,31],
1452  [53,52,51,33,34],
1453  [36,55,54,34,35],
1454  [57,56,55,36,37],
1455  [38,58,57,37,20],
1456  [40,59,58,38,39],
1457  [42,43,60,40,41],
1458  [62,61,60,43,44],
1459  [46,64,63,44,45],
1460  [48,65,64,46,47],
1461  [50,66,65,48,49],
1462  [68,67,66,50,30],
1463  [52,69,68,30,51],
1464  [71,70,69,52,53],
1465  [54,72,71,53,34],
1466  [56,73,72,54,55],
1467  [58,59,74,56,57],
1468  [76,75,74,59,40],
1469  [61,77,76,40,60],
1470  [79,78,77,61,62],
1471  [63,80,79,62,44],
1472  [65,81,80,63,64],
1473  [67,83,82,65,66],
1474  [69,70,83,67,68],
1475  [72,73,84,70,71],
1476  [86,85,84,73,56],
1477  [75,87,86,56,74],
1478  [77,78,87,75,76],
1479  [80,81,88,78,79],
1480  [82,89,88,81,65],
1481  [70,90,89,82,83],
1482  [85,91,90,70,84],
1483  [87,78,91,85,86],
1484  [89,90,91,78,88]
1485  ],
1486  [
1487  [0,1],
1488  [0,4],
1489  [0,7],
1490  [1,2],
1491  [1,9],
1492  [2,3],
1493  [2,11],
1494  [3,4],
1495  [3,13],
1496  [4,5],
1497  [4,15],
1498  [4,16],
1499  [5,6],
1500  [5,18],
1501  [6,7],
1502  [6,20],
1503  [7,8],
1504  [8,9],
1505  [8,21],
1506  [9,10],
1507  [9,23],
1508  [9,24],
1509  [10,11],
1510  [10,26],
1511  [11,12],
1512  [12,13],
1513  [12,27],
1514  [12,28],
1515  [12,47],
1516  [13,14],
1517  [14,15],
1518  [14,29],
1519  [15,31],
1520  [16,17],
1521  [16,32],
1522  [17,18],
1523  [17,34],
1524  [18,19],
1525  [19,20],
1526  [19,35],
1527  [20,21],
1528  [20,37],
1529  [20,38],
1530  [21,22],
1531  [22,23],
1532  [22,39],
1533  [23,41],
1534  [24,25],
1535  [24,42],
1536  [25,26],
1537  [25,44],
1538  [26,27],
1539  [27,45],
1540  [28,29],
1541  [28,49],
1542  [29,30],
1543  [30,31],
1544  [30,50],
1545  [30,51],
1546  [30,68],
1547  [31,32],
1548  [32,33],
1549  [33,34],
1550  [33,51],
1551  [34,35],
1552  [34,53],
1553  [34,54],
1554  [35,36],
1555  [36,37],
1556  [36,55],
1557  [37,57],
1558  [38,39],
1559  [38,58],
1560  [39,40],
1561  [40,41],
1562  [40,59],
1563  [40,60],
1564  [40,76],
1565  [41,42],
1566  [42,43],
1567  [43,44],
1568  [43,60],
1569  [44,45],
1570  [44,62],
1571  [44,63],
1572  [45,46],
1573  [46,47],
1574  [46,64],
1575  [47,48],
1576  [48,49],
1577  [48,65],
1578  [49,50],
1579  [50,66],
1580  [51,52],
1581  [52,53],
1582  [52,69],
1583  [53,71],
1584  [54,55],
1585  [54,72],
1586  [55,56],
1587  [56,57],
1588  [56,73],
1589  [56,74],
1590  [56,86],
1591  [57,58],
1592  [58,59],
1593  [59,74],
1594  [60,61],
1595  [61,62],
1596  [61,77],
1597  [62,79],
1598  [63,64],
1599  [63,80],
1600  [64,65],
1601  [65,66],
1602  [65,81],
1603  [65,82],
1604  [66,67],
1605  [67,68],
1606  [67,83],
1607  [68,69],
1608  [69,70],
1609  [70,71],
1610  [70,83],
1611  [70,84],
1612  [70,90],
1613  [71,72],
1614  [72,73],
1615  [73,84],
1616  [74,75],
1617  [75,76],
1618  [75,87],
1619  [76,77],
1620  [77,78],
1621  [78,79],
1622  [78,87],
1623  [78,88],
1624  [78,91],
1625  [79,80],
1626  [80,81],
1627  [81,88],
1628  [82,83],
1629  [82,89],
1630  [84,85],
1631  [85,86],
1632  [85,91],
1633  [86,87],
1634  [88,89],
1635  [89,90],
1636  [90,91]
1637  ]
1638  ],
1639  [
1640  "pentagonal_icositetrahedron",
1641  "Pentagonal Icositetrahedron",
1642  empty_str,
1643  "archimedean_duals",
1644  "George W. Hart, 1997. george@li.net",
1645  [
1646  [ 0.16071327325, 0.75190871675, -0.54368902931],
1647  [-0.16071322588, 0.54368899822, -0.75190873509],
1648  [-0.54368897205, 0.54368899723, -0.54368904151],
1649  [-0.54368896362, 0.75190871866, -0.16071328736],
1650  [-0.00000000676, 0.99999999488, -0.00000000731],
1651  [ 0.54368897783, 0.75190869752, 0.16071325200],
1652  [ 0.75190866563, 0.54368897418, -0.16071321670],
1653  [ 0.54368897367, 0.54368900470, -0.54368899596],
1654  [ 0.54368904340, 0.16071325571, -0.75190863643],
1655  [-0.00000000676, 0.00000001660, -1.00000000000],
1656  [-0.54368896170, -0.16071326637, -0.75190870910],
1657  [-0.75190870177, 0.16071321607, -0.54368907275],
1658  [-0.99999997485, -0.00000001528, -0.00000009448],
1659  [-0.75190869930, 0.54368899910, 0.16071317983],
1660  [-0.54368900735, 0.54368896859, 0.54368895909],
1661  [-0.16071325904, 0.75190869943, 0.54368899395],
1662  [ 0.16071317676, 0.54368899531, 0.75190868442],
1663  [ 0.54368893146, 0.54368899942, 0.54368899194],
1664  [ 0.75190868600, 0.16071324303, 0.54368899377],
1665  [ 0.99999996132, 0.00000002772, 0.00000007987],
1666  [ 0.75190873045, -0.16071319835, -0.54368892976],
1667  [ 0.54368899382, -0.54368895615, -0.54368897371],
1668  [ 0.16071325221, -0.54368889737, -0.75190857341],
1669  [-0.16071325147, -0.75190867567, -0.54368898591],
1670  [-0.54368894499, -0.54368898698, -0.54368900655],
1671  [-0.75190865186, -0.54368901104, -0.16071324937],
1672  [-0.75190873482, -0.16071325923, 0.54368899222],
1673  [-0.54368899063, 0.16071324797, 0.75190866164],
1674  [-0.00000000676, -0.00000000416, 0.99999998539],
1675  [ 0.54368897421, -0.16071320457, 0.75190867837],
1676  [ 0.54368895852, -0.54368898479, 0.54368902690],
1677  [ 0.75190865849, -0.54368893736, 0.16071325700],
1678  [ 0.54368903978, -0.75190864639, -0.16071321006],
