omdl  v0.6.1
OpenSCAD Mechanical Design Library
archimedean_duals.scad
Go to the documentation of this file.
1 //! Table of polyhedra data group: \c archimedean_duals
2 /***************************************************************************//**
3  \file archimedean_duals.scad
4  \author Roy Allen Sutton
5  \date 2017
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  \note Include this library file using the \b include statement.
42 
43  [omdl]: https://github.com/royasutton/omdl
44 
45  [Anthony Thyssen]: http://www.ict.griffith.edu.au/anthony/anthony.html
46  [Studies into Polyhedra]: http://www.ict.griffith.edu.au/anthony/graphics/polyhedra
47  [Exact Mathematics]: http://www.ict.griffith.edu.au/anthony/graphics/polyhedra/maths.shtml
48 
49  [George W. Hart]: http://www.georgehart.com
50  [Encyclopedia of Polyhedra]: http://www.georgehart.com/virtual-polyhedra/vp.html
51 
52  [Netlib]: http://www.netlib.org
53  [Polyhedron Database]: http://www.netlib.org/polyhedra
54 
55  \ingroup database_polyhedra
56 *******************************************************************************/
57 
58 //----------------------------------------------------------------------------//
59 /***************************************************************************//**
60  \addtogroup database_polyhedra
61  @{
62  <br>
63  ### Group: archimedean_duals ###
64 
65  \amu_define caption (archimedean_duals)
66  \amu_make png_files (append=db_dim extension=png)
67  \amu_make stl_files (append=db_dim extension=stl)
68 
69  \amu_shell file_cnt ("echo ${png_files} | wc -w")
70  \amu_shell cell_num ("seq -f '(%g)' -s '^' ${file_cnt}")
71 
72  \amu_shell html_cell_titles
73  (
74  "echo ${stl_files} | grep -Po 'db_dim_\K[^.]*' | tr '\n' '^'"
75  )
76 
77  \htmlonly
78  \amu_image_table
79  (
80  type=html columns=4 image_width="200" cell_files="${png_files}"
81  table_caption="${caption}" cell_captions="${cell_num}"
82  cell_titles="${html_cell_titles}" cell_urls="${stl_files}"
83  )
84  \endhtmlonly
85 
86  \amu_define caption (archimedean\_duals)
87  \amu_make eps_files (append=db_dim extension=png2eps)
88 
89  \latexonly
90  \amu_image_table
91  (
92  type=latex columns=4 image_width="1.25in" cell_files="${eps_files}"
93  table_caption="${caption}" cell_captions="${cell_num}"
94  )
95  \endlatexonly
96 
97  \amu_shell data
98  (
99  "grep -Po 'ECHO: \"\K[^\"]*' build/csg/archimedean_duals_db_autostat.log" --rmnl
100  )
101  \amu_shell columns ("echo '${data}' | awk -F '^' 'NR==1 {print NF;exit}'")
102  \amu_shell heading ("echo '${data}' | awk -F '^' 'NR==1 {print;exit}'")
103  \amu_shell texts ("echo '${data}' | awk -F '^' 'NR>1 {print}'")
104 
105  \amu_table
106  (
107  columns=${columns} column_headings="${heading}" cell_texts="${texts}"
108  )
109 *******************************************************************************/
110 //----------------------------------------------------------------------------//
111 
112 //! <matrix-2x9> \c archimedean_duals polyhedra data table columns definition.
113 //! \hideinitializer
114 dtc_polyhedra_archimedean_duals =
115 [
116  ["id", "identifier"],
117  ["n", "name"],
118  ["o", "other name"],
119  ["g", "group"],
120  ["d", "data source"],
121  ["c", "cartesian vertices"],
122  ["s", "spherical vertices"],
123  ["f", "faces"],
124  ["e", "edges"]
125 ];
126 
127 //! <matrix-9xR> \c archimedean_duals polyhedra data table rows.
128 //! \hideinitializer
129 dtr_polyhedra_archimedean_duals =
130 [
131  [
132  "disdyakis_dodecahedron",
133  "Disdyakis-Dodecahedron",
134  "Hexakis-Octahedron",
135  "archimedean_duals",
136  "Exact Mathematics",
137  [
138  [ 0.00000000000, 0.00000000000, 1.00000000000],
139  [ 0.70710678119, 0.00000000000, 0.70710678119],
140  [ 0.00000000000, 0.70710678119, 0.70710678119],
141  [-0.70710678119, 0.00000000000, 0.70710678119],
142  [ 0.00000000000, -0.70710678119, 0.70710678119],
143  [ 0.57735026919, 0.57735026919, 0.57735026919],
144  [-0.57735026919, 0.57735026919, 0.57735026919],
145  [-0.57735026919, -0.57735026919, 0.57735026919],
146  [ 0.57735026919, -0.57735026919, 0.57735026919],
147  [ 1.00000000000, 0.00000000000, 0.00000000000],
148  [ 0.70710678119, 0.70710678119, 0.00000000000],
149  [ 0.00000000000, 1.00000000000, 0.00000000000],
150  [-0.70710678119, 0.70710678119, 0.00000000000],
151  [-1.00000000000, 0.00000000000, 0.00000000000],
152  [-0.70710678119, -0.70710678119, 0.00000000000],
153  [ 0.00000000000, -1.00000000000, 0.00000000000],
154  [ 0.70710678119, -0.70710678119, 0.00000000000],
155  [ 0.57735026919, 0.57735026919, -0.57735026919],
156  [-0.57735026919, 0.57735026919, -0.57735026919],
157  [-0.57735026919, -0.57735026919, -0.57735026919],
158  [ 0.57735026919, -0.57735026919, -0.57735026919],
159  [ 0.70710678119, 0.00000000000, -0.70710678119],
160  [ 0.00000000000, 0.70710678119, -0.70710678119],
161  [-0.70710678119, 0.00000000000, -0.70710678119],
162  [ 0.00000000000, -0.70710678119, -0.70710678119],
163  [ 0.00000000000, 0.00000000000, -1.00000000000]
164  ],
165  [
166  [1.00000000000, 0.00000000000, 0.00000000000],
167  [1.00000000000, 0.00000000000, 45.00000000000],
168  [1.00000000000, 89.99999999999, 45.00000000000],
169  [1.00000000000, 179.99999999999, 45.00000000000],
170  [1.00000000000, -89.99999999999, 45.00000000000],
171  [1.00000000000, 45.00000000000, 54.73561031724],
172  [1.00000000000, 134.99999999999, 54.73561031724],
173  [1.00000000000, -134.99999999999, 54.73561031724],
174  [1.00000000000, -45.00000000000, 54.73561031724],
175  [1.00000000000, 0.00000000000, 89.99999999999],
176  [1.00000000000, 45.00000000000, 89.99999999999],
177  [1.00000000000, 89.99999999999, 89.99999999999],
178  [1.00000000000, 134.99999999999, 89.99999999999],
179  [1.00000000000, 179.99999999999, 89.99999999999],
180  [1.00000000000, -134.99999999999, 89.99999999999],
181  [1.00000000000, -89.99999999999, 89.99999999999],
182  [1.00000000000, -45.00000000000, 89.99999999999],
183  [1.00000000000, 45.00000000000, 125.26438968275],
184  [1.00000000000, 134.99999999999, 125.26438968275],
185  [1.00000000000, -134.99999999999, 125.26438968275],
186  [1.00000000000, -45.00000000000, 125.26438968275],
187  [1.00000000000, 0.00000000000, 134.99999999999],
188  [1.00000000000, 89.99999999999, 134.99999999999],
189  [1.00000000000, 179.99999999999, 134.99999999999],
190  [1.00000000000, -89.99999999999, 134.99999999999],
191  [1.00000000000, 0.00000000000, 179.99999999999]
192  ],
193  [
194  [6,3,13],
195  [3,6,0],
196  [1,5,9],
197  [5,1,0],
198  [6,2,0],
199  [2,5,0],
200  [2,6,11],
201  [5,2,11],
202  [23,18,13],
203  [18,23,25],
204  [12,6,13],
205  [18,12,13],
206  [6,12,11],
207  [12,18,11],
208  [17,21,9],
209  [21,17,25],
210  [5,10,9],
211  [10,17,9],
212  [10,5,11],
213  [17,10,11],
214  [22,18,25],
215  [17,22,25],
216  [18,22,11],
217  [22,17,11],
218  [7,3,0],
219  [3,7,13],
220  [4,7,0],
221  [7,4,15],
222  [7,14,13],
223  [14,7,15],
224  [23,19,25],
225  [19,14,15],
226  [19,23,13],
227  [14,19,13],
228  [1,8,0],
229  [8,4,0],
230  [8,1,9],
231  [16,8,9],
232  [8,16,15],
233  [4,8,15],
234  [19,24,25],
235  [24,19,15],
236  [21,20,9],
237  [20,16,9],
238  [20,21,25],
239  [24,20,25],
240  [16,20,15],
241  [20,24,15]
242  ],
243  [
244  [0,1],
245  [0,2],
246  [0,3],
247  [0,4],
248  [0,5],
249  [0,6],
250  [0,7],
251  [0,8],
252  [1,5],
253  [1,8],
254  [1,9],
255  [2,5],
256  [2,6],
257  [2,11],
258  [3,6],
259  [3,7],
260  [3,13],
261  [4,7],
262  [4,8],
263  [4,15],
264  [5,9],
265  [5,10],
266  [5,11],
267  [6,11],
268  [6,12],
269  [6,13],
270  [7,13],
271  [7,14],
272  [7,15],
273  [8,9],
274  [8,15],
275  [8,16],
276  [9,10],
277  [9,16],
278  [9,17],
279  [9,20],
280  [9,21],
281  [10,11],
282  [10,17],
283  [11,12],
284  [11,17],
285  [11,18],
286  [11,22],
287  [12,13],
288  [12,18],
289  [13,14],
290  [13,18],
291  [13,19],
292  [13,23],
293  [14,15],
294  [14,19],
295  [15,16],
296  [15,19],
297  [15,20],
298  [15,24],
299  [16,20],
300  [17,21],
301  [17,22],
302  [17,25],
303  [18,22],
304  [18,23],
305  [18,25],
306  [19,23],
307  [19,24],
308  [19,25],
309  [20,21],
310  [20,24],
311  [20,25],
312  [21,25],
313  [22,25],
314  [23,25],
315  [24,25]
316  ]
317  ],
318  [
319  "disdyakis_triacontahedron",
320  "Disdyakis-Triacontahedron",
321  "Hexakis-Icosahedron",
322  "archimedean_duals",
323  "George W. Hart, 1997. george@li.net",
324  [
325  [-0.50445781003, 0.85823482728, -0.16390828497],
326  [-0.36662979208, 0.81649657980, -0.50462268725],
327  [-0.93184127980, 0.48989796379, -0.30277358267],
328  [-0.59321945859, 0.81649657360, 0.19274866308],
329  [ 0.00000000000, 1.09544514122, 0.00000000000],
330  [-0.50445778133, 0.53041832127, -0.69432657505],
331  [-0.81622979173, 0.53041830040, 0.26520912954],
332  [ 0.00000001518, 0.85823486838, -0.53041833095],
333  [-0.59321946723, 0.19274867602, -0.81649654739],
334  [ 0.00000000000, 0.48989795293, -0.97979595711],
