omdl  v0.9.8
OpenSCAD Mechanical Design Library
trapezohedron.scad
Go to the documentation of this file.
1 //! Polyhedra data table: \c trapezohedron.
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  ### Trapezohedron ###
64  \amu_include (include/amu/includes_required.amu)
65 
66  \amu_eval
67  (
68  ++global
69  title="Examples"
70  stem=trapezohedron 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 trapezohedron polyhedra data table columns definition.
128 //! \hideinitializer
129 dtc_polyhedra_trapezohedron =
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 trapezohedron polyhedra data table rows.
143 //! \hideinitializer
144 dtr_polyhedra_trapezohedron =
145 [
146  [
147  "decagonal_trapezohedron",
148  "Decagonal Trapezohedron",
149  empty_str,
150  "trapezohedron",
151  "George W. Hart, 1997. george@li.net",
152  [
153  [ 0.08157055488, -0.02508562274, 0.26071794615],
154  [-0.00298807954, 0.02508563214, 0.27316418436],
155  [-0.08725421480, -0.02508563451, 0.25887120879],
156  [-0.00000000660, -0.99999999536, -0.00000000747],
157  [ 0.21923812649, -0.02508563811, 0.16297927459],
158  [ 0.15814447884, 0.02508563160, 0.22275080640],
159  [-0.00000000000, 1.00000000000, -0.00000000000],
160  [-0.16297928808, 0.02508564700, 0.21923811357],
161  [-0.22275082301, -0.02508562356, 0.15814446589],
162  [ 0.27316413424, -0.02508562845, 0.00298807495],
163  [ 0.25887121980, 0.02508563643, 0.08725421294],
164  [-0.26071794390, 0.02508563415, 0.08157054936],
165  [-0.27316412166, -0.02508563048, -0.00298808116],
166  [ 0.22275080881, -0.02508563042, -0.15814448224],
167  [ 0.26071794489, 0.02508562885, -0.08157054801],
168  [-0.25887121794, 0.02508563696, -0.08725420881],
169  [-0.21923811508, -0.02508563337, -0.16297929533],
170  [ 0.08725419904, -0.02508564175, -0.25887120317],
171  [ 0.16297928994, 0.02508562639, -0.21923810944],
172  [-0.15814447873, 0.02508562100, -0.22275080783],
173  [-0.08157054158, -0.02508562972, -0.26071793387],
174  [ 0.00298807400, 0.02508561395, -0.27316415966]
175  ],
176  [
177  [0.27432989509, -17.09438091172, 18.12481356295],
178  [0.27432989114, 96.79279130227, 5.28383970309],
179  [0.27432989228, -163.96002773134, 19.32627339448],
180  [0.99999999536, -90.00000037787, 90.00000042785],
181  [0.27432989135, -6.52750264244, 53.55152986257],
182  [0.27432988692, 9.01343241109, 35.71001165929],
183  [1.00000000000, 89.99999999999, 89.99999999999],
184  [0.27432988986, 171.24974747226, 36.94842526900],
185  [0.27432989220, -173.57456962451, 54.79697096798],
186  [0.27432984085, -5.24695718319, 89.37590650495],
187  [0.27432990225, 5.53490397494, 71.45417161203],
188  [0.27432989235, 174.50406060693, 72.70180860768],
189  [0.27432982858, -174.75304215454, 90.62409482042],
190  [0.27432989072, -6.42543252564, 125.20303342952],
191  [0.27432989240, 5.49593821872, 107.29819109356],
192  [0.27432989923, 174.46509587012, 108.54582768974],
193  [0.27432989412, -173.47249824405, 126.44847509514],
194  [0.27432988263, -16.03997941196, 160.67372880945],