1679  [-0.00000000676, -0.99999998245, -0.00000000731],
1680  [-0.54368899324, -0.75190871736, 0.16071321914],
1681  [-0.54368898719, -0.54368899226, 0.54368898134],
1682  [-0.16071326938, -0.54368901430, 0.75190866154],
1683  [ 0.16071331941, -0.75190902099, 0.54368916366]
1684  ],
1685  [
1686  [0.94169699751, 77.93511852297, 125.26439074846],
1687  [0.94169698611, 106.46755898307, 142.98343120091],
1688  [0.94169697775, 134.99999867304, 125.26439250807],
1689  [0.94169696351, 125.86987960572, 99.82639781431],
1690  [0.99999999488, 90.00000038747, 90.00000041864],
1691  [0.94169694881, 54.13011891836, 80.17360421411],
1692  [0.94169691521, 35.86988205269, 99.82639396007],
1693  [0.94169695669, 45.00000163481, 125.26439001937],
1694  [0.94169693852, 16.46756057926, 142.98342507151],
1695  [1.00000000000, 112.17056773351, 179.99999897318],
1696  [0.94169695119, -163.53243604711, 142.98343139242],
1697  [0.94169700087, 167.93512245650, 125.26439384143],
1698  [0.99999997485, -179.99999912453, 90.00000541347],
1699  [0.94169695019, 144.13011791868, 80.17360868494],
1700  [0.94169693400, 135.00000204233, 54.73561175152],
1701  [0.94169696083, 102.06488071124, 54.73561030871],
1702  [0.94169693560, 73.53244569490, 37.01656984339],
1703  [0.94169692696, 45.00000358086, 54.73560900079],
1704  [0.94169694728, 12.06487975387, 54.73560973856],
1705  [0.99999996132, 0.00000158816, 89.99999542382],
1706  [0.94169693819, -12.06487580597, 125.26438588242],
1707  [0.94169692745, -44.99999801492, 125.26438961939],
1708  [0.94169680330, -73.53243557609, 142.98342961421],
1709  [0.94169693593, -102.06488053029, 125.26439016391],
1710  [0.94169693602, -134.99999778726, 125.26439169819],
1711  [0.94169693107, -144.13011560493, 99.82639581021],
1712  [0.94169698813, -167.93511982564, 54.73561161174],
1713  [0.94169692686, 163.53243865866, 37.01657144033],
1714  [0.99999998539, -148.42091555625, 0.00000045483],
1715  [0.94169692333, -16.46755760552, 37.01656946502],
1716  [0.94169695432, -45.00000138421, 54.73560757295],
1717  [0.94169689513, -35.86988046874, 80.17360333945],
1718  [0.94169693658, -54.13011396871, 99.82639332499],
1719  [0.99999998245, -90.00000038747, 90.00000041864],
1720  [0.94169696793, -125.86988113486, 80.17360644450],
1721  [0.94169694888, -134.99999973330, 54.73561073359],
1722  [0.94169694410, -106.46756273772, 37.01657284190],
1723  [0.94169732588, -77.93511989808, 54.73561336722]
1724  ],
1725  [
1726  [3,2,1,0,4],
1727  [7,6,5,4,0],
1728  [9,8,7,0,1],
1729  [11,10,9,1,2],
1730  [13,12,11,2,3],
1731  [15,14,13,3,4],
1732  [17,16,15,4,5],
1733  [19,18,17,5,6],
1734  [8,20,19,6,7],
1735  [22,21,20,8,9],
1736  [24,23,22,9,10],
1737  [12,25,24,10,11],
1738  [14,27,26,12,13],
1739  [16,28,27,14,15],
1740  [18,29,28,16,17],
1741  [31,30,29,18,19],
1742  [21,32,31,19,20],
1743  [23,33,32,21,22],
1744  [25,34,33,23,24],
1745  [26,35,34,25,12],
1746  [28,36,35,26,27],
1747  [30,37,36,28,29],
1748  [32,33,37,30,31],
1749  [35,36,37,33,34]
1750  ],
1751  [
1752  [0,1],
1753  [0,4],
1754  [0,7],
1755  [1,2],
1756  [1,9],
1757  [2,3],
1758  [2,11],
1759  [3,4],
1760  [3,13],
1761  [4,5],
1762  [4,15],
1763  [5,6],
1764  [5,17],
1765  [6,7],
1766  [6,19],
1767  [7,8],
1768  [8,9],
1769  [8,20],
1770  [9,10],
1771  [9,22],
1772  [10,11],
1773  [10,24],
1774  [11,12],
1775  [12,13],
1776  [12,25],
1777  [12,26],
1778  [13,14],
1779  [14,15],
1780  [14,27],
1781  [15,16],
1782  [16,17],
1783  [16,28],
1784  [17,18],
1785  [18,19],
1786  [18,29],
1787  [19,20],
1788  [19,31],
1789  [20,21],
1790  [21,22],
1791  [21,32],
1792  [22,23],
1793  [23,24],
1794  [23,33],
1795  [24,25],
1796  [25,34],
1797  [26,27],
1798  [26,35],
1799  [27,28],
1800  [28,29],
1801  [28,36],
1802  [29,30],
1803  [30,31],
1804  [30,37],
1805  [31,32],
1806  [32,33],
1807  [33,34],
1808  [33,37],
1809  [34,35],
1810  [35,36],
1811  [36,37]
1812  ]
1813  ],
1814  [
1815  "pentakis_dodecahedron",
1816  "Pentakis-dodecahedron",
1817  empty_str,
1818  "archimedean_duals",
1819  "George W. Hart, 1997. george@li.net",
1820  [
1821  [ 0.20177410000, 0.38196600000, 0.97943210000],
1822  [-0.42923850000, -0.04863268000, 0.97943210000],
1823  [ 0.20177410000, -0.29568600000, 0.97943210000],
1824  [ 0.78140610000, -0.04863268000, 0.73002560000],
1825  [-0.40354820000, 0.59137200000, 0.75819400000],
1826  [-0.23959370000, -0.74535600000, 0.73002560000],
1827  [ 0.67036380000, 0.59137200000, 0.53695600000],
1828  [ 0.50862580000, -0.74535600000, 0.57588390000],
1829  [-0.92198690000, 0.25464400000, 0.48061910000],
1830  [ 0.09901297000, 0.95136730000, 0.48061910000],
1831  [-0.79506710000, -0.40862800000, 0.53695600000],
1832  [ 1.03687700000, 0.25464400000, 0.07707085000],
1833  [ 0.94255910000, -0.40862800000, 0.17898530000],
1834  [-0.59550950000, 0.87267800000, 0.17233570000],
1835  [ 0.03687301000, -1.02666200000, 0.17898530000],
1836  [-0.61513510000, -0.87267800000, 0.07707085000],
1837  [ 0.61513510000, 0.87267800000, -0.07707085000],