335  [-0.31177199523, 0.85823484751, 0.42911737364],
336  [-0.95984929502, 0.19274875966, 0.31187389294],
337  [-0.57590958810, 0.48989797384, 0.79267156652],
338  [ 0.36662981623, 0.81649662504, -0.50462266207],
339  [-0.81622981643, 0.00000002808, -0.59302572359],
340  [ 0.00000000558, 0.81649664218, 0.62374790189],
341  [-1.00891555440, 0.00000005159, -0.00000002191],
342  [ 0.50445781792, 0.85823483908, -0.16390823916],
343  [-0.31177210334, 0.00000001596, -0.95953570176],
344  [-0.95984928118, -0.19274864408, -0.31187392864],
345  [-0.57590955558, -0.48989798773, -0.79267154078],
346  [ 0.31177211852, 0.85823485242, 0.42911737081],
347  [-0.81622985171, 0.00000001860, 0.59302570450],
348  [-0.93184128858, -0.48989792546, 0.30277360378],
349  [ 0.50445777307, 0.53041826968, -0.69432655314],
350  [ 0.59321951559, 0.81649655588, 0.19274869309],
351  [ 0.93184128858, 0.48989792546, -0.30277360378],
352  [-0.00000002036, -0.19274873371, -1.00924525494],
353  [ 0.00000002470, 0.53041827232, 0.85823485312],
354  [ 0.57590955558, 0.48989798773, 0.79267154078],
355  [-0.59321949238, -0.19274868694, 0.81649654849],
356  [ 0.59321949238, 0.19274868694, -0.81649654849],
357  [ 0.31177214323, -0.00000007614, -0.95953585607],
358  [-0.81622981685, -0.53041833140, -0.26520912587],
359  [ 0.00000002036, 0.19274873371, 1.00924525494],
360  [-0.31177214323, 0.00000007614, 0.95953585607],
361  [ 0.81622981685, 0.53041833140, 0.26520912587],
362  [-0.00000002470, -0.53041827232, -0.85823485312],
363  [ 0.57590958810, -0.48989797384, -0.79267156652],
364  [-0.59321951559, -0.81649655588, -0.19274869309],
365  [-0.50445777307, -0.53041826968, 0.69432655314],
366  [-0.00000000000, -0.48989795293, 0.97979595711],
367  [ 0.81622985171, -0.00000001860, -0.59302570450],
368  [ 0.95984928118, 0.19274864408, 0.31187392864],
369  [-0.00000000558, -0.81649664218, -0.62374790189],
370  [-0.31177211852, -0.85823485242, -0.42911737081],
371  [ 0.31177210334, -0.00000001596, 0.95953570176],
372  [-0.36662981623, -0.81649662504, 0.50462266207],
373  [-0.50445781792, -0.85823483908, 0.16390823916],
374  [ 0.95984929502, -0.19274875966, -0.31187389294],
375  [ 1.00891555440, -0.00000005159, 0.00000002191],
376  [ 0.00000000000, -1.09544514122, 0.00000000000],
377  [ 0.59321946723, -0.19274867602, 0.81649654739],
378  [ 0.81622981643, -0.00000002808, 0.59302572359],
379  [ 0.93184127980, -0.48989796379, 0.30277358267],
380  [ 0.31177199523, -0.85823484751, -0.42911737364],
381  [-0.00000001518, -0.85823486838, 0.53041833095],
382  [ 0.81622979173, -0.53041830040, -0.26520912954],
383  [ 0.59321945859, -0.81649657360, -0.19274866308],
384  [ 0.50445778133, -0.53041832127, 0.69432657505],
385  [ 0.36662979208, -0.81649657980, 0.50462268725],
386  [ 0.50445781003, -0.85823482728, 0.16390828497]
387  ],
388  [
389  [1.00891556968, 120.44638608101, 99.34970439173],
390  [1.02748631414, 114.18141338542, 119.41445354663],
391  [1.09544512781, 152.26769800096, 106.04505691244],
392  [1.02748626651, 125.99999880122, 79.18768461129],
393  [1.09544514122, 89.99999999999, 89.99999999999],
394  [1.00891557700, 133.56299949458, 133.48707737940],
395  [1.00891552109, 146.98260050283, 74.75983830192],
396  [1.00891560357, 89.99999898680, 121.71747498907],
397  [1.02748625310, 162.00000114211, 142.62263196464],
398  [1.09544517063, 89.99999999999, 153.43495002171],
399  [1.00891553207, 109.96462504973, 64.82873988729],
400  [1.02748629119, 168.64536825352, 72.33019567813],
401  [1.09544515646, 139.61382144892, 43.64692674940],
402  [1.02748634634, 65.81858639072, 119.41445092243],
403  [1.00891556736, 179.99999802856, 126.00000226595],
404  [1.02748635602, 89.99999960836, 52.62263315940],
405  [1.00891555440, 179.99999707004, 90.00000124425],
406  [1.00891557622, 59.55361387162, 99.34970169408],
407  [1.00891556008, 179.99999706617, 161.99999705108],
408  [1.02748626742, -168.64537472596, 107.66980683355],
409  [1.09544512695, -139.61381905073, 136.35307291839],
410  [1.00891557314, 70.03536778427, 64.82874116074],
411  [1.00891558469, 179.99999869430, 53.99999978842],
412  [1.09544512397, -152.26770006971, 73.95494188062],
413  [1.00891553067, 46.43699819052, 133.48707816006],
414  [1.02748629097, 53.99999798965, 79.18768316812],
415  [1.09544512397, 27.73229993028, 106.04505811936],
416  [1.02748628164, -90.00000605311, 169.18768076305],
417  [1.00891555976, 89.99999733187, 31.71747261228],
418  [1.09544512695, 40.38618094925, 43.64692708160],
419  [1.02748627054, -162.00000090189, 37.37736920747],
420  [1.02748627054, 17.99999909809, 142.62263079252],
421  [1.00891571917, -0.00001399184, 161.99999760451],
422  [1.00891555675, -146.98259977856, 105.24016093031],
423  [1.02748628164, 89.99999394687, 10.81231923693],
424  [1.00891571917, 179.99998600815, 18.00000239548],
425  [1.00891555675, 33.01740022143, 74.75983906968],
426  [1.00891555976, -90.00000266812, 148.28252738771],
427  [1.09544515646, -40.38617855106, 136.35307325059],
428  [1.02748629097, -126.00000201034, 100.81231683187],
429  [1.00891553067, -133.56300180947, 46.51292183993],
430  [1.09544517063, -89.99999999999, 26.56504997828],
431  [1.00891558469, -0.00000130569, 126.00000021157],
432  [1.02748626742, 11.35462527402, 72.33019316644],
433  [1.02748635602, -90.00000039163, 127.37736684059],
434  [1.00891557314, -109.96463221572, 115.17125883925],
435  [1.00891556008, -0.00000293381, 18.00000294891],
436  [1.02748634634, -114.18141360927, 60.58554907756],
437  [1.00891557622, -120.44638612836, 80.65029830591],
438  [1.02748629119, -11.35463174646, 107.66980432186],
439  [1.00891555440, -0.00000292995, 89.99999875574],
440  [1.09544514122, -89.99999999999, 89.99999999999],
441  [1.02748625310, -17.99999885788, 37.37736803535],
442  [1.00891556736, -0.00000197142, 53.99999773404],
443  [1.09544512781, -27.73230199903, 73.95494308754],
444  [1.00891553207, -70.03537495026, 115.17126011270],
445  [1.00891560357, -90.00000101319, 58.28252501092],
446  [1.00891552109, -33.01739949716, 105.24016169807],
447  [1.02748626651, -54.00000119877, 100.81231538870],
448  [1.00891557700, -46.43700050541, 46.51292262059],
449  [1.02748631414, -65.81858661456, 60.58554645336],
450  [1.00891556968, -59.55361391898, 80.65029560825]
451  ],
452  [
453  [1,0,2],
454  [0,3,2],
455  [1,4,0],
456  [2,5,1],
457  [4,3,0],
458  [6,2,3],
459  [7,4,1],
460  [8,5,2],
461  [9,1,5],
462  [4,10,3],
463  [6,11,2],
464  [3,12,6],
465  [7,13,4],
466  [1,9,7],
467  [8,9,5],
468  [2,14,8],
469  [15,10,4],
470  [12,3,10],
471  [12,11,6],
472  [16,2,11],
473  [9,13,7],
474  [17,4,13],
475  [18,9,8],
476  [19,14,2],
477  [20,8,14],
478  [15,12,10],
479  [4,21,15],
480  [12,22,11],
481  [16,19,2],
482  [11,23,16],
483  [9,24,13],
484  [17,25,4],
485  [13,26,17],
486  [18,27,9],
487  [8,20,18],
488  [19,20,14],
489  [28,12,15],
490  [25,21,4],
491  [29,15,21],
492  [30,22,12],
493  [23,11,22],
494  [23,19,16],
495  [31,24,9],
496  [26,13,24],
497  [26,25,17],
498  [20,27,18],
499  [32,9,27],
500  [33,20,19],
501  [28,34,12],
502  [15,29,28],
503  [25,29,21],
504  [30,23,22],
505  [12,35,30],
506  [23,33,19],
507  [31,26,24],
508  [9,32,31],
509  [26,36,25],
510  [20,37,27],
511  [27,38,32],
512  [33,39,20],
513  [29,34,28],
514  [35,12,34],
515  [36,29,25],
516  [40,23,30],
517  [41,30,35],
518  [39,33,23],
519  [42,26,31],
520  [38,31,32],
521  [43,36,26],
522  [44,37,20],
523  [38,27,37],
524  [45,20,39],
525  [29,46,34],
526  [34,41,35],
527  [36,43,29],
528  [40,47,23],
529  [30,41,40],
530  [23,48,39],
531  [42,49,26],
532  [31,38,42],
533  [26,50,43],
534  [44,38,37],
535  [20,45,44],
536  [39,51,45],
537  [52,46,29],
538  [41,34,46],
539  [53,29,43],
540  [41,47,40],
541  [48,23,47],
542  [51,39,48],
543  [38,49,42],
544  [50,26,49],
545  [54,43,50],
546  [55,38,44],
547  [51,44,45],
548  [52,41,46],
549  [29,53,52],
550  [43,54,53],
551  [41,56,47],
552  [47,51,48],
553  [38,57,49],
554  [49,54,50],
555  [55,58,38],
556  [44,51,55],
557  [59,41,52],
558  [54,52,53],
559  [60,56,41],
560  [51,47,56],
561  [58,57,38],
562  [54,49,57],
563  [51,58,55],
564  [59,60,41],
565  [52,54,59],
566  [60,51,56],
567  [58,54,57],
568  [51,61,58],
569  [54,60,59],
570  [61,51,60],
571  [61,54,58],
572  [54,61,60]
573  ],
574  [
575  [0,1],
576  [0,2],
577  [0,3],
578  [0,4],
579  [1,2],
580  [1,4],
581  [1,5],
582  [1,7],
583  [1,9],
584  [2,3],
585  [2,5],
586  [2,6],
587  [2,8],
588  [2,11],
589  [2,14],
590  [2,16],
591  [2,19],
592  [3,4],
593  [3,6],
594  [3,10],
595  [3,12],
596  [4,7],
597  [4,10],
598  [4,13],
599  [4,15],
600  [4,17],
601  [4,21],
602  [4,25],
603  [5,8],
604  [5,9],
605  [6,11],
606  [6,12],
607  [7,9],
608  [7,13],
609  [8,9],
610  [8,14],
611  [8,18],
612  [8,20],
613  [9,13],
614  [9,18],
615  [9,24],
616  [9,27],
617  [9,31],
618  [9,32],
619  [10,12],
620  [10,15],
621  [11,12],
622  [11,16],
623  [11,22],
624  [11,23],
625  [12,15],