195  [0.27432988578, 8.75024535050, 143.05157442959],
196  [0.27432988704, 170.98657132818, 144.28998881634],
197  [0.27432988010, -162.90561198533, 161.87518775511],
198  [0.27432986483, 83.20721630672, 174.71616371452]
199  ],
200  [
201  [2,1,0,3],
202  [5,4,3,0],
203  [6,5,0,1],
204  [7,6,1,2],
205  [8,7,2,3],
206  [10,9,3,4],
207  [6,10,4,5],
208  [8,11,6,7],
209  [12,11,8,3],
210  [14,13,3,9],
211  [6,14,9,10],
212  [12,15,6,11],
213  [16,15,12,3],
214  [18,17,3,13],
215  [6,18,13,14],
216  [16,19,6,15],
217  [20,19,16,3],
218  [21,20,3,17],
219  [6,21,17,18],
220  [20,21,6,19]
221  ],
222  [
223  [0,1],
224  [0,3],
225  [0,5],
226  [1,2],
227  [1,6],
228  [2,3],
229  [2,7],
230  [3,4],
231  [3,8],
232  [3,9],
233  [3,12],
234  [3,13],
235  [3,16],
236  [3,17],
237  [3,20],
238  [4,5],
239  [4,10],
240  [5,6],
241  [6,7],
242  [6,10],
243  [6,11],
244  [6,14],
245  [6,15],
246  [6,18],
247  [6,19],
248  [6,21],
249  [7,8],
250  [8,11],
251  [9,10],
252  [9,14],
253  [11,12],
254  [12,15],
255  [13,14],
256  [13,18],
257  [15,16],
258  [16,19],
259  [17,18],
260  [17,21],
261  [19,20],
262  [20,21]
263  ]
264  ],
265  [
266  "enneagonal_trapezohedron",
267  "Enneagonal Trapezohedron",
268  empty_str,
269  "trapezohedron",
270  "George W. Hart, 1997. george@li.net",
271  [
272  [ 0.09967569853, -0.03109121041, 0.28700473236],
273  [-0.00449688147, 0.03109120560, 0.30378732765],
274  [-0.10812707432, -0.03109120337, 0.28392868530],
275  [-0.00000000000, -1.00000000000, -0.00000000000],
276  [ 0.26083909572, -0.03109119912, 0.15578806357],
277  [ 0.19182591719, 0.03109121011, 0.23560511930],
278  [ 0.00000000000, 1.00000000000, 0.00000000000],
279  [-0.19871552184, 0.03109120431, 0.22982403661],
280  [-0.26533596988, -0.03109120286, 0.14799923301],
281  [ 0.29995285209, -0.03109119664, -0.04832353760],
282  [ 0.29839124041, 0.03109120428, 0.05718066821],
283  [-0.29995285209, 0.03109119664, 0.04832353760],
284  [-0.29839124041, -0.03109120428, -0.05718066821],
285  [ 0.19871552184, -0.03109120431, -0.22982403661],
286  [ 0.26533596988, 0.03109120286, -0.14799923301],
287  [-0.26083909572, 0.03109119912, -0.15578806357],
288  [-0.19182591719, -0.03109121011, -0.23560511930],
289  [ 0.00449688147, -0.03109120560, -0.30378732765],
290  [ 0.10812707432, 0.03109120337, -0.28392868530],
291  [-0.09967569853, 0.03109121041, -0.28700473236]
292  ],
293  [
294  [0.30540730941, -17.32393663862, 19.99136596564],
295  [0.30540731073, 98.22991277939, 5.90398591727],
296  [0.30540731076, -163.95777128867, 21.61622610532],
297  [1.00000000000, -89.99999999999, 89.99999999999],
298  [0.30540729734, -6.79740536654, 59.32955244196],
299  [0.30540729869, 9.20645860564, 39.51611872633],
300  [1.00000000000, 89.99999999999, 89.99999999999],
301  [0.30540728448, 171.10754696024, 41.19115786195],
302  [0.30540728999, -173.31674427607, 61.01397561204],
303  [0.30540717128, -5.91778120996, 99.10397657184],
304  [0.30540730861, 5.94853149631, 79.20896763446],
305  [0.30540717128, 174.08221879003, 80.89602342815],