1838  [ 0.59550950000, -0.87267800000, -0.17233570000],
1839  [-0.94255910000, 0.40862800000, -0.17898530000],
1840  [-1.03687700000, -0.25464400000, -0.07707085000],
1841  [-0.03687301000, 1.02666200000, -0.17898530000],
1842  [ 0.79506710000, 0.40862800000, -0.53695600000],
1843  [ 0.92198690000, -0.25464400000, -0.48061910000],
1844  [-0.50862580000, 0.74535600000, -0.57588390000],
1845  [-0.09901297000, -0.95136730000, -0.48061910000],
1846  [-0.67036380000, -0.59137200000, -0.53695600000],
1847  [ 0.23959370000, 0.74535600000, -0.73002560000],
1848  [ 0.40354820000, -0.59137200000, -0.75819400000],
1849  [-0.78140610000, 0.04863268000, -0.73002560000],
1850  [ 0.42923850000, 0.04863268000, -0.97943210000],
1851  [-0.20177410000, 0.29568600000, -0.97943210000],
1852  [-0.20177410000, -0.38196600000, -0.97943210000]
1853  ],
1854  [
1855  [1.07046627742, 62.15468025915, 23.80018166046],
1856  [1.07046628436, -173.53595908920, 23.80018250273],
1857  [1.04279923117, -55.69064040323, 20.07675084678],
1858  [1.07046625698, -3.56134651010, 47.00224174530],
1859  [1.04279918189, 124.30935959676, 43.35819899984],
1860  [1.07046629301, -107.81993299443, 47.00224354341],
1861  [1.04279921973, 41.41763546184, 59.00803153025],
1862  [1.07046627104, -55.69064178336, 57.45411776945],
1863  [1.07046631418, 164.56035451966, 63.32167143348],
1864  [1.07046626618, 84.05836739099, 63.32167014248],
1865  [1.04279925289, -152.79891613231, 59.00803262454],
1866  [1.07046597133, 13.79804996163, 85.87127616656],
1867  [1.04279923139, -23.43819697649, 80.11685656721],
1868  [1.07046627680, 124.30936019929, 80.73556362919],
1869  [1.04279922263, -87.94308140001, 80.11685648337],
1870  [1.07046625302, -125.17932391740, 85.87127725489],
1871  [1.07046625302, 54.82067608259, 94.12872274510],
1872  [1.07046627680, -55.69063980069, 99.26443637080],
1873  [1.04279923139, 156.56180302349, 99.88314343278],
1874  [1.07046597133, -166.20195003836, 94.12872383343],
1875  [1.04279922263, 92.05691859998, 99.88314351662],
1876  [1.04279925289, 27.20108386768, 120.99196737545],
1877  [1.07046631418, -15.43964548033, 116.67832856651],
1878  [1.07046627104, 124.30935821663, 122.54588223054],
1879  [1.07046626618, -95.94163260899, 116.67832985751],
1880  [1.04279921973, -138.58236453815, 120.99196846974],
1881  [1.07046629301, 72.18006700556, 132.99775645657],
1882  [1.04279918189, -55.69064040323, 136.64180100015],
1883  [1.07046625698, 176.43865348989, 132.99775825469],
1884  [1.07046628436, 6.46404091078, 156.19981749726],
1885  [1.04279923117, 124.30935959676, 159.92324915321],
1886  [1.07046627742, -117.84531974084, 156.19981833953]
1887  ],
1888  [
1889  [1,0,2],
1890  [0,3,2],
1891  [1,4,0],
1892  [2,5,1],
1893  [6,3,0],
1894  [7,2,3],
1895  [8,4,1],
1896  [9,0,4],
1897  [7,5,2],
1898  [10,1,5],
1899  [6,11,3],
1900  [0,9,6],
1901  [3,12,7],
1902  [8,13,4],
1903  [1,10,8],
1904  [4,13,9],
1905  [7,14,5],
1906  [5,15,10],
1907  [16,11,6],
1908  [12,3,11],
1909  [16,6,9],
1910  [17,7,12],
1911  [18,13,8],
1912  [19,8,10],
1913  [20,9,13],
1914  [17,14,7],
1915  [15,5,14],
1916  [19,10,15],
1917  [16,21,11],
1918  [11,22,12],
1919  [9,20,16],
1920  [12,22,17],
1921  [18,23,13],
1922  [8,19,18],
1923  [13,23,20],
1924  [17,24,14],
1925  [14,24,15],
1926  [15,25,19],
1927  [26,21,16],
1928  [22,11,21],
1929  [26,16,20],
1930  [27,17,22],
1931  [28,23,18],
1932  [28,18,19],
1933  [26,20,23],
1934  [27,24,17],
1935  [25,15,24],
1936  [28,19,25],
1937  [26,29,21],
1938  [21,29,22],
1939  [22,29,27],
1940  [28,30,23],
1941  [23,30,26],
1942  [27,31,24],
1943  [24,31,25],
1944  [25,31,28],
1945  [30,29,26],
1946  [31,27,29],
1947  [31,30,28],
1948  [30,31,29]
1949  ],
1950  [
1951  [0,1],
1952  [0,2],
1953  [0,3],
1954  [0,4],
1955  [0,6],
1956  [0,9],
1957  [1,2],
1958  [1,4],
1959  [1,5],
1960  [1,8],
1961  [1,10],
1962  [2,3],
1963  [2,5],
1964  [2,7],
1965  [3,6],
1966  [3,7],
1967  [3,11],
1968  [3,12],
1969  [4,8],
1970  [4,9],
1971  [4,13],
1972  [5,7],
1973  [5,10],
1974  [5,14],
1975  [5,15],
1976  [6,9],
1977  [6,11],
1978  [6,16],
1979  [7,12],
1980  [7,14],
1981  [7,17],
1982  [8,10],
1983  [8,13],
1984  [8,18],
1985  [8,19],
1986  [9,13],
1987  [9,16],
1988  [9,20],
1989  [10,15],
1990  [10,19],
1991  [11,12],
1992  [11,16],
1993  [11,21],
1994  [11,22],
1995  [12,17],
1996  [12,22],
1997  [13,18],
1998  [13,20],
1999  [13,23],
2000  [14,15],
2001  [14,17],
2002  [14,24],
2003  [15,19],
2004  [15,24],
2005  [15,25],
2006  [16,20],
2007  [16,21],
2008  [16,26],
2009  [17,22],
2010  [17,24],
2011  [17,27],
2012  [18,19],
2013  [18,23],
2014  [18,28],
2015  [19,25],
2016  [19,28],
2017  [20,23],
2018  [20,26],
2019  [21,22],
2020  [21,26],
2021  [21,29],
2022  [22,27],
2023  [22,29],
2024  [23,26],
2025  [23,28],
2026  [23,30],
2027  [24,25],
2028  [24,27],
2029  [24,31],
2030  [25,28],
2031  [25,31],
2032  [26,29],
2033  [26,30],
2034  [27,29],
2035  [27,31],
2036  [28,30],
2037  [28,31],
2038  [29,30],
2039  [29,31],
2040  [30,31]
2041  ]
2042  ],
2043  [
2044  "rhombic_dodecahedron",