626  [12,22],
627  [12,28],
628  [12,30],
629  [12,34],
630  [12,35],
631  [13,17],
632  [13,24],
633  [13,26],
634  [14,19],
635  [14,20],
636  [15,21],
637  [15,28],
638  [15,29],
639  [16,19],
640  [16,23],
641  [17,25],
642  [17,26],
643  [18,20],
644  [18,27],
645  [19,20],
646  [19,23],
647  [19,33],
648  [20,27],
649  [20,33],
650  [20,37],
651  [20,39],
652  [20,44],
653  [20,45],
654  [21,25],
655  [21,29],
656  [22,23],
657  [22,30],
658  [23,30],
659  [23,33],
660  [23,39],
661  [23,40],
662  [23,47],
663  [23,48],
664  [24,26],
665  [24,31],
666  [25,26],
667  [25,29],
668  [25,36],
669  [26,31],
670  [26,36],
671  [26,42],
672  [26,43],
673  [26,49],
674  [26,50],
675  [27,32],
676  [27,37],
677  [27,38],
678  [28,29],
679  [28,34],
680  [29,34],
681  [29,36],
682  [29,43],
683  [29,46],
684  [29,52],
685  [29,53],
686  [30,35],
687  [30,40],
688  [30,41],
689  [31,32],
690  [31,38],
691  [31,42],
692  [32,38],
693  [33,39],
694  [34,35],
695  [34,41],
696  [34,46],
697  [35,41],
698  [36,43],
699  [37,38],
700  [37,44],
701  [38,42],
702  [38,44],
703  [38,49],
704  [38,55],
705  [38,57],
706  [38,58],
707  [39,45],
708  [39,48],
709  [39,51],
710  [40,41],
711  [40,47],
712  [41,46],
713  [41,47],
714  [41,52],
715  [41,56],
716  [41,59],
717  [41,60],
718  [42,49],
719  [43,50],
720  [43,53],
721  [43,54],
722  [44,45],
723  [44,51],
724  [44,55],
725  [45,51],
726  [46,52],
727  [47,48],
728  [47,51],
729  [47,56],
730  [48,51],
731  [49,50],
732  [49,54],
733  [49,57],
734  [50,54],
735  [51,55],
736  [51,56],
737  [51,58],
738  [51,60],
739  [51,61],
740  [52,53],
741  [52,54],
742  [52,59],
743  [53,54],
744  [54,57],
745  [54,58],
746  [54,59],
747  [54,60],
748  [54,61],
749  [55,58],
750  [56,60],
751  [57,58],
752  [58,61],
753  [59,60],
754  [60,61]
755  ]
756  ],
757  [
758  "kite_hexecontahedron",
759  "Kite Hexecontahedron",
760  empty_str,
761  "archimedean_duals",
762  "George W. Hart, 1997. george@li.net",
763  [
764  [ 0.31751071895, 0.00000000340, 0.97719758819],
765  [ 0.00000001127, 0.18926497122, 0.99100426972],
766  [-0.31751074542, -0.00000003162, 0.97719756131],
767  [ 0.00000000000, -0.47140450895, 0.94280907941],
768  [ 0.51374312445, -0.54018153041, 0.70710681970],
769  [ 0.58249766001, -0.18926493753, 0.80173929639],
770  [ 0.55416926303, 0.47140450330, 0.76274852191],
771  [-0.00000005975, 0.54018152913, 0.87403204499],
772  [-0.55416932145, 0.47140454384, 0.76274848242],
773  [-0.58249771487, -0.18926492629, 0.80173925260],
774  [-0.51374316338, -0.54018151801, 0.70710678126],
775  [ 0.83125389314, -0.00000002527, 0.60394129932],
776  [ 0.89666469792, -0.47140454470, 0.29134409404],
777  [-0.00000004010, -0.87403202745, 0.54018149056],
778  [ 0.36000332522, -0.80173921652, 0.49550210795],
779  [ 0.31751075905, 0.87403203813, 0.43701599790],
780  [-0.00000006329, 0.80173927623, 0.61247427683],
781  [-0.83125394207, 0.00000000773, 0.60394123806],
782  [-0.31751078833, 0.87403205872, 0.43701597508],
783  [-0.36000339413, -0.80173930908, 0.49550207363],
784  [-0.89666468978, -0.47140453296, 0.29134402622],
785  [ 0.94250097679, 0.18926497873, 0.30623723192],
786  [ 0.83125388233, 0.54018152140, 0.27009080693],
787  [ 0.51374313409, -0.87403206340, 0.16692530143],
788  [ 1.02748628783, -0.00000001240, 0.00000003844],
789  [ 0.00000000000, -1.05409255675, 0.00000000000],
790  [ 0.58249766471, 0.80173926315, 0.18926500599],
791  [ 0.00000000000, 1.05409255675, 0.00000000000],
792  [-0.83125378687, 0.54018144318, 0.27009073756],
793  [-0.94250106167, 0.18926498020, 0.30623715984],
794  [-0.58249771017, 0.80173927439, 0.18926496219],
795  [-0.51374315374, -0.87403205100, 0.16692526298],
796  [-1.02748628783, 0.00000001240, -0.00000003844],
797  [ 0.89666468978, 0.47140453296, -0.29134402622],
798  [ 0.58249771017, -0.80173927439, -0.18926496219],
799  [ 0.83125378687, -0.54018144318, -0.27009073756],
800  [ 0.94250106167, -0.18926498020, -0.30623715984],
801  [ 0.31751078833, -0.87403205872, -0.43701597508],
802  [ 0.51374315374, 0.87403205100, -0.16692526298],
803  [-0.51374313409, 0.87403206340, -0.16692530143],
804  [-0.89666469792, 0.47140454470, -0.29134409404],
805  [-0.83125388233, -0.54018152140, -0.27009080693],
806  [-0.58249766471, -0.80173926315, -0.18926500599],
807  [-0.31751075905, -0.87403203813, -0.43701599790],
808  [-0.94250097679, -0.18926497873, -0.30623723192],
809  [ 0.83125394207, -0.00000000773, -0.60394123806],
810  [ 0.55416932145, -0.47140454384, -0.76274848242],
811  [ 0.00000006329, -0.80173927623, -0.61247427683],
812  [ 0.36000339413, 0.80173930908, -0.49550207363],
813  [ 0.00000004010, 0.87403202745, -0.54018149056],
814  [ 0.51374316338, 0.54018151801, -0.70710678126],
815  [-0.36000332522, 0.80173921652, -0.49550210795],
816  [-0.83125389314, 0.00000002527, -0.60394129932],
817  [-0.51374312445, 0.54018153041, -0.70710681970],
818  [-0.55416926303, -0.47140450330, -0.76274852191],
819  [ 0.58249771487, 0.18926492629, -0.80173925260],
820  [ 0.00000005975, -0.54018152913, -0.87403204499],
821  [ 0.31751074542, 0.00000003162, -0.97719756131],
822  [ 0.00000000000, 0.47140450895, -0.94280907941],
823  [-0.58249766001, 0.18926493753, -0.80173929639],
824  [-0.31751071895, -0.00000000340, -0.97719758819],
825  [-0.00000001127, -0.18926497122, -0.99100426972]
826  ],
827  [
828  [1.02748634200, 0.00000061320, 17.99999869722],
829  [1.00891560199, 89.99999658970, 10.81231680724],
830  [1.02748632463, -179.99999429390, 18.00000056439],
831  [1.05409258193, -89.99999999999, 26.56504968170],
832  [1.02748632019, -46.43700162957, 46.51292053460],
833  [1.00891557619, -17.99999775680, 37.37736611922],
834  [1.05409254124, 40.38617586423, 43.64692761206],
835  [1.02748630166, 90.00000633706, 31.71747526862],
836  [1.05409256151, 139.61382468489, 43.64693187669],
837  [1.00891557095, -162.00000482901, 37.37736982663],
838  [1.02748630668, -133.56300119541, 46.51292277440],
839  [1.02748631518, -0.00000174191, 54.00000025335],
840  [1.05409259858, -27.73230224166, 73.95493917425],
841  [1.02748626646, -90.00000262866, 58.28252604708],
842  [1.00891550908, -65.81858650511, 60.58554777641],
843  [1.02748628614, 70.03536918416, 64.82873918611],
844  [1.00891555981, 90.00000452307, 52.62263321232],
845  [1.02748631876, 179.99999946728, 54.00000462068],
846  [1.02748630300, 109.96463207855, 64.82874103382],
847  [1.00891559036, -114.18141512172, 60.58555261657],
848  [1.05409256766, -152.26769813128, 73.95494252661],
849  [1.00891553940, 11.35462944224, 72.33018751495],
850  [1.02748631959, 33.01739826504, 74.75983516356],
851  [1.02748630742, -59.55361679393, 80.65029465008],
852  [1.02748628783, -0.00000069174, 89.99999785636],
853  [1.05409255675, -89.99999999999, 89.99999999999],
854  [1.00891556533, 54.00000029669, 79.18768078490],
855  [1.05409255675, 89.99999999999, 89.99999999999],
856  [1.02748618300, 146.98260251978, 74.75983709775],
857  [1.00891559709, 168.64537146750, 72.33019285450],
858  [1.00891559229, 126.00000144763, 79.18768360925],
859  [1.02748630045, -120.44638451846, 80.65029675853],
860  [1.02748628783, 179.99999930825, 90.00000214363],
861  [1.05409256766, 27.73230186871, 106.04505747338],
862  [1.00891559229, -53.99999855235, 100.81231639074],
863  [1.02748618300, -33.01739748021, 105.24016290224],
864  [1.00891559709, -11.35462853249, 107.66980714549],
865  [1.02748630300, -70.03536792144, 115.17125896617],
866  [1.02748630045, 59.55361548153, 99.34970324145],
867  [1.02748630742, 120.44638320606, 99.34970534991],
868  [1.05409259858, 152.26769775832, 106.04506082573],
869  [1.02748631959, -146.98260173495, 105.24016483643],
870  [1.00891556533, -125.99999970329, 100.81231921509],
871  [1.02748628614, -109.96463081583, 115.17126081388],
872  [1.00891553940, -168.64537055775, 107.66981248504],
873  [1.02748631876, -0.00000053271, 125.99999537931],
874  [1.05409256151, -40.38617531509, 136.35306812330],
875  [1.00891555981, -89.99999547692, 127.37736678767],
876  [1.00891559036, 65.81858487826, 119.41444738341],
877  [1.02748626646, 89.99999737133, 121.71747395291],
878  [1.02748630668, 46.43699880458, 133.48707722559],
879  [1.00891550908, 114.18141349487, 119.41445222357],
880  [1.02748631518, 179.99999825808, 125.99999974664],
881  [1.02748632019, 133.56299837042, 133.48707946539],
882  [1.05409254124, -139.61382413575, 136.35307238793],
883  [1.00891557095, 17.99999517097, 142.62263017336],
884  [1.02748630166, -89.99999366293, 148.28252473137],
885  [1.02748632463, 0.00000570609, 161.99999943560],
886  [1.05409258193, 89.99999999999, 153.43495031828],
887  [1.00891557619, 162.00000224318, 142.62263388077],
888  [1.02748634200, -179.99999938679, 162.00000130277],
889  [1.00891560199, -90.00000341028, 169.18768319275]
890  ],
891  [
892  [2,1,0,3],
893  [0,5,4,3],
894  [1,7,6,0],
895  [2,8,7,1],
896  [3,10,9,2],
897  [6,11,5,0],
898  [11,12,4,5],
899  [14,13,3,4],
900  [16,15,6,7],
