omdl  v1.0
OpenSCAD Mechanical Design Library
cupolas.scad
Go to the documentation of this file.
1 //! Polyhedra data table: \c cupolas.
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  ### Cupolas ###
64  \amu_include (include/amu/includes_required.amu)
65 
66  \amu_eval
67  (
68  ++global
69  title="Examples"
70  stem=cupolas 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 cupolas polyhedra data table columns definition.
128 //! \hideinitializer
129 dtc_polyhedra_cupolas =
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 cupolas polyhedra data table rows.
143 //! \hideinitializer
144 dtr_polyhedra_cupolas =
145 [
146  [
147  "pentagonal_cupola",
148  "Pentagonal Cupola",
149  "J5",
150  "cupolas",
151  "Polyhedron Database #49",
152  [
153  [ 0.30722035250, -0.10767686506, -0.94552702116],
154  [-0.30722035250, -0.10767686506, -0.94552702116],
155  [ 0.80431332487, -0.10767686506, -0.58436783636],
156  [ 0.30722035250, 0.21535373011, -0.42285253878],
157  [-0.30722035250, 0.21535373011, -0.42285253878],
158  [-0.80431332487, -0.10767686506, -0.58436783636],
159  [ 0.99418594475, -0.10767686506, 0.00000000000],
160  [ 0.49709297237, 0.21535373011, 0.16151529758],
161  [-0.49709297237, 0.21535373011, 0.16151529758],
162  [-0.99418594475, -0.10767686506, -0.00000000000],
163  [ 0.00000000000, 0.21535373011, 0.52267448238],
164  [ 0.80431332487, -0.10767686506, 0.58436783636],
165  [-0.80431332487, -0.10767686506, 0.58436783636],
166  [ 0.30722035250, -0.10767686506, 0.94552702116],
167  [-0.30722035250, -0.10767686506, 0.94552702116]
168  ],
169  [
170  [1.00000000000, -19.31492121303, 161.00148636537],
171  [1.00000000000, -160.68507878696, 161.00148636537],
172  [1.00000000000, -7.62509363515, 125.75834309459],
173  [0.56530155104, 35.02948816948, 138.41849317790],
174  [0.56530155104, 144.97051183050, 138.41849317790],
175  [1.00000000000, -172.37490636484, 125.75834309458],
176  [1.00000000000, -6.18141426338, 89.99999999999],
177  [0.56530155104, 23.42352770491, 73.39839025197],
178  [0.56530155104, 156.57647229507, 73.39839025196],
179  [1.00000000000, -173.81858573662, 89.99999999999],
180  [0.56530155104, 89.99999999997, 22.39277092895],
181  [1.00000000000, -7.62509363516, 54.24165690541],
182  [1.00000000000, -172.37490636484, 54.24165690540],
183  [1.00000000000, -19.31492121306, 18.99851363462],
184  [1.00000000000, -160.68507878694, 18.99851363462]
185  ],
186  [
187  [0,1,5,9,12,14,13,11,6,2],
188  [7,10,8,4,3],
189  [1,0,3,4],
190  [5,1,4],
191  [9,5,4,8],
192  [12,9,8],
193  [14,12,8,10],
194  [13,14,10],
195  [11,13,10,7],
196  [6,11,7],
197  [2,6,7,3],
198  [0,2,3]
199  ],
200  [
201  [0,1],
202  [0,2],
203  [0,3],
204  [1,4],
205  [1,5],
206  [2,3],
207  [2,6],
208  [3,4],
209  [3,7],
210  [4,5],
211  [4,8],
212  [5,9],
213  [6,7],
214  [6,11],
215  [7,10],
216  [7,11],
217  [8,9],
218  [8,10],
219  [8,12],
220  [9,12],
221  [10,13],
222  [10,14],
223  [11,13],
224  [12,14],
225  [13,14]
226  ]
227  ],
228  [
229  "pentagonal_gyrobicupola",
230  "Pentagonal Gyrobicupola",
231  "J31",
232  "cupolas",
233  "Polyhedron Database #75",
234  [
235  [ 0.80901699437, 0.00000000000, 0.58778525229],
236  [ 0.30901699437, 0.00000000000, 0.95105651630],
237  [ 1.00000000000, 0.00000000000, -0.00000000000],
