omdl  v0.6.1
OpenSCAD Mechanical Design Library
cupolas.scad
Go to the documentation of this file.
1 //! Table of polyhedra data group: \c cupolas
2 /***************************************************************************//**
3  \file cupolas.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: cupolas ###
64 
65  \amu_define caption (cupolas)
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 (cupolas)
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="${cell_num}"
94  )
95  \endlatexonly
96 
97  \amu_shell data
98  (
99  "grep -Po 'ECHO: \"\K[^\"]*' build/csg/cupolas_db_autostat.log" --rmnl
100  )
101  \amu_shell columns ("echo '${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 cupolas polyhedra data table columns definition.
113 //! \hideinitializer
114 dtc_polyhedra_cupolas =
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 cupolas polyhedra data table rows.
128 //! \hideinitializer
129 dtr_polyhedra_cupolas =
130 [
131  [
132  "pentagonal_cupola",
133  "Pentagonal Cupola",
134  "J5",
135  "cupolas",
136  "Polyhedron Database #49",
137  [
138  [ 0.30722035250, -0.10767686506, -0.94552702116],
139  [-0.30722035250, -0.10767686506, -0.94552702116],
140  [ 0.80431332487, -0.10767686506, -0.58436783636],
141  [ 0.30722035250, 0.21535373011, -0.42285253878],
142  [-0.30722035250, 0.21535373011, -0.42285253878],
143  [-0.80431332487, -0.10767686506, -0.58436783636],
144  [ 0.99418594475, -0.10767686506, 0.00000000000],
145  [ 0.49709297237, 0.21535373011, 0.16151529758],
146  [-0.49709297237, 0.21535373011, 0.16151529758],
147  [-0.99418594475, -0.10767686506, -0.00000000000],
148  [ 0.00000000000, 0.21535373011, 0.52267448238],
149  [ 0.80431332487, -0.10767686506, 0.58436783636],
150  [-0.80431332487, -0.10767686506, 0.58436783636],
151  [ 0.30722035250, -0.10767686506, 0.94552702116],
152  [-0.30722035250, -0.10767686506, 0.94552702116]
153  ],
154  [
155  [1.00000000000, -19.31492121303, 161.00148636537],
156  [1.00000000000, -160.68507878696, 161.00148636537],
157  [1.00000000000, -7.62509363515, 125.75834309459],
158  [0.56530155104, 35.02948816948, 138.41849317790],
159  [0.56530155104, 144.97051183050, 138.41849317790],
160  [1.00000000000, -172.37490636484, 125.75834309458],
161  [1.00000000000, -6.18141426338, 89.99999999999],
162  [0.56530155104, 23.42352770491, 73.39839025197],
163  [0.56530155104, 156.57647229507, 73.39839025196],
164  [1.00000000000, -173.81858573662, 89.99999999999],
165  [0.56530155104, 89.99999999997, 22.39277092895],
166  [1.00000000000, -7.62509363516, 54.24165690541],
167  [1.00000000000, -172.37490636484, 54.24165690540],
168  [1.00000000000, -19.31492121306, 18.99851363462],
169  [1.00000000000, -160.68507878694, 18.99851363462]
170  ],
171  [
172  [0,1,5,9,12,14,13,11,6,2],
173  [7,10,8,4,3],
174  [1,0,3,4],
175  [5,1,4],
176  [9,5,4,8],
177  [12,9,8],
178  [14,12,8,10],
179  [13,14,10],
180  [11,13,10,7],
181  [6,11,7],
182  [2,6,7,3],
183  [0,2,3]
184  ],
185  [
186  [0,1],
187  [0,2],
188  [0,3],
189  [1,4],
190  [1,5],
191  [2,3],
192  [2,6],
193  [3,4],
194  [3,7],
195  [4,5],
196  [4,8],
197  [5,9],
198  [6,7],
199  [6,11],
200  [7,10],
201  [7,11],
202  [8,9],
203  [8,10],
204  [8,12],
205  [9,12],
206  [10,13],
207  [10,14],
208  [11,13],
209  [12,14],
210  [13,14]
211  ]
212  ],
213  [
