omdl  v0.6.1
OpenSCAD Mechanical Design Library
trapezohedron.scad
Go to the documentation of this file.
1 //! Table of polyhedra data group: \c trapezohedron
2 /***************************************************************************//**
3  \file trapezohedron.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: trapezohedron ###
64 
65  \amu_define caption (trapezohedron)
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 (trapezohedron)
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="${cell_num}"
94  )
95  \endlatexonly
96 
97  \amu_shell data
98  (
99  "grep -Po 'ECHO: \"\K[^\"]*' build/csg/trapezohedron_db_autostat.log" --rmnl
100  )
101  \amu_shell columns ("echo '${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 trapezohedron polyhedra data table columns definition.
113 //! \hideinitializer
114 dtc_polyhedra_trapezohedron =
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 trapezohedron polyhedra data table rows.
128 //! \hideinitializer
129 dtr_polyhedra_trapezohedron =
130 [
131  [
132  "decagonal_trapezohedron",
133  "Decagonal Trapezohedron",
134  empty_str,
135  "trapezohedron",
136  "George W. Hart, 1997. george@li.net",
137  [
138  [ 0.08157055488, -0.02508562274, 0.26071794615],
139  [-0.00298807954, 0.02508563214, 0.27316418436],
140  [-0.08725421480, -0.02508563451, 0.25887120879],
141  [-0.00000000660, -0.99999999536, -0.00000000747],
142  [ 0.21923812649, -0.02508563811, 0.16297927459],
143  [ 0.15814447884, 0.02508563160, 0.22275080640],
144  [-0.00000000000, 1.00000000000, -0.00000000000],
145  [-0.16297928808, 0.02508564700, 0.21923811357],
146  [-0.22275082301, -0.02508562356, 0.15814446589],
147  [ 0.27316413424, -0.02508562845, 0.00298807495],
148  [ 0.25887121980, 0.02508563643, 0.08725421294],
149  [-0.26071794390, 0.02508563415, 0.08157054936],
150  [-0.27316412166, -0.02508563048, -0.00298808116],
151  [ 0.22275080881, -0.02508563042, -0.15814448224],
152  [ 0.26071794489, 0.02508562885, -0.08157054801],
153  [-0.25887121794, 0.02508563696, -0.08725420881],
154  [-0.21923811508, -0.02508563337, -0.16297929533],
155  [ 0.08725419904, -0.02508564175, -0.25887120317],
156  [ 0.16297928994, 0.02508562639, -0.21923810944],
157  [-0.15814447873, 0.02508562100, -0.22275080783],
158  [-0.08157054158, -0.02508562972, -0.26071793387],
159  [ 0.00298807400, 0.02508561395, -0.27316415966]
160  ],
161  [
162  [0.27432989509, -17.09438091172, 18.12481356295],
163  [0.27432989114, 96.79279130227, 5.28383970309],
164  [0.27432989228, -163.96002773134, 19.32627339448],
165  [0.99999999536, -90.00000037787, 90.00000042785],
166  [0.27432989135, -6.52750264244, 53.55152986257],
167  [0.27432988692, 9.01343241109, 35.71001165929],
168  [1.00000000000, 89.99999999999, 89.99999999999],
169  [0.27432988986, 171.24974747226, 36.94842526900],
170  [0.27432989220, -173.57456962451, 54.79697096798],
171  [0.27432984085, -5.24695718319, 89.37590650495],
172  [0.27432990225, 5.53490397494, 71.45417161203],
173  [0.27432989235, 174.50406060693, 72.70180860768],