901  [9,17,8,2],
902  [18,16,7,8],
903  [13,19,10,3],
904  [20,17,9,10],
905  [6,22,21,11],
906  [12,23,14,4],
907  [11,21,24,12],
908  [14,23,25,13],
909  [15,26,22,6],
910  [16,18,27,15],
911  [17,29,28,8],
912  [8,28,30,18],
913  [19,31,20,10],
914  [13,25,31,19],
915  [20,32,29,17],
916  [33,24,21,22],
917  [35,34,23,12],
918  [36,35,12,24],
919  [34,37,25,23],
920  [27,38,26,15],
921  [38,33,22,26],
922  [30,39,27,18],
923  [32,40,28,29],
924  [40,39,30,28],
925  [42,41,20,31],
926  [43,42,31,25],
927  [41,44,32,20],
928  [33,45,36,24],
929  [35,46,37,34],
930  [36,45,46,35],
931  [37,47,43,25],
932  [27,49,48,38],
933  [38,48,50,33],
934  [39,51,49,27],
935  [32,44,52,40],
936  [40,53,51,39],
937  [42,43,54,41],
938  [41,54,52,44],
939  [50,55,45,33],
940  [56,47,37,46],
941  [55,57,46,45],
942  [56,54,43,47],
943  [58,50,48,49],
944  [53,58,49,51],
945  [59,53,40,52],
946  [60,59,52,54],
947  [50,58,57,55],
948  [46,57,61,56],
949  [56,61,60,54],
950  [53,59,60,58],
951  [60,61,57,58]
952  ],
953  [
954  [0,1],
955  [0,3],
956  [0,5],
957  [0,6],
958  [1,2],
959  [1,7],
960  [2,3],
961  [2,8],
962  [2,9],
963  [3,4],
964  [3,10],
965  [3,13],
966  [4,5],
967  [4,12],
968  [4,14],
969  [5,11],
970  [6,7],
971  [6,11],
972  [6,15],
973  [6,22],
974  [7,8],
975  [7,16],
976  [8,17],
977  [8,18],
978  [8,28],
979  [9,10],
980  [9,17],
981  [10,19],
982  [10,20],
983  [11,12],
984  [11,21],
985  [12,23],
986  [12,24],
987  [12,35],
988  [13,14],
989  [13,19],
990  [13,25],
991  [14,23],
992  [15,16],
993  [15,26],
994  [15,27],
995  [16,18],
996  [17,20],
997  [17,29],
998  [18,27],
999  [18,30],
1000  [19,31],
1001  [20,31],
1002  [20,32],
1003  [20,41],
1004  [21,22],
1005  [21,24],
1006  [22,26],
1007  [22,33],
1008  [23,25],
1009  [23,34],
1010  [24,33],
1011  [24,36],
1012  [25,31],
1013  [25,37],
1014  [25,43],
1015  [26,38],
1016  [27,38],
1017  [27,39],
1018  [27,49],
1019  [28,29],
1020  [28,30],
1021  [28,40],
1022  [29,32],
1023  [30,39],
1024  [31,42],
1025  [32,40],
1026  [32,44],
1027  [33,38],
1028  [33,45],
1029  [33,50],
1030  [34,35],
1031  [34,37],
1032  [35,36],
1033  [35,46],
1034  [36,45],
1035  [37,46],
1036  [37,47],
1037  [38,48],
1038  [39,40],
1039  [39,51],
1040  [40,52],
1041  [40,53],
1042  [41,42],
1043  [41,44],
1044  [41,54],
1045  [42,43],
1046  [43,47],
1047  [43,54],
1048  [44,52],
1049  [45,46],
1050  [45,55],
1051  [46,56],
1052  [46,57],
1053  [47,56],
1054  [48,49],
1055  [48,50],
1056  [49,51],
1057  [49,58],
1058  [50,55],
1059  [50,58],
1060  [51,53],
1061  [52,54],
1062  [52,59],
1063  [53,58],
1064  [53,59],
1065  [54,56],
1066  [54,60],
1067  [55,57],
1068  [56,61],
1069  [57,58],
1070  [57,61],
1071  [58,60],
1072  [59,60],
1073  [60,61]
1074  ]
1075  ],
1076  [
1077  "kite_icositetrahedron",
1078  "Kite Icositetrahedron",
1079  empty_str,
1080  "archimedean_duals",
1081  "Exact Mathematics",
1082  [
1083  [ 0.00000000000, 0.70710678119, 0.70710678119],
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1099  [-0.70710678119, -0.70710678119, 0.00000000000],
1100  [-0.70710678119, 0.00000000000, -0.70710678119],
1101  [ 0.00000000000, -1.00000000000, 0.00000000000],
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1103  [ 0.70710678119, -0.70710678119, 0.00000000000],
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1105  [ 0.00000000000, 0.00000000000, -1.00000000000],
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1109  ],
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1120  [0.94729004188, -134.99999999999, 54.73561031724],
1121  [1.00000000000, -89.99999999999, 45.00000000000],
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1123  [1.00000000000, 0.00000000000, 89.99999999999],
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1125  [1.00000000000, 89.99999999999, 134.99999999999],
1126  [0.94729004188, 134.99999999999, 125.26438968275],
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1128  [1.00000000000, 179.99999999999, 134.99999999999],
1129  [1.00000000000, -89.99999999999, 89.99999999999],
1130  [0.94729004188, 45.00000000000, 125.26438968275],
1131  [1.00000000000, -45.00000000000, 89.99999999999],
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1135  [1.00000000000, -89.99999999999, 134.99999999999],
1136  [0.94729004188, -45.00000000000, 125.26438968275]
1137  ],
1138  [
1139  [2,1,0,3],
1140  [0,5,4,3],
1141  [1,7,6,0],
1142  [2,8,7,1],
1143  [3,10,9,2],
1144  [6,11,5,0],
1145  [11,12,4,5],
1146  [13,10,3,4],
1147  [15,14,6,7],
1148  [9,16,8,2],
1149  [17,15,7,8],
1150  [18,16,9,10],
1151  [6,14,19,11],
1152  [12,20,13,4],
1153  [11,19,21,12],
1154  [13,20,18,10],
1155  [15,17,22,14],
1156  [16,23,17,8],
1157  [18,24,23,16],
1158  [22,21,19,14],
1159  [21,25,20,12],
1160  [25,24,18,20],
1161  [23,24,22,17],
1162  [22,24,25,21]
1163  ],
1164  [
1165  [0,1],
1166  [0,3],
1167  [0,5],
1168  [0,6],
1169  [1,2],
1170  [1,7],
1171  [2,3],
1172  [2,8],
1173  [2,9],
1174  [3,4],
1175  [3,10],
1176  [4,5],
1177  [4,12],
1178  [4,13],
1179  [5,11],
1180  [6,7],
1181  [6,11],
1182  [6,14],
1183  [7,8],
1184  [7,15],
1185  [8,16],
1186  [8,17],
1187  [9,10],
1188  [9,16],
1189  [10,13],
1190  [10,18],
1191  [11,12],
1192  [11,19],
1193  [12,20],
1194  [12,21],
1195  [13,20],
1196  [14,15],
1197  [14,19],
1198  [14,22],
1199  [15,17],
1200  [16,18],
1201  [16,23],
1202  [17,22],
1203  [17,23],
1204  [18,20],
1205  [18,24],
1206  [19,21],
1207  [20,25],
1208  [21,22],
1209  [21,25],
1210  [22,24],
1211  [23,24],
1212  [24,25]
1213  ]
1214  ],
1215  [
1216  "pentagonal_hexecontahedron",
1217  "Pentagonal Hexecontahedron",
1218  empty_str,
1219  "archimedean_duals",
1220  "George W. Hart, 1997. george@li.net",
1221  [
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1425  [34,33,32,16,17],
1426  [19,35,34,17,18],
1427  [37,36,35,19,20],
1428  [22,39,38,20,21],
1429  [41,40,39,22,23],
1430  [24,42,41,23,9],
1431  [44,43,42,24,25],
1432  [27,45,44,25,26],
1433  [47,46,45,27,12],
1434  [49,48,47,12,28],
1435  [30,50,49,28,29],
1436  [32,33,51,30,31],
1437  [53,52,51,33,34],
1438  [36,55,54,34,35],
1439  [57,56,55,36,37],
1440  [38,58,57,37,20],
1441  [40,59,58,38,39],
1442  [42,43,60,40,41],
1443  [62,61,60,43,44],
1444  [46,64,63,44,45],
1445  [48,65,64,46,47],
1446  [50,66,65,48,49],
1447  [68,67,66,50,30],
1448  [52,69,68,30,51],
1449  [71,70,69,52,53],
1450  [54,72,71,53,34],
1451  [56,73,72,54,55],
1452  [58,59,74,56,57],
1453  [76,75,74,59,40],
1454  [61,77,76,40,60],
1455  [79,78,77,61,62],
1456  [63,80,79,62,44],
1457  [65,81,80,63,64],
1458  [67,83,82,65,66],
1459  [69,70,83,67,68],
1460  [72,73,84,70,71],
1461  [86,85,84,73,56],
1462  [75,87,86,56,74],
1463  [77,78,87,75,76],
1464  [80,81,88,78,79],
1465  [82,89,88,81,65],
1466  [70,90,89,82,83],
1467  [85,91,90,70,84],
1468  [87,78,91,85,86],
1469  [89,90,91,78,88]
1470  ],
1471  [
1472  [0,1],
1473  [0,4],
1474  [0,7],
1475  [1,2],
1476  [1,9],
1477  [2,3],
1478  [2,11],
1479  [3,4],
1480  [3,13],
1481  [4,5],
1482  [4,15],
1483  [4,16],
1484  [5,6],
1485  [5,18],
1486  [6,7],
1487  [6,20],
1488  [7,8],
1489  [8,9],
1490  [8,21],
1491  [9,10],
1492  [9,23],
1493  [9,24],
1494  [10,11],
1495  [10,26],
1496  [11,12],
1497  [12,13],
1498  [12,27],
1499  [12,28],
1500  [12,47],
1501  [13,14],
1502  [14,15],
1503  [14,29],
1504  [15,31],
1505  [16,17],
1506  [16,32],
1507  [17,18],
1508  [17,34],
1509  [18,19],
1510  [19,20],
1511  [19,35],
1512  [20,21],
1513  [20,37],
1514  [20,38],
1515  [21,22],
1516  [22,23],
1517  [22,39],
1518  [23,41],
1519  [24,25],
1520  [24,42],
1521  [25,26],
1522  [25,44],
1523  [26,27],
1524  [27,45],
1525  [28,29],
1526  [28,49],
1527  [29,30],
1528  [30,31],
1529  [30,50],
1530  [30,51],
1531  [30,68],
1532  [31,32],
1533  [32,33],
1534  [33,34],
1535  [33,51],
1536  [34,35],
1537  [34,53],
1538  [34,54],
1539  [35,36],
1540  [36,37],
1541  [36,55],
1542  [37,57],
1543  [38,39],
1544  [38,58],
1545  [39,40],
1546  [40,41],
1547  [40,59],
1548  [40,60],
1549  [40,76],
1550  [41,42],
1551  [42,43],
1552  [43,44],
1553  [43,60],
1554  [44,45],
1555  [44,62],
1556  [44,63],
1557  [45,46],
1558  [46,47],
1559  [46,64],
1560  [47,48],
1561  [48,49],
1562  [48,65],
1563  [49,50],
1564  [50,66],
1565  [51,52],
1566  [52,53],
1567  [52,69],
1568  [53,71],
1569  [54,55],
1570  [54,72],
1571  [55,56],
1572  [56,57],
1573  [56,73],
1574  [56,74],
1575  [56,86],
1576  [57,58],
1577  [58,59],
1578  [59,74],
1579  [60,61],
1580  [61,62],
1581  [61,77],
1582  [62,79],
1583  [63,64],
1584  [63,80],
1585  [64,65],
1586  [65,66],
1587  [65,81],
1588  [65,82],
1589  [66,67],
1590  [67,68],
1591  [67,83],
1592  [68,69],
1593  [69,70],
1594  [70,71],
1595  [70,83],
1596  [70,84],
1597  [70,90],
1598  [71,72],
1599  [72,73],
1600  [73,84],
1601  [74,75],
1602  [75,76],
1603  [75,87],
1604  [76,77],
1605  [77,78],
1606  [78,79],
1607  [78,87],
1608  [78,88],
1609  [78,91],
1610  [79,80],
1611  [80,81],