238  [-0.30901699437, 0.00000000000, 0.95105651630],
239  [ 0.30901699438, -0.32491969623, 0.42532540418],
240  [ 0.50000000000, 0.32491969623, 0.16245984812],
241  [ 0.00000000000, 0.32491969623, 0.52573111212],
242  [ 0.50000000000, -0.32491969623, -0.16245984812],
243  [-0.30901699437, -0.32491969623, 0.42532540418],
244  [ 0.80901699437, 0.00000000000, -0.58778525229],
245  [-0.80901699437, 0.00000000000, 0.58778525229],
246  [ 0.30901699437, 0.32491969623, -0.42532540418],
247  [-0.50000000000, 0.32491969623, 0.16245984812],
248  [-0.00000000000, -0.32491969623, -0.52573111212],
249  [-0.50000000000, -0.32491969623, -0.16245984812],
250  [-0.30901699438, 0.32491969623, -0.42532540418],
251  [ 0.30901699437, -0.00000000000, -0.95105651630],
252  [-1.00000000000, 0.00000000000, 0.00000000000],
253  [-0.30901699437, -0.00000000000, -0.95105651630],
254  [-0.80901699437, -0.00000000000, -0.58778525229]
255  ],
256  [
257  [1.00000000000, 0.00000000001, 54.00000000000],
258  [1.00000000000, 0.00000000002, 18.00000000000],
259  [1.00000000000, 0.00000000000, 89.99999999999],
260  [1.00000000000, 179.99999999997, 18.00000000000],
261  [0.61803398875, -46.43699940041, 46.51292225447],
262  [0.61803398875, 33.01739809414, 74.75983771732],
263  [0.61803398875, 89.99999999999, 31.71747441146],
264  [0.61803398875, -33.01739809415, 105.24016228267],
265  [0.61803398875, -133.56300059956, 46.51292225447],
266  [1.00000000000, 0.00000000000, 125.99999999999],
267  [1.00000000000, 179.99999999999, 54.00000000000],
268  [0.61803398875, 46.43699940043, 133.48707774552],
269  [0.61803398875, 146.98260190584, 74.75983771731],
270  [0.61803398875, -89.99999999999, 148.28252558853],
271  [0.61803398875, -146.98260190585, 105.24016228267],
272  [0.61803398875, 133.56300059958, 133.48707774551],
273  [1.00000000000, -0.00000000002, 161.99999999999],
274  [1.00000000000, 179.99999999999, 89.99999999999],
275  [1.00000000000, -179.99999999997, 161.99999999999],
276  [1.00000000000, -179.99999999998, 125.99999999999]
277  ],
278  [
279  [13,14,8,4,7],
280  [0,2,7,4],
281  [1,0,4],
282  [3,1,4,8],
283  [10,3,8],
284  [17,10,8,14],
285  [19,17,14],
286  [18,19,14,13],
287  [16,18,13],
288  [9,16,13,7],
289  [2,9,7],
290  [12,15,11,5,6],
291  [0,1,6,5],
292  [2,0,5],
293  [9,2,5,11],
294  [16,9,11],
295  [18,16,11,15],
296  [19,18,15],
297  [17,19,15,12],
298  [10,17,12],
299  [3,10,12,6],
300  [1,3,6]
301  ],
302  [
303  [0,1],
304  [0,2],
305  [0,4],
306  [0,5],
307  [1,3],
308  [1,4],
309  [1,6],
310  [2,5],
311  [2,7],
312  [2,9],
313  [3,6],
314  [3,8],
315  [3,10],
316  [4,7],
317  [4,8],
318  [5,6],
319  [5,11],
320  [6,12],
321  [7,9],
322  [7,13],
323  [8,10],
324  [8,14],
325  [9,11],
326  [9,16],
327  [10,12],
328  [10,17],
329  [11,15],
330  [11,16],
331  [12,15],
332  [12,17],
333  [13,14],
334  [13,16],
335  [13,18],
336  [14,17],
337  [14,19],
338  [15,18],
339  [15,19],
340  [16,18],
341  [17,19],
342  [18,19]
343  ]
344  ],
345  [
346  "pentagonal_orthobicupola",
347  "Pentagonal Orthobicupola",
348  "J30",
349  "cupolas",
350  "Polyhedron Database #74",
351  [
352  [ 0.30901699438, 0.00000000000, 0.95105651630],
353  [-0.30901699437, 0.00000000000, 0.95105651630],
354  [ 0.80901699437, 0.00000000000, 0.58778525229],
355  [ 0.00000000000, 0.32491969623, 0.52573111212],