174  [0.27432982858, -174.75304215454, 90.62409482042],
175  [0.27432989072, -6.42543252564, 125.20303342952],
176  [0.27432989240, 5.49593821872, 107.29819109356],
177  [0.27432989923, 174.46509587012, 108.54582768974],
178  [0.27432989412, -173.47249824405, 126.44847509514],
179  [0.27432988263, -16.03997941196, 160.67372880945],
180  [0.27432988578, 8.75024535050, 143.05157442959],
181  [0.27432988704, 170.98657132818, 144.28998881634],
182  [0.27432988010, -162.90561198533, 161.87518775511],
183  [0.27432986483, 83.20721630672, 174.71616371452]
184  ],
185  [
186  [2,1,0,3],
187  [5,4,3,0],
188  [6,5,0,1],
189  [7,6,1,2],
190  [8,7,2,3],
191  [10,9,3,4],
192  [6,10,4,5],
193  [8,11,6,7],
194  [12,11,8,3],
195  [14,13,3,9],
196  [6,14,9,10],
197  [12,15,6,11],
198  [16,15,12,3],
199  [18,17,3,13],
200  [6,18,13,14],
201  [16,19,6,15],
202  [20,19,16,3],
203  [21,20,3,17],
204  [6,21,17,18],
205  [20,21,6,19]
206  ],
207  [
208  [0,1],
209  [0,3],
210  [0,5],
211  [1,2],
212  [1,6],
213  [2,3],
214  [2,7],
215  [3,4],
216  [3,8],
217  [3,9],
218  [3,12],
219  [3,13],
220  [3,16],
221  [3,17],
222  [3,20],
223  [4,5],
224  [4,10],
225  [5,6],
226  [6,7],
227  [6,10],
228  [6,11],
229  [6,14],
230  [6,15],
231  [6,18],
232  [6,19],
233  [6,21],
234  [7,8],
235  [8,11],
236  [9,10],
237  [9,14],
238  [11,12],
239  [12,15],
240  [13,14],
241  [13,18],
242  [15,16],
243  [16,19],
244  [17,18],
245  [17,21],
246  [19,20],
247  [20,21]
248  ]
249  ],
250  [
251  "enneagonal_trapezohedron",
252  "Enneagonal Trapezohedron",
253  empty_str,
254  "trapezohedron",
255  "George W. Hart, 1997. george@li.net",
256  [
257  [ 0.09967569853, -0.03109121041, 0.28700473236],
258  [-0.00449688147, 0.03109120560, 0.30378732765],
259  [-0.10812707432, -0.03109120337, 0.28392868530],
260  [-0.00000000000, -1.00000000000, -0.00000000000],
261  [ 0.26083909572, -0.03109119912, 0.15578806357],
262  [ 0.19182591719, 0.03109121011, 0.23560511930],
263  [ 0.00000000000, 1.00000000000, 0.00000000000],
264  [-0.19871552184, 0.03109120431, 0.22982403661],
265  [-0.26533596988, -0.03109120286, 0.14799923301],
266  [ 0.29995285209, -0.03109119664, -0.04832353760],
267  [ 0.29839124041, 0.03109120428, 0.05718066821],
268  [-0.29995285209, 0.03109119664, 0.04832353760],
269  [-0.29839124041, -0.03109120428, -0.05718066821],
270  [ 0.19871552184, -0.03109120431, -0.22982403661],
271  [ 0.26533596988, 0.03109120286, -0.14799923301],
272  [-0.26083909572, 0.03109119912, -0.15578806357],
273  [-0.19182591719, -0.03109121011, -0.23560511930],
274  [ 0.00449688147, -0.03109120560, -0.30378732765],
275  [ 0.10812707432, 0.03109120337, -0.28392868530],
276  [-0.09967569853, 0.03109121041, -0.28700473236]
277  ],
278  [
279  [0.30540730941, -17.32393663862, 19.99136596564],
280  [0.30540731073, 98.22991277939, 5.90398591727],
281  [0.30540731076, -163.95777128867, 21.61622610532],
282  [1.00000000000, -89.99999999999, 89.99999999999],
283  [0.30540729734, -6.79740536654, 59.32955244196],
284  [0.30540729869, 9.20645860564, 39.51611872633],