214  "pentagonal_gyrobicupola",
215  "Pentagonal Gyrobicupola",
216  "J31",
217  "cupolas",
218  "Polyhedron Database #75",
219  [
220  [ 0.80901699437, 0.00000000000, 0.58778525229],
221  [ 0.30901699437, 0.00000000000, 0.95105651630],
222  [ 1.00000000000, 0.00000000000, -0.00000000000],
223  [-0.30901699437, 0.00000000000, 0.95105651630],
224  [ 0.30901699438, -0.32491969623, 0.42532540418],
225  [ 0.50000000000, 0.32491969623, 0.16245984812],
226  [ 0.00000000000, 0.32491969623, 0.52573111212],
227  [ 0.50000000000, -0.32491969623, -0.16245984812],
228  [-0.30901699437, -0.32491969623, 0.42532540418],
229  [ 0.80901699437, 0.00000000000, -0.58778525229],
230  [-0.80901699437, 0.00000000000, 0.58778525229],
231  [ 0.30901699437, 0.32491969623, -0.42532540418],
232  [-0.50000000000, 0.32491969623, 0.16245984812],
233  [-0.00000000000, -0.32491969623, -0.52573111212],
234  [-0.50000000000, -0.32491969623, -0.16245984812],
235  [-0.30901699438, 0.32491969623, -0.42532540418],
236  [ 0.30901699437, -0.00000000000, -0.95105651630],
237  [-1.00000000000, 0.00000000000, 0.00000000000],
238  [-0.30901699437, -0.00000000000, -0.95105651630],
239  [-0.80901699437, -0.00000000000, -0.58778525229]
240  ],
241  [
242  [1.00000000000, 0.00000000001, 54.00000000000],
243  [1.00000000000, 0.00000000002, 18.00000000000],
244  [1.00000000000, 0.00000000000, 89.99999999999],
245  [1.00000000000, 179.99999999997, 18.00000000000],
246  [0.61803398875, -46.43699940041, 46.51292225447],
247  [0.61803398875, 33.01739809414, 74.75983771732],
248  [0.61803398875, 89.99999999999, 31.71747441146],
249  [0.61803398875, -33.01739809415, 105.24016228267],
250  [0.61803398875, -133.56300059956, 46.51292225447],
251  [1.00000000000, 0.00000000000, 125.99999999999],
252  [1.00000000000, 179.99999999999, 54.00000000000],
253  [0.61803398875, 46.43699940043, 133.48707774552],
254  [0.61803398875, 146.98260190584, 74.75983771731],
255  [0.61803398875, -89.99999999999, 148.28252558853],
256  [0.61803398875, -146.98260190585, 105.24016228267],
257  [0.61803398875, 133.56300059958, 133.48707774551],
258  [1.00000000000, -0.00000000002, 161.99999999999],
259  [1.00000000000, 179.99999999999, 89.99999999999],
260  [1.00000000000, -179.99999999997, 161.99999999999],
261  [1.00000000000, -179.99999999998, 125.99999999999]
262  ],
263  [
264  [13,14,8,4,7],
265  [0,2,7,4],
266  [1,0,4],
267  [3,1,4,8],
268  [10,3,8],
269  [17,10,8,14],
270  [19,17,14],
271  [18,19,14,13],
272  [16,18,13],
273  [9,16,13,7],
274  [2,9,7],
275  [12,15,11,5,6],
276  [0,1,6,5],
277  [2,0,5],
278  [9,2,5,11],
279  [16,9,11],
280  [18,16,11,15],
281  [19,18,15],
282  [17,19,15,12],
283  [10,17,12],
284  [3,10,12,6],
285  [1,3,6]
286  ],
287  [
288  [0,1],
289  [0,2],
290  [0,4],
291  [0,5],
292  [1,3],
293  [1,4],
294  [1,6],
295  [2,5],
296  [2,7],
297  [2,9],
298  [3,6],
299  [3,8],
300  [3,10],
301  [4,7],
302  [4,8],
303  [5,6],
304  [5,11],
305  [6,12],
306  [7,9],
307  [7,13],
308  [8,10],
309  [8,14],
310  [9,11],
311  [9,16],
312  [10,12],
313  [10,17],
314  [11,15],
315  [11,16],
316  [12,15],
317  [12,17],
318  [13,14],
319  [13,16],
320  [13,18],
321  [14,17],
322  [14,19],
323  [15,18],
324  [15,19],
325  [16,18],
326  [17,19],
327  [18,19]
328  ]
329  ],
330  [
331  "pentagonal_orthobicupola",
332  "Pentagonal Orthobicupola",