356  [-0.00000000000, -0.32491969623, 0.52573111212],
357  [-0.80901699437, 0.00000000000, 0.58778525229],
358  [ 0.50000000000, 0.32491969623, 0.16245984812],
359  [ 0.50000000000, -0.32491969623, 0.16245984812],
360  [ 1.00000000000, 0.00000000000, -0.00000000000],
361  [-0.50000000000, 0.32491969623, 0.16245984812],
362  [-0.50000000000, -0.32491969623, 0.16245984812],
363  [-1.00000000000, 0.00000000000, 0.00000000000],
364  [ 0.30901699437, 0.32491969623, -0.42532540418],
365  [ 0.30901699437, -0.32491969623, -0.42532540418],
366  [ 0.80901699437, -0.00000000000, -0.58778525229],
367  [-0.30901699438, 0.32491969623, -0.42532540418],
368  [-0.30901699438, -0.32491969623, -0.42532540418],
369  [-0.80901699437, -0.00000000000, -0.58778525229],
370  [ 0.30901699437, -0.00000000000, -0.95105651630],
371  [-0.30901699438, 0.00000000000, -0.95105651630]
372  ],
373  [
374  [1.00000000000, 0.00000000000, 18.00000000000],
375  [1.00000000000, 179.99999999999, 17.99999999999],
376  [1.00000000000, 0.00000000001, 54.00000000000],
377  [0.61803398875, 89.99999999998, 31.71747441146],
378  [0.61803398875, -89.99999999999, 31.71747441146],
379  [1.00000000000, 179.99999999998, 53.99999999999],
380  [0.61803398875, 33.01739809414, 74.75983771732],
381  [0.61803398875, -33.01739809414, 74.75983771731],
382  [1.00000000000, 0.00000000000, 90.00000000000],
383  [0.61803398875, 146.98260190585, 74.75983771731],
384  [0.61803398875, -146.98260190585, 74.75983771731],
385  [1.00000000000, 179.99999999999, 89.99999999999],
386  [0.61803398875, 46.43699940043, 133.48707774551],
387  [0.61803398875, -46.43699940043, 133.48707774551],
388  [1.00000000000, -0.00000000001, 125.99999999999],
389  [0.61803398875, 133.56300059957, 133.48707774552],
390  [0.61803398875, -133.56300059957, 133.48707774551],
391  [1.00000000000, -179.99999999998, 125.99999999999],
392  [1.00000000000, -0.00000000002, 162.00000000000],
393  [1.00000000000, 179.99999999999, 161.99999999999]
394  ],
395  [
396  [13,16,10,4,7],
397  [0,2,7,4],
398  [1,0,4],
399  [5,1,4,10],
400  [11,5,10],
401  [17,11,10,16],
402  [19,17,16],
403  [18,19,16,13],
404  [14,18,13],
405  [8,14,13,7],
406  [2,8,7],
407  [9,15,12,6,3],
408  [2,0,3,6],
409  [8,2,6],
410  [14,8,6,12],
411  [18,14,12],
412  [19,18,12,15],
413  [17,19,15],
414  [11,17,15,9],
415  [5,11,9],
416  [1,5,9,3],
417  [0,1,3]
418  ],
419  [
420  [0,1],
421  [0,2],
422  [0,3],
423  [0,4],
424  [1,3],
425  [1,4],
426  [1,5],
427  [2,6],
428  [2,7],
429  [2,8],
430  [3,6],
431  [3,9],
432  [4,7],
433  [4,10],
434  [5,9],
435  [5,10],
436  [5,11],
437  [6,8],
438  [6,12],
439  [7,8],
440  [7,13],
441  [8,14],
442  [9,11],
443  [9,15],
444  [10,11],
445  [10,16],
446  [11,17],
447  [12,14],
448  [12,15],
449  [12,18],
450  [13,14],
451  [13,16],
452  [13,18],
453  [14,18],
454  [15,17],
455  [15,19],
456  [16,17],
457  [16,19],
458  [17,19],
459  [18,19]
460  ]
461  ],
462  [
463  "square_cupola",
464  "Square Cupola",
465  "J4",
466  "cupolas",
467  "Polyhedron Database #48",
468  [
469  [-0.90920355930, -0.17753303803, -0.37660444522],
470  [-0.90920355930, -0.17753303803, 0.37660444522],
471  [-0.37660444522, 0.35506607605, -0.37660444522],
472  [-0.37660444522, 0.35506607605, 0.37660444522],
473  [-0.37660444522, -0.17753303803, -0.90920355930],
