omdl  v1.0
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/common/polytope.scad>;
903  include <database/geometry/polyhedra/trapezohedron.scad>;
904 
905  config = 0;
906 
907  tc = dtc_polyhedra_trapezohedron;
908  tr = dtr_polyhedra_trapezohedron;
909 
910  id = "default";
911  sr = 100;
912 
913  pv = table_get_value(tr, tc, id, "c");
914  pf = table_get_value(tr, tc, id, "f");
915  pe = table_get_value(tr, tc, id, "e");
916 
917  sv = coordinate_scale3d_csc(pv, sr);
918 
919  if (config == 0) // png preview
920  {
921  $fn = 25;
922 
923  %polyhedron(sv, pf);
924 
925  polytope_frame(sv, pf, pe)
926  {
927  circle(r = sr / 25);
928  color("lightblue")
929  sphere(r = sr / 25 * (1 + 1/2));
930  }
931  }
932 
933  if (config == 1) // stl model
934  {
935  polyhedron(sv, pf);
936  }
937  END_OPENSCAD;
938 
939  BEGIN_MFSCRIPT;
940  include --path "${INCLUDE_PATH}" {var_init,var_gen_png2eps}.mfs;
941 
942  views name "views" views "diag";
943  defines name "ids" define "id"
944  strings
945  "
946  decagonal_trapezohedron
947  enneagonal_trapezohedron
948  heptagonal_trapezohedron
949  hexagonal_trapezohedron
950  octagonal_trapezohedron
951  pentagonal_trapezohedron
952  square_trapezohedron
953  triangular_trapezohedron
954  ";
955  variables add_opts_combine "views ids";
956  variables add_opts "-D config=0 --viewall --autocenter --view=axes";
957 
958  include --path "${INCLUDE_PATH}" scr_make_mf_begin.mfs;
959  include --path "${INCLUDE_PATH}" scr_make_mf_add_ext.mfs;
960 
961  include --path "${INCLUDE_PATH}" var_gen_stl.mfs;
962  variables add_opts_combine "ids";
963  variables add_opts "-D config=1";
964 
965  include --path "${INCLUDE_PATH}" scr_make_mf_add_ext.mfs;
966  include --path "${INCLUDE_PATH}" scr_make_mf_end.mfs;
967  END_MFSCRIPT;
968 END_SCOPE;
969 END_SCOPE;
970 */
971 
972 //----------------------------------------------------------------------------//
973 // end of file
974 //----------------------------------------------------------------------------//
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