1612  [81,88],
1613  [82,83],
1614  [82,89],
1615  [84,85],
1616  [85,86],
1617  [85,91],
1618  [86,87],
1619  [88,89],
1620  [89,90],
1621  [90,91]
1622  ]
1623  ],
1624  [
1625  "pentagonal_icositetrahedron",
1626  "Pentagonal Icositetrahedron",
1627  empty_str,
1628  "archimedean_duals",
1629  "George W. Hart, 1997. george@li.net",
1630  [
1631  [ 0.16071327325, 0.75190871675, -0.54368902931],
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1633  [-0.54368897205, 0.54368899723, -0.54368904151],
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1635  [-0.00000000676, 0.99999999488, -0.00000000731],
1636  [ 0.54368897783, 0.75190869752, 0.16071325200],
1637  [ 0.75190866563, 0.54368897418, -0.16071321670],
1638  [ 0.54368897367, 0.54368900470, -0.54368899596],
1639  [ 0.54368904340, 0.16071325571, -0.75190863643],
1640  [-0.00000000676, 0.00000001660, -1.00000000000],
1641  [-0.54368896170, -0.16071326637, -0.75190870910],
1642  [-0.75190870177, 0.16071321607, -0.54368907275],
1643  [-0.99999997485, -0.00000001528, -0.00000009448],
1644  [-0.75190869930, 0.54368899910, 0.16071317983],
1645  [-0.54368900735, 0.54368896859, 0.54368895909],
1646  [-0.16071325904, 0.75190869943, 0.54368899395],
1647  [ 0.16071317676, 0.54368899531, 0.75190868442],
1648  [ 0.54368893146, 0.54368899942, 0.54368899194],
1649  [ 0.75190868600, 0.16071324303, 0.54368899377],
1650  [ 0.99999996132, 0.00000002772, 0.00000007987],
1651  [ 0.75190873045, -0.16071319835, -0.54368892976],
1652  [ 0.54368899382, -0.54368895615, -0.54368897371],
1653  [ 0.16071325221, -0.54368889737, -0.75190857341],
1654  [-0.16071325147, -0.75190867567, -0.54368898591],
1655  [-0.54368894499, -0.54368898698, -0.54368900655],
1656  [-0.75190865186, -0.54368901104, -0.16071324937],
1657  [-0.75190873482, -0.16071325923, 0.54368899222],
1658  [-0.54368899063, 0.16071324797, 0.75190866164],
1659  [-0.00000000676, -0.00000000416, 0.99999998539],
1660  [ 0.54368897421, -0.16071320457, 0.75190867837],
1661  [ 0.54368895852, -0.54368898479, 0.54368902690],
1662  [ 0.75190865849, -0.54368893736, 0.16071325700],
1663  [ 0.54368903978, -0.75190864639, -0.16071321006],
1664  [-0.00000000676, -0.99999998245, -0.00000000731],
1665  [-0.54368899324, -0.75190871736, 0.16071321914],
1666  [-0.54368898719, -0.54368899226, 0.54368898134],
1667  [-0.16071326938, -0.54368901430, 0.75190866154],
1668  [ 0.16071331941, -0.75190902099, 0.54368916366]
1669  ],
1670  [
1671  [0.94169699751, 77.93511852297, 125.26439074846],
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1673  [0.94169697775, 134.99999867304, 125.26439250807],
1674  [0.94169696351, 125.86987960572, 99.82639781431],
1675  [0.99999999488, 90.00000038747, 90.00000041864],
1676  [0.94169694881, 54.13011891836, 80.17360421411],
1677  [0.94169691521, 35.86988205269, 99.82639396007],
1678  [0.94169695669, 45.00000163481, 125.26439001937],
1679  [0.94169693852, 16.46756057926, 142.98342507151],
1680  [1.00000000000, 112.17056773351, 179.99999897318],
1681  [0.94169695119, -163.53243604711, 142.98343139242],
1682  [0.94169700087, 167.93512245650, 125.26439384143],
1683  [0.99999997485, -179.99999912453, 90.00000541347],
1684  [0.94169695019, 144.13011791868, 80.17360868494],
1685  [0.94169693400, 135.00000204233, 54.73561175152],
1686  [0.94169696083, 102.06488071124, 54.73561030871],
1687  [0.94169693560, 73.53244569490, 37.01656984339],
1688  [0.94169692696, 45.00000358086, 54.73560900079],
1689  [0.94169694728, 12.06487975387, 54.73560973856],
1690  [0.99999996132, 0.00000158816, 89.99999542382],
1691  [0.94169693819, -12.06487580597, 125.26438588242],
1692  [0.94169692745, -44.99999801492, 125.26438961939],
1693  [0.94169680330, -73.53243557609, 142.98342961421],
1694  [0.94169693593, -102.06488053029, 125.26439016391],
1695  [0.94169693602, -134.99999778726, 125.26439169819],
1696  [0.94169693107, -144.13011560493, 99.82639581021],
1697  [0.94169698813, -167.93511982564, 54.73561161174],
1698  [0.94169692686, 163.53243865866, 37.01657144033],
1699  [0.99999998539, -148.42091555625, 0.00000045483],
1700  [0.94169692333, -16.46755760552, 37.01656946502],
1701  [0.94169695432, -45.00000138421, 54.73560757295],
1702  [0.94169689513, -35.86988046874, 80.17360333945],
1703  [0.94169693658, -54.13011396871, 99.82639332499],
1704  [0.99999998245, -90.00000038747, 90.00000041864],
1705  [0.94169696793, -125.86988113486, 80.17360644450],
1706  [0.94169694888, -134.99999973330, 54.73561073359],
1707  [0.94169694410, -106.46756273772, 37.01657284190],
1708  [0.94169732588, -77.93511989808, 54.73561336722]
1709  ],
1710  [
1711  [3,2,1,0,4],
1712  [7,6,5,4,0],
1713  [9,8,7,0,1],
1714  [11,10,9,1,2],
1715  [13,12,11,2,3],
1716  [15,14,13,3,4],
1717  [17,16,15,4,5],
1718  [19,18,17,5,6],
1719  [8,20,19,6,7],
1720  [22,21,20,8,9],
1721  [24,23,22,9,10],
1722  [12,25,24,10,11],
1723  [14,27,26,12,13],
1724  [16,28,27,14,15],
1725  [18,29,28,16,17],
1726  [31,30,29,18,19],
1727  [21,32,31,19,20],
1728  [23,33,32,21,22],
1729  [25,34,33,23,24],
1730  [26,35,34,25,12],
1731  [28,36,35,26,27],
1732  [30,37,36,28,29],
1733  [32,33,37,30,31],
1734  [35,36,37,33,34]
1735  ],
1736  [
1737  [0,1],
1738  [0,4],
1739  [0,7],
1740  [1,2],
1741  [1,9],
1742  [2,3],
1743  [2,11],
1744  [3,4],
1745  [3,13],
1746  [4,5],
1747  [4,15],
1748  [5,6],
1749  [5,17],
1750  [6,7],
1751  [6,19],
1752  [7,8],
1753  [8,9],
1754  [8,20],
1755  [9,10],
1756  [9,22],
1757  [10,11],
1758  [10,24],
1759  [11,12],
1760  [12,13],
1761  [12,25],
1762  [12,26],
1763  [13,14],
1764  [14,15],
1765  [14,27],
1766  [15,16],
1767  [16,17],
1768  [16,28],
1769  [17,18],
1770  [18,19],
1771  [18,29],
1772  [19,20],
1773  [19,31],
1774  [20,21],
1775  [21,22],
1776  [21,32],
1777  [22,23],
1778  [23,24],
1779  [23,33],
1780  [24,25],
1781  [25,34],
1782  [26,27],
1783  [26,35],
1784  [27,28],
1785  [28,29],
1786  [28,36],
1787  [29,30],
1788  [30,31],
1789  [30,37],
1790  [31,32],
1791  [32,33],
1792  [33,34],
1793  [33,37],
1794  [34,35],
1795  [35,36],
1796  [36,37]
1797  ]
1798  ],
1799  [
1800  "pentakis_dodecahedron",
1801  "Pentakis-dodecahedron",
1802  empty_str,
1803  "archimedean_duals",
1804  "George W. Hart, 1997. george@li.net",
1805  [
1806  [ 0.20177410000, 0.38196600000, 0.97943210000],
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1810  [-0.40354820000, 0.59137200000, 0.75819400000],
1811  [-0.23959370000, -0.74535600000, 0.73002560000],
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1814  [-0.92198690000, 0.25464400000, 0.48061910000],
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1816  [-0.79506710000, -0.40862800000, 0.53695600000],
1817  [ 1.03687700000, 0.25464400000, 0.07707085000],
1818  [ 0.94255910000, -0.40862800000, 0.17898530000],
1819  [-0.59550950000, 0.87267800000, 0.17233570000],
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1825  [-1.03687700000, -0.25464400000, -0.07707085000],
1826  [-0.03687301000, 1.02666200000, -0.17898530000],
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1830  [-0.09901297000, -0.95136730000, -0.48061910000],
1831  [-0.67036380000, -0.59137200000, -0.53695600000],
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1836  [-0.20177410000, 0.29568600000, -0.97943210000],
1837  [-0.20177410000, -0.38196600000, -0.97943210000]
1838  ],
1839  [
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1853  [1.07046627680, 124.30936019929, 80.73556362919],
1854  [1.04279922263, -87.94308140001, 80.11685648337],
1855  [1.07046625302, -125.17932391740, 85.87127725489],
1856  [1.07046625302, 54.82067608259, 94.12872274510],
1857  [1.07046627680, -55.69063980069, 99.26443637080],
1858  [1.04279923139, 156.56180302349, 99.88314343278],
1859  [1.07046597133, -166.20195003836, 94.12872383343],
1860  [1.04279922263, 92.05691859998, 99.88314351662],
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1863  [1.07046627104, 124.30935821663, 122.54588223054],
1864  [1.07046626618, -95.94163260899, 116.67832985751],
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1866  [1.07046629301, 72.18006700556, 132.99775645657],
1867  [1.04279918189, -55.69064040323, 136.64180100015],
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1869  [1.07046628436, 6.46404091078, 156.19981749726],
1870  [1.04279923117, 124.30935959676, 159.92324915321],
1871  [1.07046627742, -117.84531974084, 156.19981833953]
1872  ],
1873  [
1874  [1,0,2],
1875  [0,3,2],
1876  [1,4,0],
1877  [2,5,1],
1878  [6,3,0],
1879  [7,2,3],
1880  [8,4,1],
1881  [9,0,4],
1882  [7,5,2],
1883  [10,1,5],
1884  [6,11,3],
1885  [0,9,6],
1886  [3,12,7],
1887  [8,13,4],
1888  [1,10,8],
1889  [4,13,9],
1890  [7,14,5],
1891  [5,15,10],
1892  [16,11,6],
1893  [12,3,11],
1894  [16,6,9],
1895  [17,7,12],
1896  [18,13,8],
1897  [19,8,10],
1898  [20,9,13],
1899  [17,14,7],
1900  [15,5,14],
1901  [19,10,15],
1902  [16,21,11],
1903  [11,22,12],
1904  [9,20,16],
1905  [12,22,17],
1906  [18,23,13],