474  [-0.37660444522, -0.17753303803, 0.90920355930],
475  [ 0.37660444522, 0.35506607605, -0.37660444522],
476  [ 0.37660444522, 0.35506607605, 0.37660444522],
477  [ 0.37660444522, -0.17753303803, -0.90920355930],
478  [ 0.37660444522, -0.17753303803, 0.90920355930],
479  [ 0.90920355930, -0.17753303803, -0.37660444522],
480  [ 0.90920355930, -0.17753303803, 0.37660444522]
481  ],
482  [
483  [1.00000000000, -168.95132206550, 112.12351211134],
484  [1.00000000000, -168.95132206551, 67.87648788864],
485  [0.64010447170, 136.68614334171, 126.03989343030],
486  [0.64010447170, 136.68614334171, 53.96010656970],
487  [1.00000000000, -154.76059817930, 155.39552032235],
488  [1.00000000000, -154.76059817931, 24.60447967764],
489  [0.64010447170, 43.31385665828, 126.03989343029],
490  [0.64010447170, 43.31385665828, 53.96010656970],
491  [1.00000000000, -25.23940182068, 155.39552032235],
492  [1.00000000000, -25.23940182066, 24.60447967763],
493  [1.00000000000, -11.04867793448, 112.12351211135],
494  [1.00000000000, -11.04867793448, 67.87648788864]
495  ],
496  [
497  [0,1,5,9,11,10,8,4],
498  [6,7,3,2],
499  [1,0,2,3],
500  [5,1,3],
501  [9,5,3,7],
502  [11,9,7],
503  [10,11,7,6],
504  [8,10,6],
505  [4,8,6,2],
506  [0,4,2]
507  ],
508  [
509  [0,1],
510  [0,2],
511  [0,4],
512  [1,3],
513  [1,5],
514  [2,3],
515  [2,4],
516  [2,6],
517  [3,5],
518  [3,7],
519  [4,8],
520  [5,9],
521  [6,7],
522  [6,8],
523  [6,10],
524  [7,9],
525  [7,11],
526  [8,10],
527  [9,11],
528  [10,11]
529  ]
530  ],
531  [
532  "square_gyrobicupola",
533  "Square Gyrobicupola",
534  "J29",
535  "cupolas",
536  "Polyhedron Database #73",
537  [
538  [ 0.38268343237, 0.00000000000, 0.92387953251],
539  [-0.38268343237, -0.00000000000, 0.92387953251],
540  [ 0.92387953251, 0.00000000000, 0.38268343237],
541  [ 0.38268343237, 0.54119610015, 0.38268343237],
542  [ 0.00000000000, -0.54119610015, 0.54119610015],
543  [-0.38268343237, 0.54119610015, 0.38268343237],
544  [-0.92387953251, -0.00000000000, 0.38268343237],
545  [ 0.54119610015, -0.54119610015, -0.00000000000],
546  [ 0.92387953251, 0.00000000000, -0.38268343237],
547  [ 0.38268343237, 0.54119610015, -0.38268343237],
548  [-0.54119610015, -0.54119610015, 0.00000000000],
549  [-0.38268343237, 0.54119610015, -0.38268343237],
550  [ 0.00000000000, -0.54119610015, -0.54119610015],
551  [-0.92387953251, -0.00000000000, -0.38268343237],
552  [ 0.38268343237, 0.00000000000, -0.92387953251],
553  [-0.38268343237, 0.00000000000, -0.92387953251]
554  ],
555  [
556  [1.00000000000, 0.00000000000, 22.50000000000],
557  [1.00000000000, -179.99999999997, 22.49999999999],
558  [1.00000000000, 0.00000000001, 67.50000000000],
559  [0.76536686473, 54.73561031725, 60.00000000000],
560  [0.76536686473, -89.99999999998, 45.00000000000],
561  [0.76536686473, 125.26438968275, 60.00000000000],
562  [1.00000000000, -179.99999999998, 67.49999999999],
563  [0.76536686473, -44.99999999999, 89.99999999999],
564  [1.00000000000, 0.00000000001, 112.50000000000],
565  [0.76536686473, 54.73561031725, 119.99999999999],
566  [0.76536686473, -134.99999999999, 89.99999999999],
567  [0.76536686473, 125.26438968275, 119.99999999999],
568  [0.76536686473, -89.99999999999, 135.00000000000],
569  [1.00000000000, -179.99999999998, 112.49999999999],