306  [0.30540730861, -174.05146850368, 100.79103236553],
307  [0.30540728448, -8.89245303975, 138.80884213804],
308  [0.30540728999, 6.68325572392, 118.98602438795],
309  [0.30540729734, 173.20259463344, 120.67044755803],
310  [0.30540729869, -170.79354139435, 140.48388127366],
311  [0.30540731073, -81.77008722060, 174.09601408272],
312  [0.30540731076, 16.04222871132, 158.38377389467],
313  [0.30540730941, 162.67606336137, 160.00863403435]
314  ],
315  [
316  [2,1,0,3],
317  [5,4,3,0],
318  [6,5,0,1],
319  [7,6,1,2],
320  [8,7,2,3],
321  [10,9,3,4],
322  [6,10,4,5],
323  [8,11,6,7],
324  [12,11,8,3],
325  [14,13,3,9],
326  [6,14,9,10],
327  [12,15,6,11],
328  [16,15,12,3],
329  [18,17,3,13],
330  [6,18,13,14],
331  [16,19,6,15],
332  [17,19,16,3],
333  [6,19,17,18]
334  ],
335  [
336  [0,1],
337  [0,3],
338  [0,5],
339  [1,2],
340  [1,6],
341  [2,3],
342  [2,7],
343  [3,4],
344  [3,8],
345  [3,9],
346  [3,12],
347  [3,13],
348  [3,16],
349  [3,17],
350  [4,5],
351  [4,10],
352  [5,6],
353  [6,7],
354  [6,10],
355  [6,11],
356  [6,14],
357  [6,15],
358  [6,18],
359  [6,19],
360  [7,8],
361  [8,11],
362  [9,10],
363  [9,14],
364  [11,12],
365  [12,15],
366  [13,14],
367  [13,18],
368  [15,16],
369  [16,19],
370  [17,18],
371  [17,19]
372  ]
373  ],
374  [
375  "heptagonal_trapezohedron",
376  "Heptagonal Trapezohedron",
377  empty_str,
378  "trapezohedron",
379  "George W. Hart, 1997. george@li.net",
380  [
381  [ 0.15933687369, -0.05209510052, 0.35802671535],
382  [-0.01178440532, 0.05209506563, 0.39170460464],
383  [-0.18057162842, -0.05209509977, 0.34780059309],
384  [ 0.00000000000, -1.00000000000, 0.00000000000],
385  [ 0.37926145196, -0.05209508876, 0.09865141109],
386  [ 0.29889951735, 0.05209507083, 0.25343724148],
387  [-0.00000000000, 1.00000000000, -0.00000000000],
388  [-0.31359442195, 0.05209507236, 0.23501040648],
389  [-0.38450602213, -0.05209507830, 0.07567352614],
390  [ 0.31359442195, -0.05209507236, -0.23501040648],
391  [ 0.38450602213, 0.05209507830, -0.07567352614],
392  [-0.37926145196, 0.05209508876, -0.09865141109],
393  [-0.29889951735, -0.05209507083, -0.25343724148],
394  [ 0.01178440532, -0.05209506563, -0.39170460464],
395  [ 0.18057162842, 0.05209509977, -0.34780059309],
396  [-0.15933687369, 0.05209510052, -0.35802671535]
397  ],
398  [
399  [0.39532931553, -18.10512730588, 25.09015092726],
400  [0.39532931256, 102.74633327200, 7.76474182503],
401  [0.39532931205, -163.90709508767, 28.38484324140],
402  [1.00000000000, -89.99999999999, 89.99999999999],
403  [0.39532929075, -7.82116460645, 75.54956589793],
404  [0.39532929722, 9.88674610587, 50.12768809629],
405  [1.00000000000, 89.99999999999, 89.99999999999],
406  [0.39532929211, 170.56801928124, 53.52532102116],
407  [0.39532930678, -172.28422195910, 78.96439512595],
408  [0.39532929211, -9.43198071875, 126.47467897883],
409  [0.39532930678, 7.71577804089, 101.03560487404],
410  [0.39532929075, 172.17883539354, 104.45043410206],
411  [0.39532929722, -170.11325389411, 129.87231190370],