1907  [8,19,18],
1908  [13,23,20],
1909  [17,24,14],
1910  [14,24,15],
1911  [15,25,19],
1912  [26,21,16],
1913  [22,11,21],
1914  [26,16,20],
1915  [27,17,22],
1916  [28,23,18],
1917  [28,18,19],
1918  [26,20,23],
1919  [27,24,17],
1920  [25,15,24],
1921  [28,19,25],
1922  [26,29,21],
1923  [21,29,22],
1924  [22,29,27],
1925  [28,30,23],
1926  [23,30,26],
1927  [27,31,24],
1928  [24,31,25],
1929  [25,31,28],
1930  [30,29,26],
1931  [31,27,29],
1932  [31,30,28],
1933  [30,31,29]
1934  ],
1935  [
1936  [0,1],
1937  [0,2],
1938  [0,3],
1939  [0,4],
1940  [0,6],
1941  [0,9],
1942  [1,2],
1943  [1,4],
1944  [1,5],
1945  [1,8],
1946  [1,10],
1947  [2,3],
1948  [2,5],
1949  [2,7],
1950  [3,6],
1951  [3,7],
1952  [3,11],
1953  [3,12],
1954  [4,8],
1955  [4,9],
1956  [4,13],
1957  [5,7],
1958  [5,10],
1959  [5,14],
1960  [5,15],
1961  [6,9],
1962  [6,11],
1963  [6,16],
1964  [7,12],
1965  [7,14],
1966  [7,17],
1967  [8,10],
1968  [8,13],
1969  [8,18],
1970  [8,19],
1971  [9,13],
1972  [9,16],
1973  [9,20],
1974  [10,15],
1975  [10,19],
1976  [11,12],
1977  [11,16],
1978  [11,21],
1979  [11,22],
1980  [12,17],
1981  [12,22],
1982  [13,18],
1983  [13,20],
1984  [13,23],
1985  [14,15],
1986  [14,17],
1987  [14,24],
1988  [15,19],
1989  [15,24],
1990  [15,25],
1991  [16,20],
1992  [16,21],
1993  [16,26],
1994  [17,22],
1995  [17,24],
1996  [17,27],
1997  [18,19],
1998  [18,23],
1999  [18,28],
2000  [19,25],
2001  [19,28],
2002  [20,23],
2003  [20,26],
2004  [21,22],
2005  [21,26],
2006  [21,29],
2007  [22,27],
2008  [22,29],
2009  [23,26],
2010  [23,28],
2011  [23,30],
2012  [24,25],
2013  [24,27],
2014  [24,31],
2015  [25,28],
2016  [25,31],
2017  [26,29],
2018  [26,30],
2019  [27,29],
2020  [27,31],
2021  [28,30],
2022  [28,31],
2023  [29,30],
2024  [29,31],
2025  [30,31]
2026  ]
2027  ],
2028  [
2029  "rhombic_dodecahedron",
2030  "Rhombic Dodecahedron",
2031  empty_str,
2032  "archimedean_duals",
2033  "Exact Mathematics",
2034  [
2035  [ 0.00000000000, 0.00000000000, 1.00000000000],
2036  [ 0.50000000000, 0.50000000000, 0.50000000000],
2037  [-0.50000000000, 0.50000000000, 0.50000000000],
2038  [-0.50000000000, -0.50000000000, 0.50000000000],
2039  [ 0.50000000000, -0.50000000000, 0.50000000000],
2040  [ 1.00000000000, 0.00000000000, 0.00000000000],
2041  [ 0.00000000000, 1.00000000000, 0.00000000000],
2042  [-1.00000000000, 0.00000000000, 0.00000000000],
2043  [ 0.00000000000, -1.00000000000, 0.00000000000],
2044  [ 0.50000000000, 0.50000000000, -0.50000000000],
2045  [-0.50000000000, 0.50000000000, -0.50000000000],
2046  [-0.50000000000, -0.50000000000, -0.50000000000],
2047  [ 0.50000000000, -0.50000000000, -0.50000000000],
2048  [ 0.00000000000, 0.00000000000, -1.00000000000]
2049  ],
2050  [
2051  [1.00000000000, 0.00000000000, 0.00000000000],
2052  [0.86602540378, 45.00000000000, 54.73561031724],
2053  [0.86602540378, 134.99999999999, 54.73561031724],
2054  [0.86602540378, -134.99999999999, 54.73561031724],
2055  [0.86602540378, -45.00000000000, 54.73561031724],
2056  [1.00000000000, 0.00000000000, 89.99999999999],
2057  [1.00000000000, 89.99999999999, 89.99999999999],
2058  [1.00000000000, 179.99999999999, 89.99999999999],
2059  [1.00000000000, -89.99999999999, 89.99999999999],
2060  [0.86602540378, 45.00000000000, 125.26438968275],
2061  [0.86602540378, 134.99999999999, 125.26438968275],
2062  [0.86602540378, -134.99999999999, 125.26438968275],
2063  [0.86602540378, -45.00000000000, 125.26438968275],
2064  [1.00000000000, 0.00000000000, 179.99999999999]
2065  ],
2066  [
2067  [1,5,4,0],
2068  [2,6,1,0],
2069  [3,7,2,0],
2070  [4,8,3,0],
2071  [6,9,5,1],
2072  [7,10,6,2],
2073  [8,11,7,3],
2074  [5,12,8,4],
2075  [9,13,12,5],
2076  [10,13,9,6],
2077  [11,13,10,7],
2078  [12,13,11,8]
2079  ],
2080  [
2081  [0,1],
2082  [0,2],
2083  [0,3],
2084  [0,4],
2085  [1,5],
2086  [2,6],
2087  [3,7],
2088  [4,8],
2089  [1,6],
2090  [2,7],
2091  [3,8],
2092  [4,5],
2093  [5,9],
2094  [6,10],
2095  [7,11],
2096  [8,12],
2097  [5,12],
2098  [6,9],
2099  [7,10],
2100  [8,11],
2101  [13,9],
2102  [13,10],
2103  [13,11],
2104  [13,12]
2105  ]
2106  ],
2107  [
2108  "rhombic_triacontahedron",
2109  "Rhombic Triacontahedron",
2110  empty_str,
2111  "archimedean_duals",
2112  "George W. Hart, 1997. george@li.net",
2113  [
2114  [ 0.00000000000, 1.01807390634, 0.00000000000],
2115  [ 0.00000000000, 0.88845068543, 0.67871595830],
2116  [ 0.58778524700, 0.75882747687, 0.33935798580],
2117  [ 0.58778524700, 0.88845069778, -0.33935797250],
2118  [ 0.00000000920, 0.75882755207, -0.67871593299],
2119  [-0.58778523780, 0.88845076062, -0.33935796050],
2120  [-0.58778523780, 0.75882753971, 0.33935799780],
2121  [ 0.36327128724, 0.33935800536, 0.88845072319],
2122  [ 0.95105653425, 0.20973479681, 0.54909275069],
2123  [ 0.95105653425, 0.33935801772, -0.12962320761],
2124  [-0.00000000000, 0.20973477335, -1.09818546924],
2125  [-0.58778524700, 0.33935798191, -0.75882749674],
2126  [ 0.58778526871, 0.33935801248, -0.75882749090],
2127  [-0.95105652505, 0.20973476100, 0.54909274385],
2128  [-0.36327125634, 0.33935800013, 0.88845072219],
2129  [-0.95105652505, 0.33935798191, -0.12962321445],
2130  [ 0.00000000000, -0.20973477335, 1.09818546924],
2131  [ 0.58778524700, -0.33935798191, 0.75882749674],
2132  [ 0.95105652505, -0.20973476100, -0.54909274385],
2133  [ 0.95105652505, -0.33935798191, 0.12962321445],
2134  [-0.36327128724, -0.33935800536, -0.88845072319],
2135  [-0.95105653425, -0.20973479681, -0.54909275069],
2136  [ 0.36327125634, -0.33935800013, -0.88845072219],
2137  [-0.58778526871, -0.33935801248, 0.75882749090],
2138  [-0.95105653425, -0.33935801772, 0.12962320761],
2139  [-0.00000000920, -0.75882755207, 0.67871593299],
2140  [ 0.58778523780, -0.88845076062, 0.33935796050],
2141  [ 0.58778523780, -0.75882753971, -0.33935799780],
2142  [ 0.00000000000, -0.88845068543, -0.67871595830],
2143  [-0.58778524700, -0.75882747687, -0.33935798580],
2144  [-0.58778524700, -0.88845069778, 0.33935797250],
2145  [ 0.00000000000, -1.01807390634, 0.00000000000]
2146  ],
2147  [
2148  [1.01807390634, 89.99999999999, 89.99999999999],
2149  [1.11803397644, 89.99999999999, 52.62263066673],
2150  [1.01807390634, 52.23875557900, 70.52877834968],
2151  [1.11803397644, 56.51199476545, 107.66980724671],
2152  [1.01807395187, 89.99999930546, 131.81031225926],
2153  [1.11803401790, 123.48800295704, 107.66980592440],
2154  [1.01807395187, 127.76124168979, 70.52877853920],
2155  [1.01807395187, 43.05074810479, 29.22865434511],
2156  [1.11803401790, 12.43628246235, 60.58554897383],
2157  [1.01807395187, 19.63752482828, 97.31486796888],
2158  [1.11803398875, 89.99999999999, 169.18768244741],
2159  [1.01807391986, 149.99999917200, 138.18968508471],
2160  [1.01807393822, 30.00000214725, 138.18968343591],
2161  [1.11803400000, 167.56371947847, 60.58554885896],
2162  [1.01807393822, 136.94924990484, 29.22865308802],
2163  [1.01807393221, 160.36247691007, 97.31486849897],
2164  [1.11803398875, -89.99999999999, 10.81231755257],
2165  [1.01807391986, -30.00000082799, 41.81031491527],
2166  [1.11803400000, -12.43628052152, 119.41445114102],
2167  [1.01807393221, -19.63752308992, 82.68513150102],
2168  [1.01807395187, -136.94925189520, 150.77134565488],
2169  [1.11803401790, -167.56371753764, 119.41445102616],
2170  [1.01807393822, -43.05075009515, 150.77134691197],
2171  [1.01807393822, -149.99999785273, 41.81031656408],
2172  [1.01807395187, -160.36247517171, 82.68513203111],
2173  [1.01807395187, -90.00000069453, 48.18968774073],
2174  [1.11803401790, -56.51199704295, 72.33019407559],
2175  [1.01807395187, -52.23875831020, 109.47122146079],
2176  [1.11803397644, -89.99999999999, 127.37736933326],
2177  [1.01807390634, -127.76124442099, 109.47122165031],
2178  [1.11803397644, -123.48800523454, 72.33019275327],
2179  [1.01807390634, -89.99999999999, 89.99999999999]
2180  ],
2181  [
2182  [2,1,0,3],
2183  [0,5,4,3],
2184  [1,6,5,0],
2185  [2,8,7,1],
2186  [3,9,8,2],
2187  [11,10,4,5],
2188  [10,12,3,4],
2189  [14,13,6,1],
2190  [13,15,5,6],
2191  [17,16,7,8],
2192  [16,14,1,7],
2193  [12,18,9,3],
2194  [18,19,8,9],
2195  [11,21,20,10],
2196  [5,15,21,11],
2197  [10,22,18,12],
2198  [14,16,23,13],
2199  [13,24,21,15],
2200  [17,26,25,16],
2201  [8,19,26,17],
2202  [18,27,26,19],
2203  [29,28,20,21],
2204  [28,22,10,20],
2205  [28,27,18,22],
2206  [25,30,23,16],
2207  [30,24,13,23],
2208  [30,29,21,24],
2209  [31,30,25,26],
2210  [28,31,26,27],
2211  [29,30,31,28]
2212  ],
2213  [
2214  [0,1],
2215  [0,3],
2216  [0,5],
2217  [1,2],
2218  [1,6],
2219  [1,7],
2220  [1,14],
2221  [2,3],
2222  [2,8],
2223  [3,4],
2224  [3,9],
2225  [3,12],
2226  [4,5],
2227  [4,10],
2228  [5,6],
2229  [5,11],
2230  [5,15],
2231  [6,13],
2232  [7,8],
2233  [7,16],
2234  [8,9],
2235  [8,17],
2236  [8,19],
2237  [9,18],
2238  [10,11],
2239  [10,12],
2240  [10,20],
2241  [10,22],
2242  [11,21],
2243  [12,18],
2244  [13,14],
2245  [13,15],
2246  [13,23],