570  [1.00000000000, 0.00000000001, 157.50000000000],
571  [1.00000000000, 179.99999999999, 157.49999999999]
572  ],
573  [
574  [12,10,4,7],
575  [0,2,7,4],
576  [1,0,4],
577  [6,1,4,10],
578  [13,6,10],
579  [15,13,10,12],
580  [14,15,12],
581  [8,14,12,7],
582  [2,8,7],
583  [11,9,3,5],
584  [0,1,5,3],
585  [2,0,3],
586  [8,2,3,9],
587  [14,8,9],
588  [15,14,9,11],
589  [13,15,11],
590  [6,13,11,5],
591  [1,6,5]
592  ],
593  [
594  [0,1],
595  [0,2],
596  [0,3],
597  [0,4],
598  [1,4],
599  [1,5],
600  [1,6],
601  [2,3],
602  [2,7],
603  [2,8],
604  [3,5],
605  [3,9],
606  [4,7],
607  [4,10],
608  [5,6],
609  [5,11],
610  [6,10],
611  [6,13],
612  [7,8],
613  [7,12],
614  [8,9],
615  [8,14],
616  [9,11],
617  [9,14],
618  [10,12],
619  [10,13],
620  [11,13],
621  [11,15],
622  [12,14],
623  [12,15],
624  [13,15],
625  [14,15]
626  ]
627  ],
628  [
629  "square_orthobicupola",
630  "square orthobicupola",
631  "J28",
632  "cupolas",
633  "Polyhedron Database #72",
634  [
635  [ 0.38268343237, 0.00000000000, -0.92387953251],
636  [-0.38268343237, 0.00000000000, -0.92387953251],
637  [ 0.92387953251, -0.00000000000, -0.38268343237],
638  [ 0.38268343237, -0.54119610015, -0.38268343237],
639  [ 0.38268343237, 0.54119610015, -0.38268343237],
640  [-0.38268343237, -0.54119610015, -0.38268343237],
641  [-0.38268343237, 0.54119610015, -0.38268343237],
642  [-0.92387953251, 0.00000000000, -0.38268343237],
643  [ 0.92387953251, 0.00000000000, 0.38268343237],
644  [ 0.38268343237, -0.54119610015, 0.38268343237],
645  [ 0.38268343237, 0.54119610015, 0.38268343237],
646  [-0.38268343237, -0.54119610015, 0.38268343237],
647  [-0.38268343237, 0.54119610015, 0.38268343237],
648  [-0.92387953251, 0.00000000000, 0.38268343237],
649  [ 0.38268343237, 0.00000000000, 0.92387953251],
650  [-0.38268343237, 0.00000000000, 0.92387953251]
651  ],
652  [
653  [1.00000000000, 0.00000000000, 157.49999999999],
654  [1.00000000000, 179.99999999999, 157.49999999999],
655  [1.00000000000, -0.00000000001, 112.49999999999],
656  [0.76536686473, -54.73561031725, 119.99999999999],
657  [0.76536686473, 54.73561031725, 119.99999999999],
658  [0.76536686473, -125.26438968274, 119.99999999999],
659  [0.76536686473, 125.26438968274, 119.99999999999],
660  [1.00000000000, 179.99999999999, 112.49999999999],
661  [1.00000000000, 0.00000000000, 67.50000000000],
662  [0.76536686473, -54.73561031725, 60.00000000000],
663  [0.76536686473, 54.73561031725, 60.00000000000],
664  [0.76536686473, -125.26438968274, 59.99999999999],
665  [0.76536686473, 125.26438968274, 59.99999999999],
666  [1.00000000000, 179.99999999998, 67.50000000000],
667  [1.00000000000, 0.00000000000, 22.50000000000],
668  [1.00000000000, 179.99999999999, 22.50000000000]
669  ],
670  [
671  [11,9,3,5],
672  [0,1,5,3],
673  [2,0,3],
674  [8,2,3,9],
675  [14,8,9],
676  [15,14,9,11],
677  [13,15,11],
678  [7,13,11,5],
679  [1,7,5],
680  [10,12,6,4],
681  [1,0,4,6],
682  [7,1,6],
683  [13,7,6,12],
684  [15,13,12],
685  [14,15,12,10],
686  [8,14,10],
687  [2,8,10,4],
688  [0,2,4]
689  ],
690  [
691  [0,1],
692  [0,2],
693  [0,3],
694  [0,4],
695  [1,5],
696  [1,6],
697  [1,7],
698  [2,3],
699  [2,4],
700  [2,8],
701  [3,5],
702  [3,9],
703  [4,6],
704  [4,10],
705  [5,7],
706  [5,11],
707  [6,7],
708  [6,12],
709  [7,13],
710  [8,9],