2045  "Rhombic Dodecahedron",
2046  empty_str,
2047  "archimedean_duals",
2048  "Exact Mathematics",
2049  [
2050  [ 0.00000000000, 0.00000000000, 1.00000000000],
2051  [ 0.50000000000, 0.50000000000, 0.50000000000],
2052  [-0.50000000000, 0.50000000000, 0.50000000000],
2053  [-0.50000000000, -0.50000000000, 0.50000000000],
2054  [ 0.50000000000, -0.50000000000, 0.50000000000],
2055  [ 1.00000000000, 0.00000000000, 0.00000000000],
2056  [ 0.00000000000, 1.00000000000, 0.00000000000],
2057  [-1.00000000000, 0.00000000000, 0.00000000000],
2058  [ 0.00000000000, -1.00000000000, 0.00000000000],
2059  [ 0.50000000000, 0.50000000000, -0.50000000000],
2060  [-0.50000000000, 0.50000000000, -0.50000000000],
2061  [-0.50000000000, -0.50000000000, -0.50000000000],
2062  [ 0.50000000000, -0.50000000000, -0.50000000000],
2063  [ 0.00000000000, 0.00000000000, -1.00000000000]
2064  ],
2065  [
2066  [1.00000000000, 0.00000000000, 0.00000000000],
2067  [0.86602540378, 45.00000000000, 54.73561031724],
2068  [0.86602540378, 134.99999999999, 54.73561031724],
2069  [0.86602540378, -134.99999999999, 54.73561031724],
2070  [0.86602540378, -45.00000000000, 54.73561031724],
2071  [1.00000000000, 0.00000000000, 89.99999999999],
2072  [1.00000000000, 89.99999999999, 89.99999999999],
2073  [1.00000000000, 179.99999999999, 89.99999999999],
2074  [1.00000000000, -89.99999999999, 89.99999999999],
2075  [0.86602540378, 45.00000000000, 125.26438968275],
2076  [0.86602540378, 134.99999999999, 125.26438968275],
2077  [0.86602540378, -134.99999999999, 125.26438968275],
2078  [0.86602540378, -45.00000000000, 125.26438968275],
2079  [1.00000000000, 0.00000000000, 179.99999999999]
2080  ],
2081  [
2082  [1,5,4,0],
2083  [2,6,1,0],
2084  [3,7,2,0],
2085  [4,8,3,0],
2086  [6,9,5,1],
2087  [7,10,6,2],
2088  [8,11,7,3],
2089  [5,12,8,4],
2090  [9,13,12,5],
2091  [10,13,9,6],
2092  [11,13,10,7],
2093  [12,13,11,8]
2094  ],
2095  [
2096  [0,1],
2097  [0,2],
2098  [0,3],
2099  [0,4],
2100  [1,5],
2101  [2,6],
2102  [3,7],
2103  [4,8],
2104  [1,6],
2105  [2,7],
2106  [3,8],
2107  [4,5],
2108  [5,9],
2109  [6,10],
2110  [7,11],
2111  [8,12],
2112  [5,12],
2113  [6,9],
2114  [7,10],
2115  [8,11],
2116  [13,9],
2117  [13,10],
2118  [13,11],
2119  [13,12]
2120  ]
2121  ],
2122  [
2123  "rhombic_triacontahedron",
2124  "Rhombic Triacontahedron",
2125  empty_str,
2126  "archimedean_duals",
2127  "George W. Hart, 1997. george@li.net",
2128  [
2129  [ 0.00000000000, 1.01807390634, 0.00000000000],
2130  [ 0.00000000000, 0.88845068543, 0.67871595830],
2131  [ 0.58778524700, 0.75882747687, 0.33935798580],
2132  [ 0.58778524700, 0.88845069778, -0.33935797250],
2133  [ 0.00000000920, 0.75882755207, -0.67871593299],
2134  [-0.58778523780, 0.88845076062, -0.33935796050],
2135  [-0.58778523780, 0.75882753971, 0.33935799780],
2136  [ 0.36327128724, 0.33935800536, 0.88845072319],
2137  [ 0.95105653425, 0.20973479681, 0.54909275069],
2138  [ 0.95105653425, 0.33935801772, -0.12962320761],
2139  [-0.00000000000, 0.20973477335, -1.09818546924],
2140  [-0.58778524700, 0.33935798191, -0.75882749674],
2141  [ 0.58778526871, 0.33935801248, -0.75882749090],
2142  [-0.95105652505, 0.20973476100, 0.54909274385],
2143  [-0.36327125634, 0.33935800013, 0.88845072219],
2144  [-0.95105652505, 0.33935798191, -0.12962321445],
2145  [ 0.00000000000, -0.20973477335, 1.09818546924],
2146  [ 0.58778524700, -0.33935798191, 0.75882749674],
2147  [ 0.95105652505, -0.20973476100, -0.54909274385],
2148  [ 0.95105652505, -0.33935798191, 0.12962321445],
2149  [-0.36327128724, -0.33935800536, -0.88845072319],
2150  [-0.95105653425, -0.20973479681, -0.54909275069],
2151  [ 0.36327125634, -0.33935800013, -0.88845072219],
2152  [-0.58778526871, -0.33935801248, 0.75882749090],
2153  [-0.95105653425, -0.33935801772, 0.12962320761],
2154  [-0.00000000920, -0.75882755207, 0.67871593299],
2155  [ 0.58778523780, -0.88845076062, 0.33935796050],
2156  [ 0.58778523780, -0.75882753971, -0.33935799780],
2157  [ 0.00000000000, -0.88845068543, -0.67871595830],
2158  [-0.58778524700, -0.75882747687, -0.33935798580],
2159  [-0.58778524700, -0.88845069778, 0.33935797250],
2160  [ 0.00000000000, -1.01807390634, 0.00000000000]
2161  ],
2162  [
2163  [1.01807390634, 89.99999999999, 89.99999999999],
2164  [1.11803397644, 89.99999999999, 52.62263066673],
2165  [1.01807390634, 52.23875557900, 70.52877834968],
2166  [1.11803397644, 56.51199476545, 107.66980724671],
2167  [1.01807395187, 89.99999930546, 131.81031225926],
2168  [1.11803401790, 123.48800295704, 107.66980592440],
2169  [1.01807395187, 127.76124168979, 70.52877853920],
2170  [1.01807395187, 43.05074810479, 29.22865434511],
2171  [1.11803401790, 12.43628246235, 60.58554897383],
2172  [1.01807395187, 19.63752482828, 97.31486796888],
2173  [1.11803398875, 89.99999999999, 169.18768244741],
2174  [1.01807391986, 149.99999917200, 138.18968508471],
2175  [1.01807393822, 30.00000214725, 138.18968343591],
2176  [1.11803400000, 167.56371947847, 60.58554885896],