333  "J30",
334  "cupolas",
335  "Polyhedron Database #74",
336  [
337  [ 0.30901699438, 0.00000000000, 0.95105651630],
338  [-0.30901699437, 0.00000000000, 0.95105651630],
339  [ 0.80901699437, 0.00000000000, 0.58778525229],
340  [ 0.00000000000, 0.32491969623, 0.52573111212],
341  [-0.00000000000, -0.32491969623, 0.52573111212],
342  [-0.80901699437, 0.00000000000, 0.58778525229],
343  [ 0.50000000000, 0.32491969623, 0.16245984812],
344  [ 0.50000000000, -0.32491969623, 0.16245984812],
345  [ 1.00000000000, 0.00000000000, -0.00000000000],
346  [-0.50000000000, 0.32491969623, 0.16245984812],
347  [-0.50000000000, -0.32491969623, 0.16245984812],
348  [-1.00000000000, 0.00000000000, 0.00000000000],
349  [ 0.30901699437, 0.32491969623, -0.42532540418],
350  [ 0.30901699437, -0.32491969623, -0.42532540418],
351  [ 0.80901699437, -0.00000000000, -0.58778525229],
352  [-0.30901699438, 0.32491969623, -0.42532540418],
353  [-0.30901699438, -0.32491969623, -0.42532540418],
354  [-0.80901699437, -0.00000000000, -0.58778525229],
355  [ 0.30901699437, -0.00000000000, -0.95105651630],
356  [-0.30901699438, 0.00000000000, -0.95105651630]
357  ],
358  [
359  [1.00000000000, 0.00000000000, 18.00000000000],
360  [1.00000000000, 179.99999999999, 17.99999999999],
361  [1.00000000000, 0.00000000001, 54.00000000000],
362  [0.61803398875, 89.99999999998, 31.71747441146],
363  [0.61803398875, -89.99999999999, 31.71747441146],
364  [1.00000000000, 179.99999999998, 53.99999999999],
365  [0.61803398875, 33.01739809414, 74.75983771732],
366  [0.61803398875, -33.01739809414, 74.75983771731],
367  [1.00000000000, 0.00000000000, 90.00000000000],
368  [0.61803398875, 146.98260190585, 74.75983771731],
369  [0.61803398875, -146.98260190585, 74.75983771731],
370  [1.00000000000, 179.99999999999, 89.99999999999],
371  [0.61803398875, 46.43699940043, 133.48707774551],
372  [0.61803398875, -46.43699940043, 133.48707774551],
373  [1.00000000000, -0.00000000001, 125.99999999999],
374  [0.61803398875, 133.56300059957, 133.48707774552],
375  [0.61803398875, -133.56300059957, 133.48707774551],
376  [1.00000000000, -179.99999999998, 125.99999999999],
377  [1.00000000000, -0.00000000002, 162.00000000000],
378  [1.00000000000, 179.99999999999, 161.99999999999]
379  ],
380  [
381  [13,16,10,4,7],
382  [0,2,7,4],
383  [1,0,4],
384  [5,1,4,10],
385  [11,5,10],
386  [17,11,10,16],
387  [19,17,16],
388  [18,19,16,13],
389  [14,18,13],
390  [8,14,13,7],
391  [2,8,7],
392  [9,15,12,6,3],
393  [2,0,3,6],
394  [8,2,6],
395  [14,8,6,12],
396  [18,14,12],
397  [19,18,12,15],
398  [17,19,15],
399  [11,17,15,9],
400  [5,11,9],
401  [1,5,9,3],
402  [0,1,3]
403  ],
404  [
405  [0,1],
406  [0,2],
407  [0,3],
408  [0,4],
409  [1,3],
410  [1,4],
411  [1,5],
412  [2,6],
413  [2,7],
414  [2,8],
415  [3,6],
416  [3,9],
417  [4,7],
418  [4,10],
419  [5,9],
420  [5,10],
421  [5,11],
422  [6,8],
423  [6,12],
424  [7,8],
425  [7,13],
426  [8,14],
427  [9,11],
428  [9,15],
429  [10,11],
430  [10,16],
431  [11,17],
432  [12,14],
433  [12,15],
434  [12,18],
435  [13,14],
436  [13,16],
437  [13,18],
438  [14,18],
439  [15,17],
440  [15,19],
441  [16,17],
442  [16,19],
443  [17,19],
444  [18,19]
445  ]
446  ],
447  [
448  "square_cupola",
449  "Square Cupola",
450  "J4",
451  "cupolas",
452  "Polyhedron Database #48",
453  [