711  [8,10],
712  [8,14],
713  [9,11],
714  [9,14],
715  [10,12],
716  [10,14],
717  [11,13],
718  [11,15],
719  [12,13],
720  [12,15],
721  [13,15],
722  [14,15]
723  ]
724  ],
725  [
726  "triangular_cupola",
727  "Triangular Cupola",
728  "J3",
729  "cupolas",
730  "Polyhedron Database #47",
731  [
732  [ 0.48245064068, -0.26261286572, 0.83562902180],
733  [ 0.96490128135, -0.26261286572, 0.00000000000],
734  [ 0.48245064068, 0.52522573144, 0.27854300727],
735  [-0.48245064068, -0.26261286572, 0.83562902180],
736  [-0.48245064068, 0.52522573144, 0.27854300727],
737  [ 0.48245064068, -0.26261286572, -0.83562902180],
738  [ 0.00000000000, 0.52522573144, -0.55708601453],
739  [-0.96490128135, -0.26261286572, -0.00000000000],
740  [-0.48245064068, -0.26261286572, -0.83562902180]
741  ],
742  [
743  [1.00000000000, -28.56082521782, 33.31860684000],
744  [1.00000000000, -15.22515701068, 89.99999999999],
745  [0.76564149349, 47.43070269790, 68.66603725294],
746  [1.00000000000, -151.43917478219, 33.31860684000],
747  [0.76564149349, 132.56929730209, 68.66603725295],
748  [1.00000000000, -28.56082521781, 146.68139315999],
749  [0.76564149349, 89.99999999999, 136.68614334171],
750  [1.00000000000, -164.77484298931, 90.00000000000],
751  [1.00000000000, -151.43917478217, 146.68139315999]
752  ],
753  [
754  [1,5,8,7,3,0],
755  [4,6,2],
756  [5,1,2,6],
757  [8,5,6],
758  [7,8,6,4],
759  [3,7,4],
760  [0,3,4,2],
761  [1,0,2]
762  ],
763  [
764  [0,1],
765  [0,2],
766  [0,3],
767  [1,2],
768  [1,5],
769  [2,4],
770  [2,6],
771  [3,4],
772  [3,7],
773  [4,6],
774  [4,7],
775  [5,6],
776  [5,8],
777  [6,8],
778  [7,8]
779  ]
780  ],
781  [
782  "triangular_gyrobicupola",
783  "Triangular Gyrobicupola",
784  "Cuboctahedron",
785  "cupolas",
786  "Exact Mathematics",
787  [
788  [ 0.00000000000, -0.81649658093, -0.57735026919],
789  [-0.50000000000, -0.81649658093, 0.28867513459],
790  [-1.00000000000, 0.00000000000, -0.00000000000],
791  [-0.50000000000, 0.00000000000, -0.86602540378],
792  [ 0.50000000000, -0.81649658093, 0.28867513459],
793  [-0.50000000000, -0.00000000000, 0.86602540378],
794  [-0.50000000000, 0.81649658093, -0.28867513459],
795  [ 0.50000000000, 0.00000000000, -0.86602540378],
796  [ 1.00000000000, 0.00000000000, -0.00000000000],
797  [ 0.50000000000, -0.00000000000, 0.86602540378],
798  [ 0.00000000000, 0.81649658093, 0.57735026919],
799  [ 0.50000000000, 0.81649658093, -0.28867513459]
800  ],
801  [
802  [1.00000000000, -89.99999999999, 125.26438968275],
803  [1.00000000000, -121.48215410529, 73.22134511904],
804  [1.00000000000, 179.99999999999, 89.99999999999],
805  [1.00000000000, 179.99999999998, 149.99999999999],
806  [1.00000000000, -58.51784589470, 73.22134511904],
807  [1.00000000000, -179.99999999998, 30.00000000000],
808  [1.00000000000, 121.48215410529, 106.77865488095],
809  [1.00000000000, 0.00000000001, 149.99999999999],
810  [1.00000000000, 0.00000000000, 89.99999999999],
811  [1.00000000000, -0.00000000001, 30.00000000000],
812  [1.00000000000, 89.99999999999, 54.73561031724],
813  [1.00000000000, 58.51784589470, 106.77865488095]
814  ],
815  [
816  [3,2,1,0],
817  [0,4,8,7],
818  [1,5,9,4],
819  [2,6,10,5],
820  [3,7,11,6],
821  [8,9,10,11],
822  [0,1,4],
823  [1,2,5],
824  [2,3,6],
825  [3,0,7],
826  [4,9,8],
827  [5,10,9],