2177  [1.01807393822, 136.94924990484, 29.22865308802],
2178  [1.01807393221, 160.36247691007, 97.31486849897],
2179  [1.11803398875, -89.99999999999, 10.81231755257],
2180  [1.01807391986, -30.00000082799, 41.81031491527],
2181  [1.11803400000, -12.43628052152, 119.41445114102],
2182  [1.01807393221, -19.63752308992, 82.68513150102],
2183  [1.01807395187, -136.94925189520, 150.77134565488],
2184  [1.11803401790, -167.56371753764, 119.41445102616],
2185  [1.01807393822, -43.05075009515, 150.77134691197],
2186  [1.01807393822, -149.99999785273, 41.81031656408],
2187  [1.01807395187, -160.36247517171, 82.68513203111],
2188  [1.01807395187, -90.00000069453, 48.18968774073],
2189  [1.11803401790, -56.51199704295, 72.33019407559],
2190  [1.01807395187, -52.23875831020, 109.47122146079],
2191  [1.11803397644, -89.99999999999, 127.37736933326],
2192  [1.01807390634, -127.76124442099, 109.47122165031],
2193  [1.11803397644, -123.48800523454, 72.33019275327],
2194  [1.01807390634, -89.99999999999, 89.99999999999]
2195  ],
2196  [
2197  [2,1,0,3],
2198  [0,5,4,3],
2199  [1,6,5,0],
2200  [2,8,7,1],
2201  [3,9,8,2],
2202  [11,10,4,5],
2203  [10,12,3,4],
2204  [14,13,6,1],
2205  [13,15,5,6],
2206  [17,16,7,8],
2207  [16,14,1,7],
2208  [12,18,9,3],
2209  [18,19,8,9],
2210  [11,21,20,10],
2211  [5,15,21,11],
2212  [10,22,18,12],
2213  [14,16,23,13],
2214  [13,24,21,15],
2215  [17,26,25,16],
2216  [8,19,26,17],
2217  [18,27,26,19],
2218  [29,28,20,21],
2219  [28,22,10,20],
2220  [28,27,18,22],
2221  [25,30,23,16],
2222  [30,24,13,23],
2223  [30,29,21,24],
2224  [31,30,25,26],
2225  [28,31,26,27],
2226  [29,30,31,28]
2227  ],
2228  [
2229  [0,1],
2230  [0,3],
2231  [0,5],
2232  [1,2],
2233  [1,6],
2234  [1,7],
2235  [1,14],
2236  [2,3],
2237  [2,8],
2238  [3,4],
2239  [3,9],
2240  [3,12],
2241  [4,5],
2242  [4,10],
2243  [5,6],
2244  [5,11],
2245  [5,15],
2246  [6,13],
2247  [7,8],
2248  [7,16],
2249  [8,9],
2250  [8,17],
2251  [8,19],
2252  [9,18],
2253  [10,11],
2254  [10,12],
2255  [10,20],
2256  [10,22],
2257  [11,21],
2258  [12,18],
2259  [13,14],
2260  [13,15],
2261  [13,23],
2262  [13,24],
2263  [14,16],
2264  [15,21],
2265  [16,17],
2266  [16,23],
2267  [16,25],
2268  [17,26],
2269  [18,19],
2270  [18,22],
2271  [18,27],
2272  [19,26],
2273  [20,21],
2274  [20,28],
2275  [21,24],
2276  [21,29],
2277  [22,28],
2278  [23,30],
2279  [24,30],
2280  [25,26],
2281  [25,30],
2282  [26,27],
2283  [26,31],
2284  [27,28],
2285  [28,29],
2286  [28,31],
2287  [29,30],
2288  [30,31]
2289  ]
2290  ],
2291  [
2292  "tetrakis_hexahedron",
2293  "Tetrakis-hexahedron",
2294  empty_str,
2295  "archimedean_duals",
2296  "George W. Hart, 1997. george@li.net",
2297  [
2298  [ 0.70710678207, 0.70710678239, -0.70710681572],
2299  [-0.70710685399, 0.70710676255, -0.70710675601],
2300  [ 0.00000000000, 1.06066018679, 0.00000000000],
2301  [ 0.70710690892, 0.70710691162, 0.70710686506],
2302  [-0.00000000000, -0.00000006623, -1.06066014330],
2303  [-0.70710653501, 0.70710672864, 0.70710659847],
2304  [ 1.06066017311, 0.00000000830, -0.00000005793],
2305  [-0.70710690892, -0.70710691162, -0.70710686506],
2306  [ 0.70710653501, -0.70710672864, -0.70710659847],
2307  [-1.06066017311, -0.00000000830, 0.00000005793],
2308  [ 0.70710685399, -0.70710676255, 0.70710675601],
2309  [ 0.00000000000, 0.00000006623, 1.06066014330],
2310  [-0.70710678207, -0.70710678239, 0.70710681572],
2311  [ 0.00000000000, -1.06066018679, 0.00000000000]
2312  ],
2313  [
2314  [1.22474489254, 45.00000001273, 125.26439096213],
2315  [1.22474488813, 135.00000370435, 125.26438768675],
2316  [1.06066018679, 89.99999999999, 89.99999999999],
2317  [1.22474506887, 45.00000010944, 54.73561204440],
2318  [1.06066014330, -89.99999999999, 179.99999642215],
2319  [1.22474459343, 134.99999215502, 54.73561159120],
2320  [1.06066017311, 0.00000044850, 90.00000312934],
2321  [1.22474506887, -134.99999989055, 125.26438795559],
2322  [1.22474459343, -45.00000784497, 125.26438840879],
2323  [1.06066017311, -179.99999955149, 89.99999687065],
2324  [1.22474488813, -44.99999629564, 54.73561231324],
2325  [1.06066014330, 89.99999999999, 0.00000357784],
2326  [1.22474489254, -134.99999998726, 54.73560903786],
2327  [1.06066018679, -89.99999999999, 89.99999999999]
2328  ],
2329  [
2330  [1,0,2],
2331  [0,3,2],
2332  [1,4,0],
2333  [2,5,1],
2334  [6,3,0],
2335  [5,2,3],
2336  [7,4,1],
2337  [8,0,4],
2338  [9,1,5],
2339  [6,10,3],
2340  [0,8,6],
2341  [3,11,5],
2342  [7,8,4],
2343  [1,9,7],
2344  [5,12,9],
2345  [8,10,6],
2346  [11,3,10],
2347  [12,5,11],
2348  [13,8,7],
2349  [12,7,9],
2350  [8,13,10],
2351  [10,12,11],
2352  [7,12,13],
2353  [12,10,13]
2354  ],
2355  [
2356  [0,1],
2357  [0,2],
2358  [0,3],
2359  [0,4],
2360  [0,6],
2361  [0,8],
2362  [1,2],
2363  [1,4],
2364  [1,5],
2365  [1,7],
2366  [1,9],
2367  [2,3],
2368  [2,5],
2369  [3,5],
2370  [3,6],
2371  [3,10],
2372  [3,11],
2373  [4,7],
2374  [4,8],
2375  [5,9],
2376  [5,11],
2377  [5,12],
2378  [6,8],
2379  [6,10],
2380  [7,8],
2381  [7,9],
2382  [7,12],
2383  [7,13],
2384  [8,10],