454  [-0.90920355930, -0.17753303803, -0.37660444522],
455  [-0.90920355930, -0.17753303803, 0.37660444522],
456  [-0.37660444522, 0.35506607605, -0.37660444522],
457  [-0.37660444522, 0.35506607605, 0.37660444522],
458  [-0.37660444522, -0.17753303803, -0.90920355930],
459  [-0.37660444522, -0.17753303803, 0.90920355930],
460  [ 0.37660444522, 0.35506607605, -0.37660444522],
461  [ 0.37660444522, 0.35506607605, 0.37660444522],
462  [ 0.37660444522, -0.17753303803, -0.90920355930],
463  [ 0.37660444522, -0.17753303803, 0.90920355930],
464  [ 0.90920355930, -0.17753303803, -0.37660444522],
465  [ 0.90920355930, -0.17753303803, 0.37660444522]
466  ],
467  [
468  [1.00000000000, -168.95132206550, 112.12351211134],
469  [1.00000000000, -168.95132206551, 67.87648788864],
470  [0.64010447170, 136.68614334171, 126.03989343030],
471  [0.64010447170, 136.68614334171, 53.96010656970],
472  [1.00000000000, -154.76059817930, 155.39552032235],
473  [1.00000000000, -154.76059817931, 24.60447967764],
474  [0.64010447170, 43.31385665828, 126.03989343029],
475  [0.64010447170, 43.31385665828, 53.96010656970],
476  [1.00000000000, -25.23940182068, 155.39552032235],
477  [1.00000000000, -25.23940182066, 24.60447967763],
478  [1.00000000000, -11.04867793448, 112.12351211135],
479  [1.00000000000, -11.04867793448, 67.87648788864]
480  ],
481  [
482  [0,1,5,9,11,10,8,4],
483  [6,7,3,2],
484  [1,0,2,3],
485  [5,1,3],
486  [9,5,3,7],
487  [11,9,7],
488  [10,11,7,6],
489  [8,10,6],
490  [4,8,6,2],
491  [0,4,2]
492  ],
493  [
494  [0,1],
495  [0,2],
496  [0,4],
497  [1,3],
498  [1,5],
499  [2,3],
500  [2,4],
501  [2,6],
502  [3,5],
503  [3,7],
504  [4,8],
505  [5,9],
506  [6,7],
507  [6,8],
508  [6,10],
509  [7,9],
510  [7,11],
511  [8,10],
512  [9,11],
513  [10,11]
514  ]
515  ],
516  [
517  "square_gyrobicupola",
518  "Square Gyrobicupola",
519  "J29",
520  "cupolas",
521  "Polyhedron Database #73",
522  [
523  [ 0.38268343237, 0.00000000000, 0.92387953251],
524  [-0.38268343237, -0.00000000000, 0.92387953251],
525  [ 0.92387953251, 0.00000000000, 0.38268343237],
526  [ 0.38268343237, 0.54119610015, 0.38268343237],
527  [ 0.00000000000, -0.54119610015, 0.54119610015],
528  [-0.38268343237, 0.54119610015, 0.38268343237],
529  [-0.92387953251, -0.00000000000, 0.38268343237],
530  [ 0.54119610015, -0.54119610015, -0.00000000000],
531  [ 0.92387953251, 0.00000000000, -0.38268343237],
532  [ 0.38268343237, 0.54119610015, -0.38268343237],
533  [-0.54119610015, -0.54119610015, 0.00000000000],
534  [-0.38268343237, 0.54119610015, -0.38268343237],
535  [ 0.00000000000, -0.54119610015, -0.54119610015],
536  [-0.92387953251, -0.00000000000, -0.38268343237],
537  [ 0.38268343237, 0.00000000000, -0.92387953251],
538  [-0.38268343237, 0.00000000000, -0.92387953251]
539  ],
540  [
541  [1.00000000000, 0.00000000000, 22.50000000000],
542  [1.00000000000, -179.99999999997, 22.49999999999],
543  [1.00000000000, 0.00000000001, 67.50000000000],
544  [0.76536686473, 54.73561031725, 60.00000000000],
545  [0.76536686473, -89.99999999998, 45.00000000000],
546  [0.76536686473, 125.26438968275, 60.00000000000],
547  [1.00000000000, -179.99999999998, 67.49999999999],
548  [0.76536686473, -44.99999999999, 89.99999999999],
549  [1.00000000000, 0.00000000001, 112.50000000000],
550  [0.76536686473, 54.73561031725, 119.99999999999],