2247  [13,24],
2248  [14,16],
2249  [15,21],
2250  [16,17],
2251  [16,23],
2252  [16,25],
2253  [17,26],
2254  [18,19],
2255  [18,22],
2256  [18,27],
2257  [19,26],
2258  [20,21],
2259  [20,28],
2260  [21,24],
2261  [21,29],
2262  [22,28],
2263  [23,30],
2264  [24,30],
2265  [25,26],
2266  [25,30],
2267  [26,27],
2268  [26,31],
2269  [27,28],
2270  [28,29],
2271  [28,31],
2272  [29,30],
2273  [30,31]
2274  ]
2275  ],
2276  [
2277  "tetrakis_hexahedron",
2278  "Tetrakis-hexahedron",
2279  empty_str,
2280  "archimedean_duals",
2281  "George W. Hart, 1997. george@li.net",
2282  [
2283  [ 0.70710678207, 0.70710678239, -0.70710681572],
2284  [-0.70710685399, 0.70710676255, -0.70710675601],
2285  [ 0.00000000000, 1.06066018679, 0.00000000000],
2286  [ 0.70710690892, 0.70710691162, 0.70710686506],
2287  [-0.00000000000, -0.00000006623, -1.06066014330],
2288  [-0.70710653501, 0.70710672864, 0.70710659847],
2289  [ 1.06066017311, 0.00000000830, -0.00000005793],
2290  [-0.70710690892, -0.70710691162, -0.70710686506],
2291  [ 0.70710653501, -0.70710672864, -0.70710659847],
2292  [-1.06066017311, -0.00000000830, 0.00000005793],
2293  [ 0.70710685399, -0.70710676255, 0.70710675601],
2294  [ 0.00000000000, 0.00000006623, 1.06066014330],
2295  [-0.70710678207, -0.70710678239, 0.70710681572],
2296  [ 0.00000000000, -1.06066018679, 0.00000000000]
2297  ],
2298  [
2299  [1.22474489254, 45.00000001273, 125.26439096213],
2300  [1.22474488813, 135.00000370435, 125.26438768675],
2301  [1.06066018679, 89.99999999999, 89.99999999999],
2302  [1.22474506887, 45.00000010944, 54.73561204440],
2303  [1.06066014330, -89.99999999999, 179.99999642215],
2304  [1.22474459343, 134.99999215502, 54.73561159120],
2305  [1.06066017311, 0.00000044850, 90.00000312934],
2306  [1.22474506887, -134.99999989055, 125.26438795559],
2307  [1.22474459343, -45.00000784497, 125.26438840879],
2308  [1.06066017311, -179.99999955149, 89.99999687065],
2309  [1.22474488813, -44.99999629564, 54.73561231324],
2310  [1.06066014330, 89.99999999999, 0.00000357784],
2311  [1.22474489254, -134.99999998726, 54.73560903786],
2312  [1.06066018679, -89.99999999999, 89.99999999999]
2313  ],
2314  [
2315  [1,0,2],
2316  [0,3,2],
2317  [1,4,0],
2318  [2,5,1],
2319  [6,3,0],
2320  [5,2,3],
2321  [7,4,1],
2322  [8,0,4],
2323  [9,1,5],
2324  [6,10,3],
2325  [0,8,6],
2326  [3,11,5],
2327  [7,8,4],
2328  [1,9,7],
2329  [5,12,9],
2330  [8,10,6],
2331  [11,3,10],
2332  [12,5,11],
2333  [13,8,7],
2334  [12,7,9],
2335  [8,13,10],
2336  [10,12,11],
2337  [7,12,13],
2338  [12,10,13]
2339  ],
2340  [
2341  [0,1],
2342  [0,2],
2343  [0,3],
2344  [0,4],
2345  [0,6],
2346  [0,8],
2347  [1,2],
2348  [1,4],
2349  [1,5],
2350  [1,7],
2351  [1,9],
2352  [2,3],
2353  [2,5],
2354  [3,5],
2355  [3,6],
2356  [3,10],
2357  [3,11],
2358  [4,7],
2359  [4,8],
2360  [5,9],
2361  [5,11],
2362  [5,12],
2363  [6,8],
2364  [6,10],
2365  [7,8],
2366  [7,9],
2367  [7,12],
2368  [7,13],
2369  [8,10],
2370  [8,13],
2371  [9,12],
2372  [10,11],
2373  [10,12],
2374  [10,13],
2375  [11,12],
2376  [12,13]
2377  ]
2378  ],
2379  [
2380  "triakis_icosahedron",
2381  "Triakis-icosahedron",
2382  empty_str,
2383  "archimedean_duals",
2384  "George W. Hart, 1997. george@li.net",
2385  [
2386  [-0.00000000000, 0.93417236382, 0.71364415491],
2387  [-0.61803396134, 0.93417232764, -0.35682211804],
2388  [-0.58017872165, 0.74900752253, 0.33496628596],
2389  [-1.00000006691, 0.22052823141, 0.57735025290],
2390  [ 0.00000000000, 1.00489899512, 0.00000000000],
2391  [-0.35857021344, 0.33496638403, 0.87695321245],
2392  [ 0.61803402629, 0.93417228051, -0.35682205521],
2393  [-0.93874890906, 0.33496634823, -0.12794580758],
2394  [ 0.00000009630, -0.22052800883, 1.15470021259],
2395  [-0.00000000807, 0.74900749069, -0.66993269090],
2396  [ 0.58017868755, 0.74900752648, 0.33496632913],
2397  [-0.99999964147, -0.22052809857, -0.57735011790],
2398  [-0.58017883007, -0.33496629413, 0.74900748268],
2399  [ 0.35857007899, 0.33496635276, 0.87695329026],
2400  [-0.00000009630, 0.22052800883, -1.15470021259],
2401  [ 0.99999964147, 0.22052809857, 0.57735011790],
2402  [-0.58017865557, 0.33496636593, -0.74900752152],
2403  [-0.93874890790, -0.33496628904, 0.12794577195],
2404  [-0.61803402629, -0.93417228051, 0.35682205521],
2405  [ 0.58017883007, 0.33496629413, -0.74900748268],
2406  [ 0.93874890790, 0.33496628904, -0.12794577195],
2407  [ 0.00000000807, -0.74900749069, 0.66993269090],
2408  [ 0.58017865557, -0.33496636593, 0.74900752152],
2409  [ 1.00000006691, -0.22052823141, -0.57735025290],
2410  [-0.35857007899, -0.33496635276, -0.87695329026],
2411  [-0.58017868755, -0.74900752648, -0.33496632913],
2412  [ 0.61803396134, -0.93417232764, 0.35682211804],
2413  [ 0.35857021344, -0.33496638403, -0.87695321245],
2414  [ 0.93874890906, -0.33496634823, 0.12794580758],
2415  [ 0.00000000000, -0.93417236382, -0.71364415491],
2416  [ 0.00000000000, -1.00489899512, 0.00000000000],
2417  [ 0.58017872165, -0.74900752253, -0.33496628596]
2418  ],
2419  [
2420  [1.17557049349, 89.99999999999, 52.62263295694],
2421  [1.17557047387, 123.48800484353, 107.66980902983],
2422  [1.00489901512, 127.76124340324, 70.52878253520],
2423  [1.17557056326, 167.56371727190, 60.58555153741],
2424  [1.00489899512, 89.99999999999, 89.99999999999],
2425  [1.00489900648, 136.94925257836, 29.22865737676],
2426  [1.17557045149, 56.51199105535, 107.66980616365],
2427  [1.00489904885, 160.36247714599, 97.31487112602],
2428  [1.17557015257, -89.99997498012, 10.81231177567],
2429  [1.00489901554, 90.00000061707, 131.81031595691],
2430  [1.00489901277, 52.23875837347, 70.52877987717],
2431  [1.17557011013, -167.56371940336, 119.41445336076],
2432  [1.00489905074, -150.00000811670, 41.81031888524],
2433  [1.00489901598, 43.05075547144, 29.22864925989],
2434  [1.17557015257, 90.00002501987, 169.18768822431],
2435  [1.17557011013, 12.43628059663, 60.58554663923],
2436  [1.00489900288, 149.99999533713, 138.18968748766],
2437  [1.00489902350, -160.36248032812, 82.68513073645],
2438  [1.17557045149, -123.48800894464, 72.33019383634],
2439  [1.00489905074, 29.99999188329, 138.18968111474],
2440  [1.00489902350, 19.63751967187, 97.31486926354],
2441  [1.00489901554, -89.99999938292, 48.18968404308],
2442  [1.00489900288, -30.00000466286, 41.81031251233],
2443  [1.17557056326, -12.43628272809, 119.41444846258],
2444  [1.00489901598, -136.94924452855, 150.77135074010],
2445  [1.00489901277, -127.76124162652, 109.47122012281],
2446  [1.17557047387, -56.51199515646, 72.33019097016],
2447  [1.00489900648, -43.05074742162, 150.77134262323],
2448  [1.00489904885, -19.63752285400, 82.68512887397],
2449  [1.17557049349, -89.99999999999, 127.37736704305],
2450  [1.00489899512, -89.99999999999, 89.99999999999],
2451  [1.00489901512, -52.23875659675, 109.47121746479]
2452  ],
2453  [
2454  [1,0,2],
2455  [0,3,2],
2456  [1,4,0],
2457  [2,3,1],
2458  [5,3,0],
2459  [6,4,1],
2460  [6,0,4],
2461  [7,1,3],
2462  [5,8,3],
2463  [0,8,5],
2464  [1,9,6],
2465  [6,10,0],
2466  [7,11,1],
2467  [3,11,7],
2468  [12,3,8],
2469  [13,8,0],
2470  [14,9,1],
2471  [14,6,9],
2472  [15,10,6],
2473  [15,0,10],
2474  [16,1,11],
2475  [17,11,3],
2476  [12,18,3],
2477  [8,18,12],
2478  [13,15,8],
2479  [0,15,13],
2480  [1,16,14],
2481  [14,19,6],
2482  [6,20,15],
2483  [11,14,16],
2484  [17,18,11],
2485  [3,18,17],
2486  [21,18,8],
2487  [22,8,15],
2488  [23,19,14],
2489  [23,6,19],
2490  [23,20,6],
2491  [23,15,20],
2492  [24,14,11],
2493  [25,11,18],
2494  [21,26,18],
2495  [8,26,21],
2496  [22,26,8],
2497  [15,26,22],
2498  [14,27,23],
2499  [23,28,15],
2500  [24,29,14],
2501  [11,29,24],
2502  [25,29,11],
2503  [18,29,25],
2504  [30,18,26],
2505  [28,26,15],
2506  [29,27,14],
2507  [29,23,27],
2508  [26,28,23],
2509  [30,29,18],
2510  [26,29,30],
2511  [29,31,23],
2512  [23,31,26],
2513  [31,29,26]
2514  ],
2515  [
2516  [0,1],
2517  [0,2],
2518  [0,3],
2519  [0,4],
2520  [0,5],
2521  [0,6],
2522  [0,8],
2523  [0,10],
2524  [0,13],
2525  [0,15],
2526  [1,2],
2527  [1,3],
2528  [1,4],
2529  [1,6],
2530  [1,7],
2531  [1,9],
2532  [1,11],
2533  [1,14],
2534  [1,16],
2535  [2,3],
2536  [3,5],
2537  [3,7],
2538  [3,8],
2539  [3,11],
2540  [3,12],
2541  [3,17],
2542  [3,18],
2543  [4,6],
2544  [5,8],
2545  [6,9],
2546  [6,10],
2547  [6,14],
2548  [6,15],
2549  [6,19],
2550  [6,20],
2551  [6,23],
2552  [7,11],
2553  [8,12],
2554  [8,13],
2555  [8,15],
2556  [8,18],
2557  [8,21],
2558  [8,22],
2559  [8,26],
2560  [9,14],
2561  [10,15],
2562  [11,14],
2563  [11,16],
2564  [11,17],
2565  [11,18],
2566  [11,24],
2567  [11,25],
2568  [11,29],
2569  [12,18],
2570  [13,15],
2571  [14,16],
2572  [14,19],
2573  [14,23],
2574  [14,24],
2575  [14,27],
2576  [14,29],
2577  [15,20],
2578  [15,22],
2579  [15,23],
2580  [15,26],
2581  [15,28],
2582  [17,18],
2583  [18,21],
2584  [18,25],
2585  [18,26],
2586  [18,29],
2587  [18,30],
2588  [19,23],
2589  [20,23],
2590  [21,26],
2591  [22,26],