285  [1.00000000000, 89.99999999999, 89.99999999999],
286  [0.30540728448, 171.10754696024, 41.19115786195],
287  [0.30540728999, -173.31674427607, 61.01397561204],
288  [0.30540717128, -5.91778120996, 99.10397657184],
289  [0.30540730861, 5.94853149631, 79.20896763446],
290  [0.30540717128, 174.08221879003, 80.89602342815],
291  [0.30540730861, -174.05146850368, 100.79103236553],
292  [0.30540728448, -8.89245303975, 138.80884213804],
293  [0.30540728999, 6.68325572392, 118.98602438795],
294  [0.30540729734, 173.20259463344, 120.67044755803],
295  [0.30540729869, -170.79354139435, 140.48388127366],
296  [0.30540731073, -81.77008722060, 174.09601408272],
297  [0.30540731076, 16.04222871132, 158.38377389467],
298  [0.30540730941, 162.67606336137, 160.00863403435]
299  ],
300  [
301  [2,1,0,3],
302  [5,4,3,0],
303  [6,5,0,1],
304  [7,6,1,2],
305  [8,7,2,3],
306  [10,9,3,4],
307  [6,10,4,5],
308  [8,11,6,7],
309  [12,11,8,3],
310  [14,13,3,9],
311  [6,14,9,10],
312  [12,15,6,11],
313  [16,15,12,3],
314  [18,17,3,13],
315  [6,18,13,14],
316  [16,19,6,15],
317  [17,19,16,3],
318  [6,19,17,18]
319  ],
320  [
321  [0,1],
322  [0,3],
323  [0,5],
324  [1,2],
325  [1,6],
326  [2,3],
327  [2,7],
328  [3,4],
329  [3,8],
330  [3,9],
331  [3,12],
332  [3,13],
333  [3,16],
334  [3,17],
335  [4,5],
336  [4,10],
337  [5,6],
338  [6,7],
339  [6,10],
340  [6,11],
341  [6,14],
342  [6,15],
343  [6,18],
344  [6,19],
345  [7,8],
346  [8,11],
347  [9,10],
348  [9,14],
349  [11,12],
350  [12,15],
351  [13,14],
352  [13,18],
353  [15,16],
354  [16,19],
355  [17,18],
356  [17,19]
357  ]
358  ],
359  [
360  "heptagonal_trapezohedron",
361  "Heptagonal Trapezohedron",
362  empty_str,
363  "trapezohedron",
364  "George W. Hart, 1997. george@li.net",
365  [
366  [ 0.15933687369, -0.05209510052, 0.35802671535],
367  [-0.01178440532, 0.05209506563, 0.39170460464],
368  [-0.18057162842, -0.05209509977, 0.34780059309],
369  [ 0.00000000000, -1.00000000000, 0.00000000000],
370  [ 0.37926145196, -0.05209508876, 0.09865141109],
371  [ 0.29889951735, 0.05209507083, 0.25343724148],
372  [-0.00000000000, 1.00000000000, -0.00000000000],
373  [-0.31359442195, 0.05209507236, 0.23501040648],
374  [-0.38450602213, -0.05209507830, 0.07567352614],
375  [ 0.31359442195, -0.05209507236, -0.23501040648],
376  [ 0.38450602213, 0.05209507830, -0.07567352614],
377  [-0.37926145196, 0.05209508876, -0.09865141109],
378  [-0.29889951735, -0.05209507083, -0.25343724148],
379  [ 0.01178440532, -0.05209506563, -0.39170460464],
380  [ 0.18057162842, 0.05209509977, -0.34780059309],
381  [-0.15933687369, 0.05209510052, -0.35802671535]
382  ],
383  [
384  [0.39532931553, -18.10512730588, 25.09015092726],
385  [0.39532931256, 102.74633327200, 7.76474182503],
386  [0.39532931205, -163.90709508767, 28.38484324140],
387  [1.00000000000, -89.99999999999, 89.99999999999],
388  [0.39532929075, -7.82116460645, 75.54956589793],
389  [0.39532929722, 9.88674610587, 50.12768809629],
390  [1.00000000000, 89.99999999999, 89.99999999999],
391  [0.39532929211, 170.56801928124, 53.52532102116],