551  [0.76536686473, -134.99999999999, 89.99999999999],
552  [0.76536686473, 125.26438968275, 119.99999999999],
553  [0.76536686473, -89.99999999999, 135.00000000000],
554  [1.00000000000, -179.99999999998, 112.49999999999],
555  [1.00000000000, 0.00000000001, 157.50000000000],
556  [1.00000000000, 179.99999999999, 157.49999999999]
557  ],
558  [
559  [12,10,4,7],
560  [0,2,7,4],
561  [1,0,4],
562  [6,1,4,10],
563  [13,6,10],
564  [15,13,10,12],
565  [14,15,12],
566  [8,14,12,7],
567  [2,8,7],
568  [11,9,3,5],
569  [0,1,5,3],
570  [2,0,3],
571  [8,2,3,9],
572  [14,8,9],
573  [15,14,9,11],
574  [13,15,11],
575  [6,13,11,5],
576  [1,6,5]
577  ],
578  [
579  [0,1],
580  [0,2],
581  [0,3],
582  [0,4],
583  [1,4],
584  [1,5],
585  [1,6],
586  [2,3],
587  [2,7],
588  [2,8],
589  [3,5],
590  [3,9],
591  [4,7],
592  [4,10],
593  [5,6],
594  [5,11],
595  [6,10],
596  [6,13],
597  [7,8],
598  [7,12],
599  [8,9],
600  [8,14],
601  [9,11],
602  [9,14],
603  [10,12],
604  [10,13],
605  [11,13],
606  [11,15],
607  [12,14],
608  [12,15],
609  [13,15],
610  [14,15]
611  ]
612  ],
613  [
614  "square_orthobicupola",
615  "square orthobicupola",
616  "J28",
617  "cupolas",
618  "Polyhedron Database #72",
619  [
620  [ 0.38268343237, 0.00000000000, -0.92387953251],
621  [-0.38268343237, 0.00000000000, -0.92387953251],
622  [ 0.92387953251, -0.00000000000, -0.38268343237],
623  [ 0.38268343237, -0.54119610015, -0.38268343237],
624  [ 0.38268343237, 0.54119610015, -0.38268343237],
625  [-0.38268343237, -0.54119610015, -0.38268343237],
626  [-0.38268343237, 0.54119610015, -0.38268343237],
627  [-0.92387953251, 0.00000000000, -0.38268343237],
628  [ 0.92387953251, 0.00000000000, 0.38268343237],
629  [ 0.38268343237, -0.54119610015, 0.38268343237],
630  [ 0.38268343237, 0.54119610015, 0.38268343237],
631  [-0.38268343237, -0.54119610015, 0.38268343237],
632  [-0.38268343237, 0.54119610015, 0.38268343237],
633  [-0.92387953251, 0.00000000000, 0.38268343237],
634  [ 0.38268343237, 0.00000000000, 0.92387953251],
635  [-0.38268343237, 0.00000000000, 0.92387953251]
636  ],
637  [
638  [1.00000000000, 0.00000000000, 157.49999999999],
639  [1.00000000000, 179.99999999999, 157.49999999999],
640  [1.00000000000, -0.00000000001, 112.49999999999],
641  [0.76536686473, -54.73561031725, 119.99999999999],
642  [0.76536686473, 54.73561031725, 119.99999999999],
643  [0.76536686473, -125.26438968274, 119.99999999999],
644  [0.76536686473, 125.26438968274, 119.99999999999],
645  [1.00000000000, 179.99999999999, 112.49999999999],
646  [1.00000000000, 0.00000000000, 67.50000000000],
647  [0.76536686473, -54.73561031725, 60.00000000000],
648  [0.76536686473, 54.73561031725, 60.00000000000],
649  [0.76536686473, -125.26438968274, 59.99999999999],
650  [0.76536686473, 125.26438968274, 59.99999999999],
651  [1.00000000000, 179.99999999998, 67.50000000000],
652  [1.00000000000, 0.00000000000, 22.50000000000],
653  [1.00000000000, 179.99999999999, 22.50000000000]
654  ],
655  [
656  [11,9,3,5],
657  [0,1,5,3],
658  [2,0,3],
659  [8,2,3,9],
660  [14,8,9],
661  [15,14,9,11],
662  [13,15,11],
663  [7,13,11,5],
664  [1,7,5],
665  [10,12,6,4],
666  [1,0,4,6],
667  [7,1,6],
668  [13,7,6,12],
669  [15,13,12],
670  [14,15,12,10],
671  [8,14,10],
672  [2,8,10,4],
673  [0,2,4]
674  ],
675  [
676  [0,1],
677  [0,2],
678  [0,3],
679  [0,4],