828  [6,11,10],
829  [7,8,11]
830  ],
831  [
832  [0,1],
833  [1,2],
834  [2,3],
835  [3,0],
836  [4,0],
837  [0,7],
838  [7,8],
839  [8,4],
840  [5,1],
841  [1,4],
842  [4,9],
843  [9,5],
844  [6,2],
845  [2,5],
846  [5,10],
847  [10,6],
848  [7,3],
849  [3,6],
850  [6,11],
851  [11,7],
852  [8,9],
853  [9,10],
854  [10,11],
855  [11,8]
856  ]
857  ],
858  [
859  "triangular_orthobicupola",
860  "Triangular Orthobicupola",
861  "J27",
862  "cupolas",
863  "Polyhedron Database #71",
864  [
865  [-0.50000000000, -0.00000000000, -0.86602540378],
866  [ 0.50000000000, 0.00000000000, -0.86602540378],
867  [ 0.00000000000, 0.81649658093, -0.57735026919],
868  [ 0.00000000000, -0.81649658093, -0.57735026919],
869  [-1.00000000000, -0.00000000000, -0.00000000000],
870  [-0.50000000000, 0.81649658093, 0.28867513459],
871  [-0.50000000000, -0.81649658093, 0.28867513459],
872  [ 1.00000000000, 0.00000000000, 0.00000000000],
873  [ 0.50000000000, 0.81649658093, 0.28867513459],
874  [ 0.50000000000, -0.81649658093, 0.28867513459],
875  [-0.50000000000, 0.00000000000, 0.86602540378],
876  [ 0.50000000000, 0.00000000000, 0.86602540378]
877  ],
878  [
879  [1.00000000000, -179.99999999998, 150.00000000000],
880  [1.00000000000, 0.00000000000, 149.99999999998],
881  [1.00000000000, 89.99999999999, 125.26438968275],
882  [1.00000000000, -89.99999999999, 125.26438968275],
883  [1.00000000000, -179.99999999998, 89.99999999999],
884  [1.00000000000, 121.48215410529, 73.22134511904],
885  [1.00000000000, -121.48215410529, 73.22134511904],
886  [1.00000000000, 0.00000000001, 89.99999999999],
887  [1.00000000000, 58.51784589470, 73.22134511903],
888  [1.00000000000, -58.51784589470, 73.22134511903],
889  [1.00000000000, 179.99999999999, 30.00000000000],
890  [1.00000000000, 0.00000000001, 29.99999999999]
891  ],
892  [
893  [8,5,2],
894  [4,0,2,5],
895  [10,4,5],
896  [11,10,5,8],
897  [7,11,8],
898  [1,7,8,2],
899  [0,1,2],
900  [9,3,6],
901  [0,4,6,3],
902  [1,0,3],
903  [7,1,3,9],
904  [11,7,9],
905  [10,11,9,6],
906  [4,10,6]
907  ],
908  [
909  [0,1],
910  [0,2],
911  [0,3],
912  [0,4],
913  [1,2],
914  [1,3],
915  [1,7],
916  [2,5],
917  [2,8],
918  [3,6],
919  [3,9],
920  [4,5],
921  [4,6],
922  [4,10],
923  [5,8],
924  [5,10],
925  [6,9],
926  [6,10],
927  [7,8],
928  [7,9],
929  [7,11],
930  [8,11],
931  [9,11],
932  [10,11]
933  ]
934  ]
935 ];
936 
937 //! @}
938 
939 //----------------------------------------------------------------------------//
940 // openscad-amu auxiliary scripts
941 //----------------------------------------------------------------------------//
942 
943 /*
944 BEGIN_SCOPE db;
945 BEGIN_SCOPE autostat;
946  BEGIN_OPENSCAD;
947  include <omdl-base.scad>;
948  include <database/geometry/polyhedra/cupolas.scad>;
949 
950  fs = "^";
951 
952  tc = dtc_polyhedra_cupolas;
953  tr = dtr_polyhedra_cupolas;
954 
955  ids = table_get_row_ids(tr);
956 
957  echo
958  (
959  str
960  (
961  "no.", fs, "id", fs, "other name", fs,
962  "vertices", fs, "faces", fs, "edges",
963 
964  fs, "face-verticies",
965  fs, "face-angles",
966  fs, "edge-lengths",
967  fs, "edge-angles"
968  )
969  );
970 
971  for ( id = ids )
972  {
973  i = first(find(id, ids, c=1))+1;
974 
975  n = table_get_value(tr, tc, id, "n");
976  o = table_get_value(tr, tc, id, "o");