392  [0.39532930678, -172.28422195910, 78.96439512595],
393  [0.39532929211, -9.43198071875, 126.47467897883],
394  [0.39532930678, 7.71577804089, 101.03560487404],
395  [0.39532929075, 172.17883539354, 104.45043410206],
396  [0.39532929722, -170.11325389411, 129.87231190370],
397  [0.39532931256, -77.25366672798, 172.23525817496],
398  [0.39532931205, 16.09290491232, 151.61515675859],
399  [0.39532931553, 161.89487269411, 154.90984907273]
400  ],
401  [
402  [2,1,0,3],
403  [5,4,3,0],
404  [6,5,0,1],
405  [7,6,1,2],
406  [8,7,2,3],
407  [10,9,3,4],
408  [6,10,4,5],
409  [8,11,6,7],
410  [12,11,8,3],
411  [14,13,3,9],
412  [6,14,9,10],
413  [12,15,6,11],
414  [13,15,12,3],
415  [6,15,13,14]
416  ],
417  [
418  [0,1],
419  [0,3],
420  [0,5],
421  [1,2],
422  [1,6],
423  [2,3],
424  [2,7],
425  [3,4],
426  [3,8],
427  [3,9],
428  [3,12],
429  [3,13],
430  [4,5],
431  [4,10],
432  [5,6],
433  [6,7],
434  [6,10],
435  [6,11],
436  [6,14],
437  [6,15],
438  [7,8],
439  [8,11],
440  [9,10],
441  [9,14],
442  [11,12],
443  [12,15],
444  [13,14],
445  [13,15]
446  ]
447  ],
448  [
449  "hexagonal_trapezohedron",
450  "Hexagonal Trapezohedron",
451  empty_str,
452  "trapezohedron",
453  "George W. Hart, 1997. george@li.net",
454  [
455  [ 0.21077945274, -0.07179671220, 0.40719463133],
456  [-0.02105696444, 0.07179681426, 0.45803062041],
457  [-0.24725117903, -0.07179674075, 0.38613767351],
458  [ 0.00000001746, -1.00000000000, -0.00000001939],
459  [ 0.45803058721, -0.07179671638, 0.02105695657],
460  [ 0.38613769213, 0.07179681752, 0.24725117466],
461  [-0.00000000000, 0.99999999466, -0.00000000000],
462  [-0.40719463483, 0.07179675601, 0.21077944864],
463  [-0.45803063391, -0.07179678648, -0.02105696269],
464  [ 0.24725117677, -0.07179676068, -0.38613770590],
465  [ 0.40719468018, 0.07179677996, -0.21077948352],
466  [-0.38613769009, 0.07179672747, -0.24725120767],
467  [-0.21077946131, -0.07179681703, -0.40719467592],
468  [ 0.02105695713, 0.07179664363, -0.45803045003]
469  ],
470  [
471  [0.46410151192, -18.81011682832, 28.67176760585],
472  [0.46410152717, 106.34564790761, 9.27753217454],
473  [0.46410151952, -163.80777174223, 33.69410290051],
474  [1.00000000000, -89.99999899976, 90.00000111118],
475  [0.46410147891, -8.90867366573, 87.39951472962],
476  [0.46410154456, 10.53305205986, 57.80839267192],
477  [0.99999999466, 89.99999999999, 89.99999999999],
478  [0.46410151990, 170.00036088461, 62.98866993565],
479  [0.46410153612, -171.09131867014, 92.60048570555],
480  [0.46410154835, -16.19223265656, 146.30589896998],
481  [0.46410157924, 9.99964129133, 117.01133116296],
482  [0.46410154652, 169.46696080222, 122.19161199084],
483  [0.46410157115, -161.18985834971, 151.32823049523],
484  [0.46410133229, 73.65432069463, 170.72248463514]
485  ],
486  [
487  [2,1,0,3],
488  [5,4,3,0],
489  [6,5,0,1],
490  [7,6,1,2],
491  [8,7,2,3],
492  [10,9,3,4],
493  [6,10,4,5],
494  [8,11,6,7],
495  [12,11,8,3],
496  [13,12,3,9],
497  [6,13,9,10],
498  [12,13,6,11]
499  ],
500  [
501  [0,1],
502  [0,3],
503  [0,5],