680  [1,5],
681  [1,6],
682  [1,7],
683  [2,3],
684  [2,4],
685  [2,8],
686  [3,5],
687  [3,9],
688  [4,6],
689  [4,10],
690  [5,7],
691  [5,11],
692  [6,7],
693  [6,12],
694  [7,13],
695  [8,9],
696  [8,10],
697  [8,14],
698  [9,11],
699  [9,14],
700  [10,12],
701  [10,14],
702  [11,13],
703  [11,15],
704  [12,13],
705  [12,15],
706  [13,15],
707  [14,15]
708  ]
709  ],
710  [
711  "triangular_cupola",
712  "Triangular Cupola",
713  "J3",
714  "cupolas",
715  "Polyhedron Database #47",
716  [
717  [ 0.48245064068, -0.26261286572, 0.83562902180],
718  [ 0.96490128135, -0.26261286572, 0.00000000000],
719  [ 0.48245064068, 0.52522573144, 0.27854300727],
720  [-0.48245064068, -0.26261286572, 0.83562902180],
721  [-0.48245064068, 0.52522573144, 0.27854300727],
722  [ 0.48245064068, -0.26261286572, -0.83562902180],
723  [ 0.00000000000, 0.52522573144, -0.55708601453],
724  [-0.96490128135, -0.26261286572, -0.00000000000],
725  [-0.48245064068, -0.26261286572, -0.83562902180]
726  ],
727  [
728  [1.00000000000, -28.56082521782, 33.31860684000],
729  [1.00000000000, -15.22515701068, 89.99999999999],
730  [0.76564149349, 47.43070269790, 68.66603725294],
731  [1.00000000000, -151.43917478219, 33.31860684000],
732  [0.76564149349, 132.56929730209, 68.66603725295],
733  [1.00000000000, -28.56082521781, 146.68139315999],
734  [0.76564149349, 89.99999999999, 136.68614334171],
735  [1.00000000000, -164.77484298931, 90.00000000000],
736  [1.00000000000, -151.43917478217, 146.68139315999]
737  ],
738  [
739  [1,5,8,7,3,0],
740  [4,6,2],
741  [5,1,2,6],
742  [8,5,6],
743  [7,8,6,4],
744  [3,7,4],
745  [0,3,4,2],
746  [1,0,2]
747  ],
748  [
749  [0,1],
750  [0,2],
751  [0,3],
752  [1,2],
753  [1,5],
754  [2,4],
755  [2,6],
756  [3,4],
757  [3,7],
758  [4,6],
759  [4,7],
760  [5,6],
761  [5,8],
762  [6,8],
763  [7,8]
764  ]
765  ],
766  [
767  "triangular_gyrobicupola",
768  "Triangular Gyrobicupola",
769  "Cuboctahedron",
770  "cupolas",
771  "Exact Mathematics",
772  [
773  [ 0.00000000000, -0.81649658093, -0.57735026919],
774  [-0.50000000000, -0.81649658093, 0.28867513459],
775  [-1.00000000000, 0.00000000000, -0.00000000000],
776  [-0.50000000000, 0.00000000000, -0.86602540378],
777  [ 0.50000000000, -0.81649658093, 0.28867513459],
778  [-0.50000000000, -0.00000000000, 0.86602540378],
779  [-0.50000000000, 0.81649658093, -0.28867513459],
780  [ 0.50000000000, 0.00000000000, -0.86602540378],
781  [ 1.00000000000, 0.00000000000, -0.00000000000],
782  [ 0.50000000000, -0.00000000000, 0.86602540378],
783  [ 0.00000000000, 0.81649658093, 0.57735026919],
784  [ 0.50000000000, 0.81649658093, -0.28867513459]
785  ],
786  [
787  [1.00000000000, -89.99999999999, 125.26438968275],
788  [1.00000000000, -121.48215410529, 73.22134511904],
789  [1.00000000000, 179.99999999999, 89.99999999999],
790  [1.00000000000, 179.99999999998, 149.99999999999],
791  [1.00000000000, -58.51784589470, 73.22134511904],
792  [1.00000000000, -179.99999999998, 30.00000000000],
793  [1.00000000000, 121.48215410529, 106.77865488095],
794  [1.00000000000, 0.00000000001, 149.99999999999],
795  [1.00000000000, 0.00000000000, 89.99999999999],
796  [1.00000000000, -0.00000000001, 30.00000000000],
797  [1.00000000000, 89.99999999999, 54.73561031724],
798  [1.00000000000, 58.51784589470, 106.77865488095]
799  ],
800  [