2385  [8,13],
2386  [9,12],
2387  [10,11],
2388  [10,12],
2389  [10,13],
2390  [11,12],
2391  [12,13]
2392  ]
2393  ],
2394  [
2395  "triakis_icosahedron",
2396  "Triakis-icosahedron",
2397  empty_str,
2398  "archimedean_duals",
2399  "George W. Hart, 1997. george@li.net",
2400  [
2401  [-0.00000000000, 0.93417236382, 0.71364415491],
2402  [-0.61803396134, 0.93417232764, -0.35682211804],
2403  [-0.58017872165, 0.74900752253, 0.33496628596],
2404  [-1.00000006691, 0.22052823141, 0.57735025290],
2405  [ 0.00000000000, 1.00489899512, 0.00000000000],
2406  [-0.35857021344, 0.33496638403, 0.87695321245],
2407  [ 0.61803402629, 0.93417228051, -0.35682205521],
2408  [-0.93874890906, 0.33496634823, -0.12794580758],
2409  [ 0.00000009630, -0.22052800883, 1.15470021259],
2410  [-0.00000000807, 0.74900749069, -0.66993269090],
2411  [ 0.58017868755, 0.74900752648, 0.33496632913],
2412  [-0.99999964147, -0.22052809857, -0.57735011790],
2413  [-0.58017883007, -0.33496629413, 0.74900748268],
2414  [ 0.35857007899, 0.33496635276, 0.87695329026],
2415  [-0.00000009630, 0.22052800883, -1.15470021259],
2416  [ 0.99999964147, 0.22052809857, 0.57735011790],
2417  [-0.58017865557, 0.33496636593, -0.74900752152],
2418  [-0.93874890790, -0.33496628904, 0.12794577195],
2419  [-0.61803402629, -0.93417228051, 0.35682205521],
2420  [ 0.58017883007, 0.33496629413, -0.74900748268],
2421  [ 0.93874890790, 0.33496628904, -0.12794577195],
2422  [ 0.00000000807, -0.74900749069, 0.66993269090],
2423  [ 0.58017865557, -0.33496636593, 0.74900752152],
2424  [ 1.00000006691, -0.22052823141, -0.57735025290],
2425  [-0.35857007899, -0.33496635276, -0.87695329026],
2426  [-0.58017868755, -0.74900752648, -0.33496632913],
2427  [ 0.61803396134, -0.93417232764, 0.35682211804],
2428  [ 0.35857021344, -0.33496638403, -0.87695321245],
2429  [ 0.93874890906, -0.33496634823, 0.12794580758],
2430  [ 0.00000000000, -0.93417236382, -0.71364415491],
2431  [ 0.00000000000, -1.00489899512, 0.00000000000],
2432  [ 0.58017872165, -0.74900752253, -0.33496628596]
2433  ],
2434  [
2435  [1.17557049349, 89.99999999999, 52.62263295694],
2436  [1.17557047387, 123.48800484353, 107.66980902983],
2437  [1.00489901512, 127.76124340324, 70.52878253520],
2438  [1.17557056326, 167.56371727190, 60.58555153741],
2439  [1.00489899512, 89.99999999999, 89.99999999999],
2440  [1.00489900648, 136.94925257836, 29.22865737676],
2441  [1.17557045149, 56.51199105535, 107.66980616365],
2442  [1.00489904885, 160.36247714599, 97.31487112602],
2443  [1.17557015257, -89.99997498012, 10.81231177567],
2444  [1.00489901554, 90.00000061707, 131.81031595691],
2445  [1.00489901277, 52.23875837347, 70.52877987717],
2446  [1.17557011013, -167.56371940336, 119.41445336076],
2447  [1.00489905074, -150.00000811670, 41.81031888524],
2448  [1.00489901598, 43.05075547144, 29.22864925989],
2449  [1.17557015257, 90.00002501987, 169.18768822431],
2450  [1.17557011013, 12.43628059663, 60.58554663923],
2451  [1.00489900288, 149.99999533713, 138.18968748766],
2452  [1.00489902350, -160.36248032812, 82.68513073645],
2453  [1.17557045149, -123.48800894464, 72.33019383634],
2454  [1.00489905074, 29.99999188329, 138.18968111474],
2455  [1.00489902350, 19.63751967187, 97.31486926354],
2456  [1.00489901554, -89.99999938292, 48.18968404308],
2457  [1.00489900288, -30.00000466286, 41.81031251233],
2458  [1.17557056326, -12.43628272809, 119.41444846258],
2459  [1.00489901598, -136.94924452855, 150.77135074010],
2460  [1.00489901277, -127.76124162652, 109.47122012281],
2461  [1.17557047387, -56.51199515646, 72.33019097016],
2462  [1.00489900648, -43.05074742162, 150.77134262323],
2463  [1.00489904885, -19.63752285400, 82.68512887397],
2464  [1.17557049349, -89.99999999999, 127.37736704305],
2465  [1.00489899512, -89.99999999999, 89.99999999999],
2466  [1.00489901512, -52.23875659675, 109.47121746479]
2467  ],
2468  [
2469  [1,0,2],
2470  [0,3,2],
2471  [1,4,0],
2472  [2,3,1],
2473  [5,3,0],
2474  [6,4,1],
2475  [6,0,4],
2476  [7,1,3],
2477  [5,8,3],
2478  [0,8,5],
2479  [1,9,6],
2480  [6,10,0],
2481  [7,11,1],
2482  [3,11,7],
2483  [12,3,8],
2484  [13,8,0],
2485  [14,9,1],
2486  [14,6,9],
2487  [15,10,6],
2488  [15,0,10],
2489  [16,1,11],
2490  [17,11,3],
2491  [12,18,3],
2492  [8,18,12],
2493  [13,15,8],
2494  [0,15,13],
2495  [1,16,14],
2496  [14,19,6],
2497  [6,20,15],
2498  [11,14,16],
2499  [17,18,11],
2500  [3,18,17],
2501  [21,18,8],
2502  [22,8,15],
2503  [23,19,14],
2504  [23,6,19],
2505  [23,20,6],
2506  [23,15,20],
2507  [24,14,11],
2508  [25,11,18],
2509  [21,26,18],
2510  [8,26,21],
2511  [22,26,8],
2512  [15,26,22],
2513  [14,27,23],
2514  [23,28,15],
2515  [24,29,14],
2516  [11,29,24],
2517  [25,29,11],
2518  [18,29,25],
2519  [30,18,26],
2520  [28,26,15],
2521  [29,27,14],
2522  [29,23,27],
2523  [26,28,23],
2524  [30,29,18],
2525  [26,29,30],
2526  [29,31,23],
2527  [23,31,26],
2528  [31,29,26]
2529  ],
2530  [
2531  [0,1],
2532  [0,2],
2533  [0,3],
2534  [0,4],
2535  [0,5],
2536  [0,6],
2537  [0,8],
2538  [0,10],