504  [1,2],
505  [1,6],
506  [2,3],
507  [2,7],
508  [3,4],
509  [3,8],
510  [3,9],
511  [3,12],
512  [4,5],
513  [4,10],
514  [5,6],
515  [6,7],
516  [6,10],
517  [6,11],
518  [6,13],
519  [7,8],
520  [8,11],
521  [9,10],
522  [9,13],
523  [11,12],
524  [12,13]
525  ]
526  ],
527  [
528  "octagonal_trapezohedron",
529  "Octagonal Trapezohedron",
530  empty_str,
531  "trapezohedron",
532  "George W. Hart, 1997. george@li.net",
533  [
534  [ 0.12440374180, -0.03956610710, 0.31883630933],
535  [-0.00707929049, 0.03956612081, 0.34217358778],
536  [-0.13748458654, -0.03956612082, 0.31341805381],
537  [ 0.00000000328, -0.99999999972, -0.00000000691],
538  [ 0.31341805431, -0.03956611462, 0.13748458160],
539  [ 0.23694744249, 0.03956612970, 0.24695906900],
540  [ 0.00000000000, 1.00000000000, 0.00000000000],
541  [-0.24695908004, 0.03956613350, 0.23694744807],
542  [-0.31883629862, -0.03956614368, 0.12440375701],
543  [ 0.31883630448, -0.03956613242, -0.12440374250],
544  [ 0.34217360200, 0.03956614317, 0.00707928788],
545  [-0.34217356974, 0.03956611153, -0.00707929452],
546  [-0.31341804435, -0.03956612986, -0.13748455659],
547  [ 0.13748456384, -0.03956610907, -0.31341806002],
548  [ 0.24695907885, 0.03956612319, -0.23694744766],
549  [-0.23694744654, 0.03956610486, -0.24695907595],
550  [-0.12440376449, -0.03956612279, -0.31883631554],
551  [ 0.00707928976, 0.03956611334, -0.34217359479]
552  ],
553  [
554  [0.34452628340, -17.64305529000, 22.26612222536],
555  [0.34452628121, 100.14419358069, 6.69971877848],
556  [0.34452629204, -163.94492938135, 24.53507780455],
557  [0.99999999972, -89.99999981201, 90.00000039578],
558  [0.34452628981, -7.19499886627, 66.48094949675],
559  [0.34452627024, 9.47994070259, 44.20846013907],
560  [1.00000000000, 89.99999999999, 89.99999999999],
561  [0.34452628242, 170.89780636105, 46.54785043727],
562  [0.34452628318, -172.92601715801, 68.83306913392],
563  [0.34452628207, -7.07398072018, 111.16692834963],
564  [0.34452629784, 6.59591976996, 88.82260986090],
565  [0.34452626231, 173.40408484199, 91.17739136390],
566  [0.34452627252, -172.80499816432, 113.51904721890],
567  [0.34452628728, -16.05506861288, 155.46492641463],
568  [0.34452628011, 9.10219134903, 133.45214983518],
569  [0.34452627515, 170.52006530125, 135.79154067723],
570  [0.34452629914, -162.35694116392, 157.73387410580],
571  [0.34452628730, 79.85580556086, 173.30028259374]
572  ],
573  [
574  [2,1,0,3],
575  [5,4,3,0],
576  [6,5,0,1],
577  [7,6,1,2],
578  [8,7,2,3],
579  [10,9,3,4],
580  [6,10,4,5],
581  [8,11,6,7],
582  [12,11,8,3],
583  [14,13,3,9],
584  [6,14,9,10],
585  [12,15,6,11],
586  [16,15,12,3],
587  [17,16,3,13],
588  [6,17,13,14],
589  [16,17,6,15]
590  ],
591  [
592  [0,1],
593  [0,3],
594  [0,5],
595  [1,2],
596  [1,6],
597  [2,3],
598  [2,7],
599  [3,4],
600  [3,8],
601  [3,9],
602  [3,12],
603  [3,13],
604  [3,16],
605  [4,5],
606  [4,10],
607  [5,6],
608  [6,7],
609  [6,10],
610  [6,11],
611  [6,14],
612  [6,15],
613  [6,17],
614  [7,8],
615  [8,11],
616  [9,10],
617  [9,14],