801  [3,2,1,0],
802  [0,4,8,7],
803  [1,5,9,4],
804  [2,6,10,5],
805  [3,7,11,6],
806  [8,9,10,11],
807  [0,1,4],
808  [1,2,5],
809  [2,3,6],
810  [3,0,7],
811  [4,9,8],
812  [5,10,9],
813  [6,11,10],
814  [7,8,11]
815  ],
816  [
817  [0,1],
818  [1,2],
819  [2,3],
820  [3,0],
821  [4,0],
822  [0,7],
823  [7,8],
824  [8,4],
825  [5,1],
826  [1,4],
827  [4,9],
828  [9,5],
829  [6,2],
830  [2,5],
831  [5,10],
832  [10,6],
833  [7,3],
834  [3,6],
835  [6,11],
836  [11,7],
837  [8,9],
838  [9,10],
839  [10,11],
840  [11,8]
841  ]
842  ],
843  [
844  "triangular_orthobicupola",
845  "Triangular Orthobicupola",
846  "J27",
847  "cupolas",
848  "Polyhedron Database #71",
849  [
850  [-0.50000000000, -0.00000000000, -0.86602540378],
851  [ 0.50000000000, 0.00000000000, -0.86602540378],
852  [ 0.00000000000, 0.81649658093, -0.57735026919],
853  [ 0.00000000000, -0.81649658093, -0.57735026919],
854  [-1.00000000000, -0.00000000000, -0.00000000000],
855  [-0.50000000000, 0.81649658093, 0.28867513459],
856  [-0.50000000000, -0.81649658093, 0.28867513459],
857  [ 1.00000000000, 0.00000000000, 0.00000000000],
858  [ 0.50000000000, 0.81649658093, 0.28867513459],
859  [ 0.50000000000, -0.81649658093, 0.28867513459],
860  [-0.50000000000, 0.00000000000, 0.86602540378],
861  [ 0.50000000000, 0.00000000000, 0.86602540378]
862  ],
863  [
864  [1.00000000000, -179.99999999998, 150.00000000000],
865  [1.00000000000, 0.00000000000, 149.99999999998],
866  [1.00000000000, 89.99999999999, 125.26438968275],
867  [1.00000000000, -89.99999999999, 125.26438968275],
868  [1.00000000000, -179.99999999998, 89.99999999999],
869  [1.00000000000, 121.48215410529, 73.22134511904],
870  [1.00000000000, -121.48215410529, 73.22134511904],
871  [1.00000000000, 0.00000000001, 89.99999999999],
872  [1.00000000000, 58.51784589470, 73.22134511903],
873  [1.00000000000, -58.51784589470, 73.22134511903],
874  [1.00000000000, 179.99999999999, 30.00000000000],
875  [1.00000000000, 0.00000000001, 29.99999999999]
876  ],
877  [
878  [8,5,2],
879  [4,0,2,5],
880  [10,4,5],
881  [11,10,5,8],
882  [7,11,8],
883  [1,7,8,2],
884  [0,1,2],
885  [9,3,6],
886  [0,4,6,3],
887  [1,0,3],
888  [7,1,3,9],
889  [11,7,9],
890  [10,11,9,6],
891  [4,10,6]
892  ],
893  [
894  [0,1],
895  [0,2],
896  [0,3],
897  [0,4],
898  [1,2],
899  [1,3],
900  [1,7],
901  [2,5],
902  [2,8],
903  [3,6],
904  [3,9],
905  [4,5],
906  [4,6],
907  [4,10],
908  [5,8],
909  [5,10],
910  [6,9],
911  [6,10],
912  [7,8],
913  [7,9],
914  [7,11],
915  [8,11],
916  [9,11],
917  [10,11]
918  ]
919  ]
920 ];
921 
922 //! @}
923 
924 //----------------------------------------------------------------------------//
925 // openscad-amu auxiliary scripts
926 //----------------------------------------------------------------------------//
927 
928 /*
929 BEGIN_SCOPE db;
930 BEGIN_SCOPE autostat;
931  BEGIN_OPENSCAD;
932  include <math/math_polytope.scad>;
933  include <math/math_utility.scad>;
934  include <datatypes/datatypes_table.scad>;
935  include <database/geometry/polyhedra/cupolas.scad>;
936 
937  fs = "^";
938 
939  tc = dtc_polyhedra_cupolas;
940  tr = dtr_polyhedra_cupolas;
941 
942  ids = get_table_ridl(tr);
943 
944  echo
945  (
946  str
947  (
948  "no.", fs, "table id", fs, "other name", fs,
949  "vertices", fs, "faces", fs, "edges",
950 
951  fs, "face-verticies",