2539  [0,13],
2540  [0,15],
2541  [1,2],
2542  [1,3],
2543  [1,4],
2544  [1,6],
2545  [1,7],
2546  [1,9],
2547  [1,11],
2548  [1,14],
2549  [1,16],
2550  [2,3],
2551  [3,5],
2552  [3,7],
2553  [3,8],
2554  [3,11],
2555  [3,12],
2556  [3,17],
2557  [3,18],
2558  [4,6],
2559  [5,8],
2560  [6,9],
2561  [6,10],
2562  [6,14],
2563  [6,15],
2564  [6,19],
2565  [6,20],
2566  [6,23],
2567  [7,11],
2568  [8,12],
2569  [8,13],
2570  [8,15],
2571  [8,18],
2572  [8,21],
2573  [8,22],
2574  [8,26],
2575  [9,14],
2576  [10,15],
2577  [11,14],
2578  [11,16],
2579  [11,17],
2580  [11,18],
2581  [11,24],
2582  [11,25],
2583  [11,29],
2584  [12,18],
2585  [13,15],
2586  [14,16],
2587  [14,19],
2588  [14,23],
2589  [14,24],
2590  [14,27],
2591  [14,29],
2592  [15,20],
2593  [15,22],
2594  [15,23],
2595  [15,26],
2596  [15,28],
2597  [17,18],
2598  [18,21],
2599  [18,25],
2600  [18,26],
2601  [18,29],
2602  [18,30],
2603  [19,23],
2604  [20,23],
2605  [21,26],
2606  [22,26],
2607  [23,26],
2608  [23,27],
2609  [23,28],
2610  [23,29],
2611  [23,31],
2612  [24,29],
2613  [25,29],
2614  [26,28],
2615  [26,29],
2616  [26,30],
2617  [26,31],
2618  [27,29],
2619  [29,30],
2620  [29,31]
2621  ]
2622  ],
2623  [
2624  "triakis_octahedron",
2625  "Triakis-octahedron",
2626  empty_str,
2627  "archimedean_duals",
2628  "George W. Hart, 1997. george@li.net",
2629  [
2630  [ 0.00000000000, 1.41421356691, 0.00000000000],
2631  [-0.00000000000, 0.00000003680, -1.41421356830],
2632  [-0.58578641907, 0.58578642733, -0.58578648469],
2633  [-1.41421370446, -0.00000001119, 0.00000004562],
2634  [ 0.58578643764, 0.58578646663, -0.58578633512],
2635  [-0.58578646823, 0.58578646484, 0.58578644204],
2636  [ 1.41421370446, 0.00000001119, -0.00000004562],
2637  [-0.58578642040, -0.58578641355, -0.58578648780],
2638  [ 0.00000000000, -0.00000003680, 1.41421356830],
2639  [ 0.58578646823, -0.58578646484, -0.58578644204],
2640  [ 0.58578642040, 0.58578641355, 0.58578648780],
2641  [ 0.00000000000, -1.41421356691, 0.00000000000],
2642  [-0.58578643764, -0.58578646663, 0.58578633512],
2643  [ 0.58578641907, -0.58578642733, 0.58578648469]
2644  ],
2645  [
2646  [1.41421356691, 89.99999999999, 89.99999999999],
2647  [1.41421356830, 89.99999999999, 179.99999850913],
2648  [1.01461188287, 134.99999959623, 125.26439251769],
2649  [1.41421370446, -179.99999954681, 89.99999815161],
2650  [1.01461182992, 45.00000141798, 125.26438428773],
2651  [1.01461190828, 135.00000016553, 54.73561144661],
2652  [1.41421370446, 0.00000045318, 90.00000184838],
2653  [1.01461187748, -135.00000033463, 125.26439294822],
2654  [1.41421356830, -89.99999999999, 0.00000149086],
2655  [1.01461190828, -44.99999983445, 125.26438855338],
2656  [1.01461187748, 44.99999966536, 54.73560705177],
2657  [1.41421356691, -89.99999999999, 89.99999999999],
2658  [1.01461182992, -134.99999858201, 54.73561571226],
2659  [1.01461188287, -45.00000040376, 54.73560748230]
2660  ],
2661  [
2662  [1,0,2],
2663  [0,3,2],
2664  [1,4,0],
2665  [2,3,1],
2666  [5,3,0],
2667  [6,4,1],
2668  [6,0,4],
2669  [7,1,3],
2670  [5,8,3],
2671  [0,8,5],
2672  [1,9,6],
2673  [6,10,0],
2674  [7,11,1],
2675  [3,11,7],
2676  [12,3,8],
2677  [10,8,0],
2678  [11,9,1],
2679  [11,6,9],
2680  [8,10,6],
2681  [12,11,3],
2682  [8,11,12],
2683  [11,13,6],
2684  [6,13,8],
2685  [13,11,8]
2686  ],
2687  [
2688  [0,1],
2689  [0,2],
2690  [0,3],
2691  [0,4],
2692  [0,5],
2693  [0,6],
2694  [0,8],
2695  [0,10],
2696  [1,2],
2697  [1,3],
2698  [1,4],
2699  [1,6],
2700  [1,7],
2701  [1,9],
2702  [1,11],
2703  [2,3],
2704  [3,5],
2705  [3,7],
2706  [3,8],
2707  [3,11],
2708  [3,12],
2709  [4,6],
2710  [5,8],
2711  [6,8],
2712  [6,9],
2713  [6,10],
2714  [6,11],
2715  [6,13],
2716  [7,11],
2717  [8,10],
2718  [8,11],
2719  [8,12],
2720  [8,13],
2721  [9,11],
2722  [11,12],
2723  [11,13]
2724  ]
2725  ],
2726  [
2727  "triakis_tetrahedron",
2728  "Triakis-tetrahedron",
2729  empty_str,
2730  "archimedean_duals",
2731  "George W. Hart, 1997. george@li.net",
2732  [
2733  [ 0.00000000000, 1.73205113922, 0.00000000000],
2734  [ 1.41421310220, -0.57735025671, -0.81649662287],
2735  [-0.00000000000, 0.34640998257, -0.97979591140],
2736  [-1.41421344981, -0.57735038744, -0.81649643800],
2737  [ 0.84852816886, 0.34641021829, 0.48989788285],
2738  [-0.84852813268, 0.34641022788, 0.48989786928],
2739  [-0.00000005168, -0.57735016964, 1.63299346667],
2740  [ 0.00000005427, -1.03923045335, 0.00000019409]
2741  ],
2742  [
2743  [1.73205113922, 89.99999999999, 89.99999999999],
2744  [1.73205044746, -22.20766038913, 118.12551364281],
2745  [1.03923043836, 89.99999999999, 160.52878892978],
2746  [1.73205068770, -157.79233999925, 118.12550246063],
2747  [1.03923049816, 22.20765684163, 61.87449880719],
2748  [1.03923046542, 157.79234174813, 61.87449869060],
2749  [1.73205106177, -90.00000512871, 19.47121416866],
2750  [1.03923045335, -89.99999700782, 89.99998929901]
2751  ],
2752  [
2753  [1,0,2],
2754  [0,3,2],
2755  [1,4,0],
2756  [2,3,1],
2757  [5,3,0],
2758  [6,4,1],
2759  [6,0,4],