618  [11,12],
619  [12,15],
620  [13,14],
621  [13,17],
622  [15,16],
623  [16,17]
624  ]
625  ],
626  [
627  "pentagonal_trapezohedron",
628  "Pentagonal Trapezohedron",
629  empty_str,
630  "trapezohedron",
631  "George W. Hart, 1997. george@li.net",
632  [
633  [ 0.29061700374, -0.10557280512, 0.47022819599],
634  [-0.04127909262, 0.10557281662, 0.55124299653],
635  [-0.35740800281, -0.10557280588, 0.42170170398],
636  [ 0.00000000000, -1.00000000000, 0.00000000000],
637  [ 0.53701907744, -0.10557277682, -0.13108468003],
638  [ 0.51150729951, 0.10557282394, 0.20960220829],
639  [-0.00000000000, 1.00000000000, -0.00000000000],
640  [-0.53701907744, 0.10557277682, 0.13108468003],
641  [-0.51150729951, -0.10557282394, -0.20960220829],
642  [ 0.04127909262, -0.10557281662, -0.55124299653],
643  [ 0.35740800281, 0.10557280588, -0.42170170398],
644  [-0.29061700374, 0.10557280512, -0.47022819599]
645  ],
646  [
647  [0.56277741279, -19.96462853971, 33.32693587180],
648  [0.56277741988, 111.35555548884, 11.62015183686],
649  [0.56277742044, -163.54367316283, 41.46828745750],
650  [1.00000000000, -89.99999999999, 89.99999999999],
651  [0.56277730416, -11.12196599899, 103.46931672415],
652  [0.56277741988, 11.66183878548, 68.13367063006],
653  [1.00000000000, 89.99999999999, 89.99999999999],
654  [0.56277730416, 168.87803400100, 76.53068327584],
655  [0.56277741988, -168.33816121451, 111.86632936993],
656  [0.56277741988, -68.64444451115, 168.37984816312],
657  [0.56277742044, 16.45632683715, 138.53171254249],
658  [0.56277741279, 160.03537146028, 146.67306412819]
659  ],
660  [
661  [2,1,0,3],
662  [5,4,3,0],
663  [6,5,0,1],
664  [7,6,1,2],
665  [8,7,2,3],
666  [10,9,3,4],
667  [6,10,4,5],
668  [8,11,6,7],
669  [9,11,8,3],
670  [6,11,9,10]
671  ],
672  [
673  [0,1],
674  [0,3],
675  [0,5],
676  [1,2],
677  [1,6],
678  [2,3],
679  [2,7],
680  [3,4],
681  [3,8],
682  [3,9],
683  [4,5],
684  [4,10],
685  [5,6],
686  [6,7],
687  [6,10],
688  [6,11],
689  [7,8],
690  [8,11],
691  [9,10],
692  [9,11]
693  ]
694  ],
695  [
696  "square_trapezohedron",
697  "Square Trapezohedron",
698  empty_str,
699  "trapezohedron",
700  "George W. Hart, 1997. george@li.net",
701  [
702  [ 0.42339344824, -0.17157294543, 0.55319018257],
703  [-0.09178014666, 0.17157285464, 0.69054892905],
704  [-0.55319020733, -0.17157287656, 0.42339344003],
705  [-0.00000002205, -0.99999998335, -0.00000000805],
706  [ 0.55319017981, -0.17157290218, -0.42339346671],
707  [ 0.69054891796, 0.17157284736, 0.09178015628],
708  [-0.00000000000, 1.00000000000, -0.00000000000],
709  [-0.69054887577, 0.17157293950, -0.09178015299],
710  [-0.42339347576, -0.17157283330, -0.55319020925],
711  [ 0.09178018156, 0.17157289932, -0.69054887093]
712  ],
713  [
714  [0.71743896305, -22.05940926920, 39.55061574902],
715  [0.71743896130, 118.14383936173, 15.73644755891],
716  [0.71743896083, -162.76863505583, 53.83265949178],
717  [0.99999998335, -90.00000126364, 90.00000046134],
718  [0.71743896148, -17.23136817104, 126.16734310920],
719  [0.71743895011, 13.95309503880, 82.65015437581],