952  fs, "face-angles",
953  fs, "edge-lengths",
954  fs, "edge-angles"
955  )
956  );
957 
958  for ( id = ids )
959  {
960  i = first(find(id, ids, c=1))+1;
961 
962  n = get_table_v(tr, tc, id, "n");
963  o = get_table_v(tr, tc, id, "o");
964  g = get_table_v(tr, tc, id, "g");
965  d = get_table_v(tr, tc, id, "d");
966 
967  c = get_table_v(tr, tc, id, "c");
968  s = get_table_v(tr, tc, id, "s");
969  f = get_table_v(tr, tc, id, "f");
970  e = get_table_v(tr, tc, id, "e");
971 
972  fo = is_empty(o) ? "-" : o;
973 
974  echo
975  (
976  str
977  (
978  i, fs, id, fs, fo, fs,
979  len(c), fs, len(f), fs, len(e),
980 
981  fs, hist(qsort(polytope_face_vcounts(f)), m=9),
982  fs, hist(qsort(dround(polytope_face_angles(c, f), d=1)), m=9),
983  fs, hist(qsort(sround(polytope_edge_lengths(c, e), d=3)), m=9),
984  fs, hist(qsort(dround(polytope_edge_angles(c, f), d=1)), m=9),
985 
986  fs
987  )
988  );
989  }
990  END_OPENSCAD;
991 
992  BEGIN_MFSCRIPT;
993  include --path "${INCLUDE_PATH}" {config_base,config_csg}.mfs;
994  include --path "${INCLUDE_PATH}" script_std.mfs;
995  END_MFSCRIPT;
996 END_SCOPE;
997 END_SCOPE;
998 */
999 
1000 /*
1001 BEGIN_SCOPE db;
1002 BEGIN_SCOPE dim;
1003  BEGIN_OPENSCAD;
1004  include <units/units_coordinate.scad>;
1005  include <tools/tools_polytope.scad>;
1006  include <datatypes/datatypes_table.scad>;
1007  include <database/geometry/polyhedra/cupolas.scad>;
1008 
1009  config = 0;
1010 
1011  tc = dtc_polyhedra_cupolas;
1012  tr = dtr_polyhedra_cupolas;
1013 
1014  id = "default";
1015  sr = 100;
1016 
1017  pv = get_table_v(tr, tc, id, "c");
1018  pf = get_table_v(tr, tc, id, "f");
1019  pe = get_table_v(tr, tc, id, "e");
1020 
1021  sv = coordinates_csc(pv, sr);
1022 
1023  if (config == 0) // png preview
1024  {
1025  $fn = 25;
1026 
1027  %polyhedron(sv, pf);
1028 
1029  polytope_frame(sv, pf, pe)
1030  {
1031  circle(r = sr / 25);
1032  color("lightblue")
1033  sphere(r = sr / 25 * (1 + 1/2));
1034  }
1035  }
1036 
1037  if (config == 1) // stl model
1038  {
1039  polyhedron(sv, pf);
1040  }
1041  END_OPENSCAD;
1042 
1043  BEGIN_MFSCRIPT;
1044  include --path "${INCLUDE_PATH}" {config_base,config_png}.mfs;
1045 
1046  views name "views" views "diag";
1047  defines name "ids" define "id"
1048  strings
1049  "
1050  pentagonal_cupola
1051  pentagonal_gyrobicupola
1052  pentagonal_orthobicupola
1053  square_cupola
1054  square_gyrobicupola
1055  square_orthobicupola
1056  triangular_cupola
1057  triangular_gyrobicupola
1058  triangular_orthobicupola
1059  ";
1060  variables add_opts_combine "views ids";
1061  variables add_opts "-D config=0 --viewall --autocenter";
1062 
1063  include --path "${INCLUDE_PATH}" script_new.mfs;
1064 
1065  include --path "${INCLUDE_PATH}" config_stl.mfs;
1066  variables add_opts_combine "ids";
1067  variables add_opts "-D config=1";
1068 
1069  include --path "${INCLUDE_PATH}" script_app.mfs;
1070  END_MFSCRIPT;
1071 END_SCOPE;
1072 END_SCOPE;
1073 */
1074 
1075 //----------------------------------------------------------------------------//
1076 // end of file
1077 //----------------------------------------------------------------------------//
dtc_polyhedra_cupolas
dtc_polyhedra_cupolas
Definition: cupolas.scad:114
dtr_polyhedra_cupolas
dtr_polyhedra_cupolas
Definition: cupolas.scad:129