omdl  v0.9.8
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/align.scad>;
1020  include <tools/polytope.scad>;
1021  include <database/geometry/polyhedra/cupolas.scad>;
1022 
1023  config = 0;
1024 
1025  tc = dtc_polyhedra_cupolas;
1026  tr = dtr_polyhedra_cupolas;
1027 
1028  id = "default";
1029  sr = 100;
1030 
1031  pv = table_get_value(tr, tc, id, "c");
1032  pf = table_get_value(tr, tc, id, "f");
1033  pe = table_get_value(tr, tc, id, "e");
1034 
1035  sv = coordinate_scale3d_csc(pv, sr);
1036 
1037  if (config == 0) // png preview
1038  {
1039  $fn = 25;
1040 
1041  %polyhedron(sv, pf);
1042 
1043  polytope_frame(sv, pf, pe)
1044  {
1045  circle(r = sr / 25);
1046  color("lightblue")
1047  sphere(r = sr / 25 * (1 + 1/2));
1048  }
1049  }
1050 
1051  if (config == 1) // stl model
1052  {
1053  polyhedron(sv, pf);
1054  }
1055  END_OPENSCAD;
1056 
1057  BEGIN_MFSCRIPT;
1058  include --path "${INCLUDE_PATH}" {var_init,var_gen_png2eps}.mfs;
1059 
1060  views name "views" views "diag";
1061  defines name "ids" define "id"
1062  strings
1063  "
1064  pentagonal_cupola
1065  pentagonal_gyrobicupola
1066  pentagonal_orthobicupola
1067  square_cupola
1068  square_gyrobicupola
1069  square_orthobicupola
1070  triangular_cupola
1071  triangular_gyrobicupola
1072  triangular_orthobicupola
1073  ";
1074  variables add_opts_combine "views ids";
1075  variables add_opts "-D config=0 --viewall --autocenter --view=axes";
1076 
1077  include --path "${INCLUDE_PATH}" scr_make_mf_begin.mfs;
1078  include --path "${INCLUDE_PATH}" scr_make_mf_add_ext.mfs;
1079 
1080  include --path "${INCLUDE_PATH}" var_gen_stl.mfs;
1081  variables add_opts_combine "ids";
1082  variables add_opts "-D config=1";
1083 
1084  include --path "${INCLUDE_PATH}" scr_make_mf_add_ext.mfs;
1085  include --path "${INCLUDE_PATH}" scr_make_mf_end.mfs;
1086  END_MFSCRIPT;
1087 END_SCOPE;
1088 END_SCOPE;
1089 */
1090 
1091 //----------------------------------------------------------------------------//
1092 // end of file
1093 //----------------------------------------------------------------------------//
dtc_polyhedra_cupolas
dtc_polyhedra_cupolas
Definition: cupolas.scad:197
dtr_polyhedra_cupolas
dtr_polyhedra_cupolas
Definition: cupolas.scad:212