720  [1.00000000000, 89.99999999999, 89.99999999999],
721  [0.71743893111, 166.04689694206, 97.34984555507],
722  [0.71743897305, -157.94060506039, 140.44938663065],
723  [0.71743892050, 61.85615778289, 164.26354688847]
724  ],
725  [
726  [2,1,0,3],
727  [5,4,3,0],
728  [6,5,0,1],
729  [7,6,1,2],
730  [8,7,2,3],
731  [9,8,3,4],
732  [6,9,4,5],
733  [8,9,6,7]
734  ],
735  [
736  [0,1],
737  [0,3],
738  [0,5],
739  [1,2],
740  [1,6],
741  [2,3],
742  [2,7],
743  [3,4],
744  [3,8],
745  [4,5],
746  [4,9],
747  [5,6],
748  [6,7],
749  [6,9],
750  [7,8],
751  [8,9]
752  ]
753  ],
754  [
755  "triangular_trapezohedron",
756  "Triangular Trapezohedron",
757  "Cube",
758  "trapezohedron",
759  "Exact Mathematics",
760  [
761  [ 0.00000000000, 1.00000000000, 0.00000000000],
762  [ 0.00000000000, 0.33333333333, 0.94280904158],
763  [-0.81649658093, 0.33333333333, -0.47140452079],
764  [-0.81649658093, -0.33333333333, 0.47140452079],
765  [ 0.81649658093, 0.33333333333, -0.47140452079],
766  [ 0.81649658093, -0.33333333333, 0.47140452079],
767  [-0.00000000000, -0.33333333333, -0.94280904158],
768  [ 0.00000000000, -1.00000000000, 0.00000000000]
769  ],
770  [
771  [1.00000000000, 89.99999999999, 89.99999999999],
772  [1.00000000000, 89.99999999999, 19.47122063449],
773  [1.00000000000, 157.79234570139, 118.12550570205],
774  [1.00000000000, -157.79234570139, 61.87449429794],
775  [1.00000000000, 22.20765429859, 118.12550570205],
776  [1.00000000000, -22.20765429859, 61.87449429794],
777  [1.00000000000, -89.99999999999, 160.52877936550],
778  [1.00000000000, -89.99999999999, 89.99999999999]
779  ],
780  [
781  [6,4,0,2],
782  [5,1,0,4],
783  [7,5,4,6],
784  [1,3,2,0],
785  [3,7,6,2],
786  [7,3,1,5]
787  ],
788  [
789  [0,1],
790  [0,2],
791  [0,4],
792  [1,3],
793  [1,5],
794  [2,3],
795  [2,6],
796  [3,7],
797  [4,5],
798  [4,6],
799  [5,7],
800  [6,7]
801  ]
802  ]
803 ];
804 
805 //! @}
806 
807 //----------------------------------------------------------------------------//
808 // openscad-amu auxiliary scripts
809 //----------------------------------------------------------------------------//
810 
811 /*
812 BEGIN_SCOPE db;
813 BEGIN_SCOPE autostat;
814  BEGIN_OPENSCAD;
815  include <math/math_polytope.scad>;
816  include <math/math_utility.scad>;
817  include <datatypes/datatypes_table.scad>;
818  include <database/geometry/polyhedra/trapezohedron.scad>;
819 
820  fs = "^";
821 
822  tc = dtc_polyhedra_trapezohedron;
823  tr = dtr_polyhedra_trapezohedron;
824 
825  ids = get_table_ridl(tr);
826 
827  echo
828  (
829  str
830  (
831  "no.", fs, "table id", fs, "other name", fs,
832  "vertices", fs, "faces", fs, "edges",
833 
834  fs, "face-verticies",
835  fs, "face-angles",
836  fs, "edge-lengths",
837  fs, "edge-angles"
838  )
839  );
840 
841  for ( id = ids )
842  {
843  i = first(find(id, ids, c=1))+1;
844 
845  n = get_table_v(tr, tc, id, "n");
846  o = get_table_v(tr, tc, id, "o");
847  g = get_table_v(tr, tc, id, "g");
848  d = get_table_v(tr, tc, id, "d");
849 