977  g = table_get_value(tr, tc, id, "g");
978  d = table_get_value(tr, tc, id, "d");
979 
980  c = table_get_value(tr, tc, id, "c");
981  s = table_get_value(tr, tc, id, "s");
982  f = table_get_value(tr, tc, id, "f");
983  e = table_get_value(tr, tc, id, "e");
984 
985  fo = is_empty(o) ? "-" : o;
986 
987  echo
988  (
989  str
990  (
991  i, fs, id, fs, fo, fs,
992  len(c), fs, len(f), fs, len(e),
993 
994  fs, histogram(sort_q(polytope_face_vertex_counts(f)), m=9),
995  fs, histogram(sort_q(round_d(polytope_face_angles(c, f), d=1)), m=9),
996  fs, histogram(sort_q(round_s(polytope_edge_lengths(c, e), d=3)), m=9),
997  fs, histogram(sort_q(round_d(polytope_edge_angles(c, f), d=1)), m=9),
998 
999  fs
1000  )
1001  );
1002  }
1003  END_OPENSCAD;
1004 
1005  BEGIN_MFSCRIPT;
1006  include --path "${INCLUDE_PATH}" {var_init,var_gen_term}.mfs;
1007  include --path "${INCLUDE_PATH}" scr_make_mf.mfs;
1008  END_MFSCRIPT;
1009 END_SCOPE;
1010 END_SCOPE;
1011 */
1012 
1013 /*
1014 BEGIN_SCOPE db;
1015 BEGIN_SCOPE dim;
1016  BEGIN_OPENSCAD;
1017  include <omdl-base.scad>;
1018  include <units/coordinate.scad>;
1019  include <tools/common/polytope.scad>;
1020  include <database/geometry/polyhedra/cupolas.scad>;
1021 
1022  config = 0;
1023 
1024  tc = dtc_polyhedra_cupolas;
1025  tr = dtr_polyhedra_cupolas;
1026 
1027  id = "default";
1028  sr = 100;
1029 
1030  pv = table_get_value(tr, tc, id, "c");
1031  pf = table_get_value(tr, tc, id, "f");
1032  pe = table_get_value(tr, tc, id, "e");
1033 
1034  sv = coordinate_scale3d_csc(pv, sr);
1035 
1036  if (config == 0) // png preview
1037  {
1038  $fn = 25;
1039 
1040  %polyhedron(sv, pf);
1041 
1042  polytope_frame(sv, pf, pe)
1043  {
1044  circle(r = sr / 25);
1045  color("lightblue")
1046  sphere(r = sr / 25 * (1 + 1/2));
1047  }
1048  }
1049 
1050  if (config == 1) // stl model
1051  {
1052  polyhedron(sv, pf);
1053  }
1054  END_OPENSCAD;
1055 
1056  BEGIN_MFSCRIPT;
1057  include --path "${INCLUDE_PATH}" {var_init,var_gen_png2eps}.mfs;
1058 
1059  views name "views" views "diag";
1060  defines name "ids" define "id"
1061  strings
1062  "
1063  pentagonal_cupola
1064  pentagonal_gyrobicupola
1065  pentagonal_orthobicupola
1066  square_cupola
1067  square_gyrobicupola
1068  square_orthobicupola
1069  triangular_cupola
1070  triangular_gyrobicupola
1071  triangular_orthobicupola
1072  ";
1073  variables add_opts_combine "views ids";
1074  variables add_opts "-D config=0 --viewall --autocenter --view=axes";
1075 
1076  include --path "${INCLUDE_PATH}" scr_make_mf_begin.mfs;
1077  include --path "${INCLUDE_PATH}" scr_make_mf_add_ext.mfs;
1078 
1079  include --path "${INCLUDE_PATH}" var_gen_stl.mfs;
1080  variables add_opts_combine "ids";
1081  variables add_opts "-D config=1";
1082 
1083  include --path "${INCLUDE_PATH}" scr_make_mf_add_ext.mfs;
1084  include --path "${INCLUDE_PATH}" scr_make_mf_end.mfs;
1085  END_MFSCRIPT;
1086 END_SCOPE;
1087 END_SCOPE;
1088 */
1089 
1090 //----------------------------------------------------------------------------//
1091 // end of file
1092 //----------------------------------------------------------------------------//
dtc_polyhedra_cupolas
dtc_polyhedra_cupolas
Definition: cupolas.scad:197
dtr_polyhedra_cupolas
dtr_polyhedra_cupolas
Definition: cupolas.scad:212