412  [0.39532931256, -77.25366672798, 172.23525817496],
413  [0.39532931205, 16.09290491232, 151.61515675859],
414  [0.39532931553, 161.89487269411, 154.90984907273]
415  ],
416  [
417  [2,1,0,3],
418  [5,4,3,0],
419  [6,5,0,1],
420  [7,6,1,2],
421  [8,7,2,3],
422  [10,9,3,4],
423  [6,10,4,5],
424  [8,11,6,7],
425  [12,11,8,3],
426  [14,13,3,9],
427  [6,14,9,10],
428  [12,15,6,11],
429  [13,15,12,3],
430  [6,15,13,14]
431  ],
432  [
433  [0,1],
434  [0,3],
435  [0,5],
436  [1,2],
437  [1,6],
438  [2,3],
439  [2,7],
440  [3,4],
441  [3,8],
442  [3,9],
443  [3,12],
444  [3,13],
445  [4,5],
446  [4,10],
447  [5,6],
448  [6,7],
449  [6,10],
450  [6,11],
451  [6,14],
452  [6,15],
453  [7,8],
454  [8,11],
455  [9,10],
456  [9,14],
457  [11,12],
458  [12,15],
459  [13,14],
460  [13,15]
461  ]
462  ],
463  [
464  "hexagonal_trapezohedron",
465  "Hexagonal Trapezohedron",
466  empty_str,
467  "trapezohedron",
468  "George W. Hart, 1997. george@li.net",
469  [
470  [ 0.21077945274, -0.07179671220, 0.40719463133],
471  [-0.02105696444, 0.07179681426, 0.45803062041],
472  [-0.24725117903, -0.07179674075, 0.38613767351],
473  [ 0.00000001746, -1.00000000000, -0.00000001939],
474  [ 0.45803058721, -0.07179671638, 0.02105695657],
475  [ 0.38613769213, 0.07179681752, 0.24725117466],
476  [-0.00000000000, 0.99999999466, -0.00000000000],
477  [-0.40719463483, 0.07179675601, 0.21077944864],
478  [-0.45803063391, -0.07179678648, -0.02105696269],
479  [ 0.24725117677, -0.07179676068, -0.38613770590],
480  [ 0.40719468018, 0.07179677996, -0.21077948352],
481  [-0.38613769009, 0.07179672747, -0.24725120767],
482  [-0.21077946131, -0.07179681703, -0.40719467592],
483  [ 0.02105695713, 0.07179664363, -0.45803045003]
484  ],
485  [
486  [0.46410151192, -18.81011682832, 28.67176760585],
487  [0.46410152717, 106.34564790761, 9.27753217454],
488  [0.46410151952, -163.80777174223, 33.69410290051],
489  [1.00000000000, -89.99999899976, 90.00000111118],
490  [0.46410147891, -8.90867366573, 87.39951472962],
491  [0.46410154456, 10.53305205986, 57.80839267192],
492  [0.99999999466, 89.99999999999, 89.99999999999],
493  [0.46410151990, 170.00036088461, 62.98866993565],
494  [0.46410153612, -171.09131867014, 92.60048570555],
495  [0.46410154835, -16.19223265656, 146.30589896998],
496  [0.46410157924, 9.99964129133, 117.01133116296],
497  [0.46410154652, 169.46696080222, 122.19161199084],
498  [0.46410157115, -161.18985834971, 151.32823049523],
499  [0.46410133229, 73.65432069463, 170.72248463514]
500  ],
501  [
502  [2,1,0,3],
503  [5,4,3,0],
504  [6,5,0,1],
505  [7,6,1,2],
506  [8,7,2,3],
507  [10,9,3,4],
508  [6,10,4,5],
509  [8,11,6,7],
510  [12,11,8,3],
511  [13,12,3,9],
512  [6,13,9,10],
513  [12,13,6,11]
514  ],
515  [
516  [0,1],
517  [0,3],
518  [0,5],
519  [1,2],
520  [1,6],
521  [2,3],
522  [2,7],
523  [3,4],
524  [3,8],
525  [3,9],
526  [3,12],
527  [4,5],
528  [4,10],
529  [5,6],
530  [6,7],
531  [6,10],
532  [6,11],
533  [6,13],
534  [7,8],
535  [8,11],
536  [9,10],
537  [9,13],