850  c = get_table_v(tr, tc, id, "c");
851  s = get_table_v(tr, tc, id, "s");
852  f = get_table_v(tr, tc, id, "f");
853  e = get_table_v(tr, tc, id, "e");
854 
855  fo = is_empty(o) ? "-" : o;
856 
857  echo
858  (
859  str
860  (
861  i, fs, id, fs, fo, fs,
862  len(c), fs, len(f), fs, len(e),
863 
864  fs, hist(qsort(polytope_face_vcounts(f)), m=9),
865  fs, hist(qsort(dround(polytope_face_angles(c, f), d=1)), m=9),
866  fs, hist(qsort(sround(polytope_edge_lengths(c, e), d=3)), m=9),
867  fs, hist(qsort(dround(polytope_edge_angles(c, f), d=1)), m=9),
868 
869  fs
870  )
871  );
872  }
873  END_OPENSCAD;
874 
875  BEGIN_MFSCRIPT;
876  include --path "${INCLUDE_PATH}" {config_base,config_csg}.mfs;
877  include --path "${INCLUDE_PATH}" script_std.mfs;
878  END_MFSCRIPT;
879 END_SCOPE;
880 END_SCOPE;
881 */
882 
883 /*
884 BEGIN_SCOPE db;
885 BEGIN_SCOPE dim;
886  BEGIN_OPENSCAD;
887  include <units/units_coordinate.scad>;
888  include <tools/tools_polytope.scad>;
889  include <datatypes/datatypes_table.scad>;
890  include <database/geometry/polyhedra/trapezohedron.scad>;
891 
892  config = 0;
893 
894  tc = dtc_polyhedra_trapezohedron;
895  tr = dtr_polyhedra_trapezohedron;
896 
897  id = "default";
898  sr = 100;
899 
900  pv = get_table_v(tr, tc, id, "c");
901  pf = get_table_v(tr, tc, id, "f");
902  pe = get_table_v(tr, tc, id, "e");
903 
904  sv = coordinates_csc(pv, sr);
905 
906  if (config == 0) // png preview
907  {
908  $fn = 25;
909 
910  %polyhedron(sv, pf);
911 
912  polytope_frame(sv, pf, pe)
913  {
914  circle(r = sr / 25);
915  color("lightblue")
916  sphere(r = sr / 25 * (1 + 1/2));
917  }
918  }
919 
920  if (config == 1) // stl model
921  {
922  polyhedron(sv, pf);
923  }
924  END_OPENSCAD;
925 
926  BEGIN_MFSCRIPT;
927  include --path "${INCLUDE_PATH}" {config_base,config_png}.mfs;
928 
929  views name "views" views "diag";
930  defines name "ids" define "id"
931  strings
932  "
933  decagonal_trapezohedron
934  enneagonal_trapezohedron
935  heptagonal_trapezohedron
936  hexagonal_trapezohedron
937  octagonal_trapezohedron
938  pentagonal_trapezohedron
939  square_trapezohedron
940  triangular_trapezohedron
941  ";
942  variables add_opts_combine "views ids";
943  variables add_opts "-D config=0 --viewall --autocenter";
944 
945  include --path "${INCLUDE_PATH}" script_new.mfs;
946 
947  include --path "${INCLUDE_PATH}" config_stl.mfs;
948  variables add_opts_combine "ids";
949  variables add_opts "-D config=1";
950 
951  include --path "${INCLUDE_PATH}" script_app.mfs;
952  END_MFSCRIPT;
953 END_SCOPE;
954 END_SCOPE;
955 */
956 
957 //----------------------------------------------------------------------------//
958 // end of file
959 //----------------------------------------------------------------------------//
empty_str
empty_str
A string with no characters (the empty string).
Definition: constants.scad:77
dtr_polyhedra_trapezohedron
dtr_polyhedra_trapezohedron
Definition: trapezohedron.scad:129
dtc_polyhedra_trapezohedron
dtc_polyhedra_trapezohedron
Definition: trapezohedron.scad:114