2760  [7,1,3],
2761  [5,6,3],
2762  [0,6,5],
2763  [1,7,6],
2764  [3,6,7]
2765  ],
2766  [
2767  [0,1],
2768  [0,2],
2769  [0,3],
2770  [0,4],
2771  [0,5],
2772  [0,6],
2773  [1,2],
2774  [1,3],
2775  [1,4],
2776  [1,6],
2777  [1,7],
2778  [2,3],
2779  [3,5],
2780  [3,6],
2781  [3,7],
2782  [4,6],
2783  [5,6],
2784  [6,7]
2785  ]
2786  ]
2787 ];
2788 
2789 //! @}
2790 
2791 //----------------------------------------------------------------------------//
2792 // openscad-amu auxiliary scripts
2793 //----------------------------------------------------------------------------//
2794 
2795 /*
2796 BEGIN_SCOPE db;
2797 BEGIN_SCOPE autostat;
2798  BEGIN_OPENSCAD;
2799  include <omdl-base.scad>;
2800  include <database/geometry/polyhedra/archimedean_duals.scad>;
2801 
2802  fs = "^";
2803 
2804  tc = dtc_polyhedra_archimedean_duals;
2805  tr = dtr_polyhedra_archimedean_duals;
2806 
2807  ids = table_get_row_ids(tr);
2808 
2809  echo
2810  (
2811  str
2812  (
2813  "no.", fs, "id", fs, "other name", fs,
2814  "vertices", fs, "faces", fs, "edges",
2815 
2816  fs, "face-verticies",
2817  fs, "face-angles",
2818  fs, "edge-lengths",
2819  fs, "edge-angles"
2820  )
2821  );
2822 
2823  for ( id = ids )
2824  {
2825  i = first(find(id, ids, c=1))+1;
2826 
2827  n = table_get_value(tr, tc, id, "n");
2828  o = table_get_value(tr, tc, id, "o");
2829  g = table_get_value(tr, tc, id, "g");
2830  d = table_get_value(tr, tc, id, "d");
2831 
2832  c = table_get_value(tr, tc, id, "c");
2833  s = table_get_value(tr, tc, id, "s");
2834  f = table_get_value(tr, tc, id, "f");
2835  e = table_get_value(tr, tc, id, "e");
2836 
2837  fo = is_empty(o) ? "-" : o;
2838 
2839  echo
2840  (
2841  str
2842  (
2843  i, fs, id, fs, fo, fs,
2844  len(c), fs, len(f), fs, len(e),
2845 
2846  fs, histogram(sort_q(polytope_face_vertex_counts(f)), m=9),
2847  fs, histogram(sort_q(round_d(polytope_face_angles(c, f), d=1)), m=9),
2848  fs, histogram(sort_q(round_s(polytope_edge_lengths(c, e), d=3)), m=9),
2849  fs, histogram(sort_q(round_d(polytope_edge_angles(c, f), d=1)), m=9),
2850 
2851  fs
2852  )
2853  );
2854  }
2855  END_OPENSCAD;
2856 
2857  BEGIN_MFSCRIPT;
2858  include --path "${INCLUDE_PATH}" {var_init,var_gen_term}.mfs;
2859  include --path "${INCLUDE_PATH}" scr_make_mf.mfs;
2860  END_MFSCRIPT;
2861 END_SCOPE;
2862 END_SCOPE;
2863 */
2864 
2865 /*
2866 BEGIN_SCOPE db;
2867 BEGIN_SCOPE dim;
2868  BEGIN_OPENSCAD;
2869  include <omdl-base.scad>;
2870  include <units/coordinate.scad>;
2871  include <tools/align.scad>;
2872  include <tools/polytope.scad>;
2873  include <database/geometry/polyhedra/archimedean_duals.scad>;
2874 
2875  config = 0;
2876 
2877  tc = dtc_polyhedra_archimedean_duals;
2878  tr = dtr_polyhedra_archimedean_duals;
2879 
2880  id = "default";
2881  sr = 100;
2882 
2883  pv = table_get_value(tr, tc, id, "c");
2884  pf = table_get_value(tr, tc, id, "f");
2885  pe = table_get_value(tr, tc, id, "e");
2886 
2887  sv = coordinate_scale3d_csc(pv, sr);
2888 
2889  if (config == 0) // png preview
2890  {
2891  $fn = 25;
2892 
2893  %polyhedron(sv, pf);
2894 
2895  polytope_frame(sv, pf, pe)
2896  {
2897  circle(r = sr / 25);
2898  color("lightblue")
2899  sphere(r = sr / 25 * (1 + 1/2));
2900  }
2901  }
2902 
2903  if (config == 1) // stl model
2904  {
2905  polyhedron(sv, pf);
2906  }
2907  END_OPENSCAD;
2908 
2909  BEGIN_MFSCRIPT;
2910  include --path "${INCLUDE_PATH}" {var_init,var_gen_png2eps}.mfs;
2911 
2912  views name "views" views "diag";
2913  defines name "ids" define "id"
2914  strings
2915  "
2916  disdyakis_dodecahedron
2917  disdyakis_triacontahedron
2918  kite_hexecontahedron
2919  kite_icositetrahedron
2920  pentagonal_hexecontahedron
2921  pentagonal_icositetrahedron
2922  pentakis_dodecahedron
2923  rhombic_dodecahedron
2924  rhombic_triacontahedron
2925  tetrakis_hexahedron
2926  triakis_icosahedron
2927  triakis_octahedron
2928  triakis_tetrahedron
2929  ";
2930  variables add_opts_combine "views ids";
2931  variables add_opts "-D config=0 --viewall --autocenter --view=axes";
2932 
2933  include --path "${INCLUDE_PATH}" scr_make_mf_begin.mfs;
2934  include --path "${INCLUDE_PATH}" scr_make_mf_add_ext.mfs;
2935 
2936  include --path "${INCLUDE_PATH}" var_gen_stl.mfs;
2937  variables add_opts_combine "ids";
2938  variables add_opts "-D config=1";
2939 
2940  include --path "${INCLUDE_PATH}" scr_make_mf_add_ext.mfs;
2941  include --path "${INCLUDE_PATH}" scr_make_mf_end.mfs;
2942  END_MFSCRIPT;
2943 END_SCOPE;
2944 END_SCOPE;
2945 */
2946 
2947 //----------------------------------------------------------------------------//
2948 // end of file
2949 //----------------------------------------------------------------------------//
empty_str
empty_str
<string> A string with no characters (the empty string).
Definition: constants.scad:301
dtr_polyhedra_archimedean_duals
dtr_polyhedra_archimedean_duals
Definition: archimedean_duals.scad:212
dtc_polyhedra_archimedean_duals
dtc_polyhedra_archimedean_duals
Definition: archimedean_duals.scad:197