538  [11,12],
539  [12,13]
540  ]
541  ],
542  [
543  "octagonal_trapezohedron",
544  "Octagonal Trapezohedron",
545  empty_str,
546  "trapezohedron",
547  "George W. Hart, 1997. george@li.net",
548  [
549  [ 0.12440374180, -0.03956610710, 0.31883630933],
550  [-0.00707929049, 0.03956612081, 0.34217358778],
551  [-0.13748458654, -0.03956612082, 0.31341805381],
552  [ 0.00000000328, -0.99999999972, -0.00000000691],
553  [ 0.31341805431, -0.03956611462, 0.13748458160],
554  [ 0.23694744249, 0.03956612970, 0.24695906900],
555  [ 0.00000000000, 1.00000000000, 0.00000000000],
556  [-0.24695908004, 0.03956613350, 0.23694744807],
557  [-0.31883629862, -0.03956614368, 0.12440375701],
558  [ 0.31883630448, -0.03956613242, -0.12440374250],
559  [ 0.34217360200, 0.03956614317, 0.00707928788],
560  [-0.34217356974, 0.03956611153, -0.00707929452],
561  [-0.31341804435, -0.03956612986, -0.13748455659],
562  [ 0.13748456384, -0.03956610907, -0.31341806002],
563  [ 0.24695907885, 0.03956612319, -0.23694744766],
564  [-0.23694744654, 0.03956610486, -0.24695907595],
565  [-0.12440376449, -0.03956612279, -0.31883631554],
566  [ 0.00707928976, 0.03956611334, -0.34217359479]
567  ],
568  [
569  [0.34452628340, -17.64305529000, 22.26612222536],
570  [0.34452628121, 100.14419358069, 6.69971877848],
571  [0.34452629204, -163.94492938135, 24.53507780455],
572  [0.99999999972, -89.99999981201, 90.00000039578],
573  [0.34452628981, -7.19499886627, 66.48094949675],
574  [0.34452627024, 9.47994070259, 44.20846013907],
575  [1.00000000000, 89.99999999999, 89.99999999999],
576  [0.34452628242, 170.89780636105, 46.54785043727],
577  [0.34452628318, -172.92601715801, 68.83306913392],
578  [0.34452628207, -7.07398072018, 111.16692834963],
579  [0.34452629784, 6.59591976996, 88.82260986090],
580  [0.34452626231, 173.40408484199, 91.17739136390],
581  [0.34452627252, -172.80499816432, 113.51904721890],
582  [0.34452628728, -16.05506861288, 155.46492641463],
583  [0.34452628011, 9.10219134903, 133.45214983518],
584  [0.34452627515, 170.52006530125, 135.79154067723],
585  [0.34452629914, -162.35694116392, 157.73387410580],
586  [0.34452628730, 79.85580556086, 173.30028259374]
587  ],
588  [
589  [2,1,0,3],
590  [5,4,3,0],
591  [6,5,0,1],
592  [7,6,1,2],
593  [8,7,2,3],
594  [10,9,3,4],
595  [6,10,4,5],
596  [8,11,6,7],
597  [12,11,8,3],
598  [14,13,3,9],
599  [6,14,9,10],
600  [12,15,6,11],
601  [16,15,12,3],
602  [17,16,3,13],
603  [6,17,13,14],
604  [16,17,6,15]
605  ],
606  [
607  [0,1],
608  [0,3],
609  [0,5],
610  [1,2],
611  [1,6],
612  [2,3],
613  [2,7],
614  [3,4],
615  [3,8],
616  [3,9],
617  [3,12],
618  [3,13],
619  [3,16],
620  [4,5],
621  [4,10],
622  [5,6],
623  [6,7],
624  [6,10],
625  [6,11],
626  [6,14],
627  [6,15],
628  [6,17],
629  [7,8],
630  [8,11],
631  [9,10],
632  [9,14],
633  [11,12],
634  [12,15],
635  [13,14],
636  [13,17],
637  [15,16],
638  [16,17]
639  ]
640  ],
641  [
642  "pentagonal_trapezohedron",
643  "Pentagonal Trapezohedron",
644  empty_str,
645  "trapezohedron",