2592  [23,26],
2593  [23,27],
2594  [23,28],
2595  [23,29],
2596  [23,31],
2597  [24,29],
2598  [25,29],
2599  [26,28],
2600  [26,29],
2601  [26,30],
2602  [26,31],
2603  [27,29],
2604  [29,30],
2605  [29,31]
2606  ]
2607  ],
2608  [
2609  "triakis_octahedron",
2610  "Triakis-octahedron",
2611  empty_str,
2612  "archimedean_duals",
2613  "George W. Hart, 1997. george@li.net",
2614  [
2615  [ 0.00000000000, 1.41421356691, 0.00000000000],
2616  [-0.00000000000, 0.00000003680, -1.41421356830],
2617  [-0.58578641907, 0.58578642733, -0.58578648469],
2618  [-1.41421370446, -0.00000001119, 0.00000004562],
2619  [ 0.58578643764, 0.58578646663, -0.58578633512],
2620  [-0.58578646823, 0.58578646484, 0.58578644204],
2621  [ 1.41421370446, 0.00000001119, -0.00000004562],
2622  [-0.58578642040, -0.58578641355, -0.58578648780],
2623  [ 0.00000000000, -0.00000003680, 1.41421356830],
2624  [ 0.58578646823, -0.58578646484, -0.58578644204],
2625  [ 0.58578642040, 0.58578641355, 0.58578648780],
2626  [ 0.00000000000, -1.41421356691, 0.00000000000],
2627  [-0.58578643764, -0.58578646663, 0.58578633512],
2628  [ 0.58578641907, -0.58578642733, 0.58578648469]
2629  ],
2630  [
2631  [1.41421356691, 89.99999999999, 89.99999999999],
2632  [1.41421356830, 89.99999999999, 179.99999850913],
2633  [1.01461188287, 134.99999959623, 125.26439251769],
2634  [1.41421370446, -179.99999954681, 89.99999815161],
2635  [1.01461182992, 45.00000141798, 125.26438428773],
2636  [1.01461190828, 135.00000016553, 54.73561144661],
2637  [1.41421370446, 0.00000045318, 90.00000184838],
2638  [1.01461187748, -135.00000033463, 125.26439294822],
2639  [1.41421356830, -89.99999999999, 0.00000149086],
2640  [1.01461190828, -44.99999983445, 125.26438855338],
2641  [1.01461187748, 44.99999966536, 54.73560705177],
2642  [1.41421356691, -89.99999999999, 89.99999999999],
2643  [1.01461182992, -134.99999858201, 54.73561571226],
2644  [1.01461188287, -45.00000040376, 54.73560748230]
2645  ],
2646  [
2647  [1,0,2],
2648  [0,3,2],
2649  [1,4,0],
2650  [2,3,1],
2651  [5,3,0],
2652  [6,4,1],
2653  [6,0,4],
2654  [7,1,3],
2655  [5,8,3],
2656  [0,8,5],
2657  [1,9,6],
2658  [6,10,0],
2659  [7,11,1],
2660  [3,11,7],
2661  [12,3,8],
2662  [10,8,0],
2663  [11,9,1],
2664  [11,6,9],
2665  [8,10,6],
2666  [12,11,3],
2667  [8,11,12],
2668  [11,13,6],
2669  [6,13,8],
2670  [13,11,8]
2671  ],
2672  [
2673  [0,1],
2674  [0,2],
2675  [0,3],
2676  [0,4],
2677  [0,5],
2678  [0,6],
2679  [0,8],
2680  [0,10],
2681  [1,2],
2682  [1,3],
2683  [1,4],
2684  [1,6],
2685  [1,7],
2686  [1,9],
2687  [1,11],
2688  [2,3],
2689  [3,5],
2690  [3,7],
2691  [3,8],
2692  [3,11],
2693  [3,12],
2694  [4,6],
2695  [5,8],
2696  [6,8],
2697  [6,9],
2698  [6,10],
2699  [6,11],
2700  [6,13],
2701  [7,11],
2702  [8,10],
2703  [8,11],
2704  [8,12],
2705  [8,13],
2706  [9,11],
2707  [11,12],
2708  [11,13]
2709  ]
2710  ],
2711  [
2712  "triakis_tetrahedron",
2713  "Triakis-tetrahedron",
2714  empty_str,
2715  "archimedean_duals",
2716  "George W. Hart, 1997. george@li.net",
2717  [
2718  [ 0.00000000000, 1.73205113922, 0.00000000000],
2719  [ 1.41421310220, -0.57735025671, -0.81649662287],
2720  [-0.00000000000, 0.34640998257, -0.97979591140],
2721  [-1.41421344981, -0.57735038744, -0.81649643800],
2722  [ 0.84852816886, 0.34641021829, 0.48989788285],
2723  [-0.84852813268, 0.34641022788, 0.48989786928],
2724  [-0.00000005168, -0.57735016964, 1.63299346667],
2725  [ 0.00000005427, -1.03923045335, 0.00000019409]
2726  ],
2727  [
2728  [1.73205113922, 89.99999999999, 89.99999999999],
2729  [1.73205044746, -22.20766038913, 118.12551364281],
2730  [1.03923043836, 89.99999999999, 160.52878892978],
2731  [1.73205068770, -157.79233999925, 118.12550246063],
2732  [1.03923049816, 22.20765684163, 61.87449880719],
2733  [1.03923046542, 157.79234174813, 61.87449869060],
2734  [1.73205106177, -90.00000512871, 19.47121416866],
2735  [1.03923045335, -89.99999700782, 89.99998929901]
2736  ],
2737  [
2738  [1,0,2],
2739  [0,3,2],
2740  [1,4,0],
2741  [2,3,1],
2742  [5,3,0],
2743  [6,4,1],
2744  [6,0,4],
2745  [7,1,3],
2746  [5,6,3],
2747  [0,6,5],
2748  [1,7,6],
2749  [3,6,7]
2750  ],
2751  [
2752  [0,1],
2753  [0,2],
2754  [0,3],
2755  [0,4],
2756  [0,5],
2757  [0,6],
2758  [1,2],
2759  [1,3],
2760  [1,4],
2761  [1,6],
2762  [1,7],
2763  [2,3],
2764  [3,5],
2765  [3,6],
2766  [3,7],
2767  [4,6],
2768  [5,6],
2769  [6,7]
2770  ]
2771  ]
2772 ];
2773 
2774 //! @}
2775 
2776 //----------------------------------------------------------------------------//
2777 // openscad-amu auxiliary scripts
2778 //----------------------------------------------------------------------------//
2779 
2780 /*
2781 BEGIN_SCOPE db;
2782 BEGIN_SCOPE autostat;
2783  BEGIN_OPENSCAD;
2784  include <math/math_polytope.scad>;
2785  include <math/math_utility.scad>;
2786  include <datatypes/datatypes_table.scad>;
2787  include <database/geometry/polyhedra/archimedean_duals.scad>;
2788 
2789  fs = "^";
2790 
2791  tc = dtc_polyhedra_archimedean_duals;
2792  tr = dtr_polyhedra_archimedean_duals;
2793 
2794  ids = get_table_ridl(tr);
2795 
2796  echo
2797  (
2798  str
2799  (
2800  "no.", fs, "table id", fs, "other name", fs,
2801  "vertices", fs, "faces", fs, "edges",
2802 
2803  fs, "face-verticies",
2804  fs, "face-angles",
2805  fs, "edge-lengths",
2806  fs, "edge-angles"
2807  )
2808  );
2809 
2810  for ( id = ids )
2811  {
2812  i = first(find(id, ids, c=1))+1;
2813 
2814  n = get_table_v(tr, tc, id, "n");
2815  o = get_table_v(tr, tc, id, "o");
2816  g = get_table_v(tr, tc, id, "g");
2817  d = get_table_v(tr, tc, id, "d");
2818 
2819  c = get_table_v(tr, tc, id, "c");
2820  s = get_table_v(tr, tc, id, "s");
2821  f = get_table_v(tr, tc, id, "f");
2822  e = get_table_v(tr, tc, id, "e");
2823 
2824  fo = is_empty(o) ? "-" : o;
2825 
2826  echo
2827  (
2828  str
2829  (
2830  i, fs, id, fs, fo, fs,
2831  len(c), fs, len(f), fs, len(e),
2832 
2833  fs, hist(qsort(polytope_face_vcounts(f)), m=9),
2834  fs, hist(qsort(dround(polytope_face_angles(c, f), d=1)), m=9),
2835  fs, hist(qsort(sround(polytope_edge_lengths(c, e), d=3)), m=9),
2836  fs, hist(qsort(dround(polytope_edge_angles(c, f), d=1)), m=9),
2837 
2838  fs
2839  )
2840  );
2841  }
2842  END_OPENSCAD;
2843 
2844  BEGIN_MFSCRIPT;
2845  include --path "${INCLUDE_PATH}" {config_base,config_csg}.mfs;
2846  include --path "${INCLUDE_PATH}" script_std.mfs;
2847  END_MFSCRIPT;
2848 END_SCOPE;
2849 END_SCOPE;
2850 */
2851 
2852 /*
2853 BEGIN_SCOPE db;
2854 BEGIN_SCOPE dim;
2855  BEGIN_OPENSCAD;
2856  include <units/units_coordinate.scad>;
2857  include <tools/tools_polytope.scad>;
2858  include <datatypes/datatypes_table.scad>;
2859  include <database/geometry/polyhedra/archimedean_duals.scad>;
2860 
2861  config = 0;
2862 
2863  tc = dtc_polyhedra_archimedean_duals;
2864  tr = dtr_polyhedra_archimedean_duals;
2865 
2866  id = "default";
2867  sr = 100;
2868 
2869  pv = get_table_v(tr, tc, id, "c");
2870  pf = get_table_v(tr, tc, id, "f");
2871  pe = get_table_v(tr, tc, id, "e");
2872 
2873  sv = coordinates_csc(pv, sr);
2874 
2875  if (config == 0) // png preview
2876  {
2877  $fn = 25;
2878 
2879  %polyhedron(sv, pf);
2880 
2881  polytope_frame(sv, pf, pe)
2882  {
2883  circle(r = sr / 25);
2884  color("lightblue")
2885  sphere(r = sr / 25 * (1 + 1/2));
2886  }
2887  }
2888 
2889  if (config == 1) // stl model
2890  {
2891  polyhedron(sv, pf);
2892  }
2893  END_OPENSCAD;
2894 
2895  BEGIN_MFSCRIPT;
2896  include --path "${INCLUDE_PATH}" {config_base,config_png}.mfs;
2897 
2898  views name "views" views "diag";
2899  defines name "ids" define "id"
2900  strings
2901  "
2902  disdyakis_dodecahedron
2903  disdyakis_triacontahedron
2904  kite_hexecontahedron
2905  kite_icositetrahedron
2906  pentagonal_hexecontahedron
2907  pentagonal_icositetrahedron
2908  pentakis_dodecahedron
2909  rhombic_dodecahedron
2910  rhombic_triacontahedron
2911  tetrakis_hexahedron
2912  triakis_icosahedron
2913  triakis_octahedron
2914  triakis_tetrahedron
2915  ";
2916  variables add_opts_combine "views ids";
2917  variables add_opts "-D config=0 --viewall --autocenter";
2918 
2919  include --path "${INCLUDE_PATH}" script_new.mfs;
2920 
2921  include --path "${INCLUDE_PATH}" config_stl.mfs;
2922  variables add_opts_combine "ids";
2923  variables add_opts "-D config=1";
2924 
2925  include --path "${INCLUDE_PATH}" script_app.mfs;
2926  END_MFSCRIPT;
2927 END_SCOPE;
2928 END_SCOPE;
2929 */
2930 
2931 //----------------------------------------------------------------------------//
2932 // end of file
2933 //----------------------------------------------------------------------------//
dtc_polyhedra_archimedean_duals
dtc_polyhedra_archimedean_duals
Definition: archimedean_duals.scad:114
empty_str
empty_str
A string with no characters (the empty string).
Definition: constants.scad:77
dtr_polyhedra_archimedean_duals
dtr_polyhedra_archimedean_duals
Definition: archimedean_duals.scad:129