646  "George W. Hart, 1997. george@li.net",
647  [
648  [ 0.29061700374, -0.10557280512, 0.47022819599],
649  [-0.04127909262, 0.10557281662, 0.55124299653],
650  [-0.35740800281, -0.10557280588, 0.42170170398],
651  [ 0.00000000000, -1.00000000000, 0.00000000000],
652  [ 0.53701907744, -0.10557277682, -0.13108468003],
653  [ 0.51150729951, 0.10557282394, 0.20960220829],
654  [-0.00000000000, 1.00000000000, -0.00000000000],
655  [-0.53701907744, 0.10557277682, 0.13108468003],
656  [-0.51150729951, -0.10557282394, -0.20960220829],
657  [ 0.04127909262, -0.10557281662, -0.55124299653],
658  [ 0.35740800281, 0.10557280588, -0.42170170398],
659  [-0.29061700374, 0.10557280512, -0.47022819599]
660  ],
661  [
662  [0.56277741279, -19.96462853971, 33.32693587180],
663  [0.56277741988, 111.35555548884, 11.62015183686],
664  [0.56277742044, -163.54367316283, 41.46828745750],
665  [1.00000000000, -89.99999999999, 89.99999999999],
666  [0.56277730416, -11.12196599899, 103.46931672415],
667  [0.56277741988, 11.66183878548, 68.13367063006],
668  [1.00000000000, 89.99999999999, 89.99999999999],
669  [0.56277730416, 168.87803400100, 76.53068327584],
670  [0.56277741988, -168.33816121451, 111.86632936993],
671  [0.56277741988, -68.64444451115, 168.37984816312],
672  [0.56277742044, 16.45632683715, 138.53171254249],
673  [0.56277741279, 160.03537146028, 146.67306412819]
674  ],
675  [
676  [2,1,0,3],
677  [5,4,3,0],
678  [6,5,0,1],
679  [7,6,1,2],
680  [8,7,2,3],
681  [10,9,3,4],
682  [6,10,4,5],
683  [8,11,6,7],
684  [9,11,8,3],
685  [6,11,9,10]
686  ],
687  [
688  [0,1],
689  [0,3],
690  [0,5],
691  [1,2],
692  [1,6],
693  [2,3],
694  [2,7],
695  [3,4],
696  [3,8],
697  [3,9],
698  [4,5],
699  [4,10],
700  [5,6],
701  [6,7],
702  [6,10],
703  [6,11],
704  [7,8],
705  [8,11],
706  [9,10],
707  [9,11]
708  ]
709  ],
710  [
711  "square_trapezohedron",
712  "Square Trapezohedron",
713  empty_str,
714  "trapezohedron",
715  "George W. Hart, 1997. george@li.net",
716  [
717  [ 0.42339344824, -0.17157294543, 0.55319018257],
718  [-0.09178014666, 0.17157285464, 0.69054892905],
719  [-0.55319020733, -0.17157287656, 0.42339344003],
720  [-0.00000002205, -0.99999998335, -0.00000000805],
721  [ 0.55319017981, -0.17157290218, -0.42339346671],
722  [ 0.69054891796, 0.17157284736, 0.09178015628],
723  [-0.00000000000, 1.00000000000, -0.00000000000],
724  [-0.69054887577, 0.17157293950, -0.09178015299],
725  [-0.42339347576, -0.17157283330, -0.55319020925],
726  [ 0.09178018156, 0.17157289932, -0.69054887093]
727  ],
728  [
729  [0.71743896305, -22.05940926920, 39.55061574902],
730  [0.71743896130, 118.14383936173, 15.73644755891],
731  [0.71743896083, -162.76863505583, 53.83265949178],
732  [0.99999998335, -90.00000126364, 90.00000046134],
733  [0.71743896148, -17.23136817104, 126.16734310920],
734  [0.71743895011, 13.95309503880, 82.65015437581],
735  [1.00000000000, 89.99999999999, 89.99999999999],
736  [0.71743893111, 166.04689694206, 97.34984555507],
737  [0.71743897305, -157.94060506039, 140.44938663065],
738  [0.71743892050, 61.85615778289, 164.26354688847]
739  ],
740  [
741  [2,1,0,3],
742  [5,4,3,0],
743  [6,5,0,1],
744  [7,6,1,2],
745  [8,7,2,3],
746  [9,8,3,4],
747  [6,9,4,5],
748  [8,9,6,7]
749  ],
750  [
751  [0,1],
752  [0,3],
753  [0,5],
754  [1,2],
755  [1,6],
756  [2,3],
757  [2,7],
758  [3,4],
759  [3,8],
760  [4,5],
761  [4,9],
762  [5,6],
763  [6,7],
764  [6,9],
765  [7,8],
766  [8,9]
767  ]
768  ],
769  [
770  "triangular_trapezohedron",
771  "Triangular Trapezohedron",
772  "Cube",
773  "trapezohedron",
774  "Exact Mathematics",
775  [
776  [ 0.00000000000, 1.00000000000, 0.00000000000],
777  [ 0.00000000000, 0.33333333333, 0.94280904158],
778  [-0.81649658093, 0.33333333333, -0.47140452079],
779  [-0.81649658093, -0.33333333333, 0.47140452079],
780  [ 0.81649658093, 0.33333333333, -0.47140452079],
781  [ 0.81649658093, -0.33333333333, 0.47140452079],
782  [-0.00000000000, -0.33333333333, -0.94280904158],
783  [ 0.00000000000, -1.00000000000, 0.00000000000]
784  ],
785  [
786  [1.00000000000, 89.99999999999, 89.99999999999],
787  [1.00000000000, 89.99999999999, 19.47122063449],
788  [1.00000000000, 157.79234570139, 118.12550570205],
789  [1.00000000000, -157.79234570139, 61.87449429794],
790  [1.00000000000, 22.20765429859, 118.12550570205],
791  [1.00000000000, -22.20765429859, 61.87449429794],
792  [1.00000000000, -89.99999999999, 160.52877936550],
793  [1.00000000000, -89.99999999999, 89.99999999999]
794  ],
795  [
796  [6,4,0,2],
797  [5,1,0,4],
798  [7,5,4,6],
799  [1,3,2,0],
800  [3,7,6,2],
801  [7,3,1,5]
802  ],
803  [
804  [0,1],
805  [0,2],
806  [0,4],
807  [1,3],
808  [1,5],
809  [2,3],
810  [2,6],
811  [3,7],
812  [4,5],
813  [4,6],
814  [5,7],
815  [6,7]
816  ]
817  ]
818 ];
819 
820 //! @}
821 
822 //----------------------------------------------------------------------------//
823 // openscad-amu auxiliary scripts
824 //----------------------------------------------------------------------------//
825 
826 /*
827 BEGIN_SCOPE db;
828 BEGIN_SCOPE autostat;
829  BEGIN_OPENSCAD;
830  include <omdl-base.scad>;
831  include <database/geometry/polyhedra/trapezohedron.scad>;
832 
833  fs = "^";
834 
835  tc = dtc_polyhedra_trapezohedron;
836  tr = dtr_polyhedra_trapezohedron;
837 
838  ids = table_get_row_ids(tr);
839 
840  echo
841  (
842  str
843  (
844  "no.", fs, "id", fs, "other name", fs,
845  "vertices", fs, "faces", fs, "edges",
846 
847  fs, "face-verticies",
848  fs, "face-angles",
849  fs, "edge-lengths",
850  fs, "edge-angles"
851  )
852  );
853 
854  for ( id = ids )
855  {
856  i = first(find(id, ids, c=1))+1;
857 
858  n = table_get_value(tr, tc, id, "n");
859  o = table_get_value(tr, tc, id, "o");
860  g = table_get_value(tr, tc, id, "g");
861  d = table_get_value(tr, tc, id, "d");
862 
863  c = table_get_value(tr, tc, id, "c");
864  s = table_get_value(tr, tc, id, "s");
865  f = table_get_value(tr, tc, id, "f");
866  e = table_get_value(tr, tc, id, "e");
867 
868  fo = is_empty(o) ? "-" : o;
869 
870  echo
871  (
872  str
873  (
874  i, fs, id, fs, fo, fs,
875  len(c), fs, len(f), fs, len(e),
876 
877  fs, histogram(sort_q(polytope_face_vertex_counts(f)), m=9),
878  fs, histogram(sort_q(round_d(polytope_face_angles(c, f), d=1)), m=9),
879  fs, histogram(sort_q(round_s(polytope_edge_lengths(c, e), d=3)), m=9),
880  fs, histogram(sort_q(round_d(polytope_edge_angles(c, f), d=1)), m=9),
881 
882  fs
883  )
884  );
885  }
886  END_OPENSCAD;
887 
888  BEGIN_MFSCRIPT;
889  include --path "${INCLUDE_PATH}" {var_init,var_gen_term}.mfs;
890  include --path "${INCLUDE_PATH}" scr_make_mf.mfs;
891  END_MFSCRIPT;
892 END_SCOPE;
893 END_SCOPE;
894 */
895 
896 /*
897 BEGIN_SCOPE db;
898 BEGIN_SCOPE dim;
899  BEGIN_OPENSCAD;
900  include <omdl-base.scad>;
901  include <units/coordinate.scad>;
902  include <tools/align.scad>;
903  include <tools/polytope.scad>;
904  include <database/geometry/polyhedra/trapezohedron.scad>;
905 
906  config = 0;
907 
908  tc = dtc_polyhedra_trapezohedron;
909  tr = dtr_polyhedra_trapezohedron;
910 
911  id = "default";
912  sr = 100;
913 
914  pv = table_get_value(tr, tc, id, "c");
915  pf = table_get_value(tr, tc, id, "f");
916  pe = table_get_value(tr, tc, id, "e");
917 
918  sv = coordinate_scale3d_csc(pv, sr);
919 
920  if (config == 0) // png preview
921  {
922  $fn = 25;
923 
924  %polyhedron(sv, pf);
925 
926  polytope_frame(sv, pf, pe)
927  {
928  circle(r = sr / 25);
929  color("lightblue")
930  sphere(r = sr / 25 * (1 + 1/2));
931  }
932  }
933 
934  if (config == 1) // stl model
935  {
936  polyhedron(sv, pf);
937  }
938  END_OPENSCAD;
939 
940  BEGIN_MFSCRIPT;
941  include --path "${INCLUDE_PATH}" {var_init,var_gen_png2eps}.mfs;
942 
943  views name "views" views "diag";
944  defines name "ids" define "id"
945  strings
946  "
947  decagonal_trapezohedron
948  enneagonal_trapezohedron
949  heptagonal_trapezohedron
950  hexagonal_trapezohedron
951  octagonal_trapezohedron
952  pentagonal_trapezohedron
953  square_trapezohedron
954  triangular_trapezohedron
955  ";
956  variables add_opts_combine "views ids";
957  variables add_opts "-D config=0 --viewall --autocenter --view=axes";
958 
959  include --path "${INCLUDE_PATH}" scr_make_mf_begin.mfs;
960  include --path "${INCLUDE_PATH}" scr_make_mf_add_ext.mfs;
961 
962  include --path "${INCLUDE_PATH}" var_gen_stl.mfs;
963  variables add_opts_combine "ids";
964  variables add_opts "-D config=1";
965 
966  include --path "${INCLUDE_PATH}" scr_make_mf_add_ext.mfs;
967  include --path "${INCLUDE_PATH}" scr_make_mf_end.mfs;
968  END_MFSCRIPT;
969 END_SCOPE;
970 END_SCOPE;
971 */
972 
973 //----------------------------------------------------------------------------//
974 // end of file
975 //----------------------------------------------------------------------------//
empty_str
empty_str
<string> A string with no characters (the empty string).
Definition: constants.scad:301
dtc_polyhedra_trapezohedron
dtc_polyhedra_trapezohedron
Definition: trapezohedron.scad:197
dtr_polyhedra_trapezohedron
dtr_polyhedra_trapezohedron
Definition: trapezohedron.scad:212