318:
311:
418:
151:
29:
512:
381:
370:
407:
compound can be generated by rotating tetrahedra about lines extending from the center of each face and through the centroid (as altitudes), with varying degrees of rotation.
447:
360:
279:
222:
466:
286:
50:
673:
617:
622:
186:
39:
656:
627:
296:
Below are two perspective viewpoints of the uniform compound of four tetrahedra, with each color representing one
28:
317:
310:
417:
79:
297:
165:
127:
67:
556:
232:
373:. In this case, these tetrahedra share a symmetric arrangement over the common axis of symmetry
411:
564:
540:
424:
337:
256:
243:
199:
122:
599:
579:
552:
410:
A model for this compound polyhedron was first published by Robert Webb, using his program
568:
548:
518:
236:
189:
of four tetrahedra can be constructed by rotating tetrahedra along an axis of symmetry
102:
150:
667:
560:
458:
650:
544:
174:
169:
380:
that is rotated by equal and opposite angles. This compound is indexed as
644:
160:
118:
639:
507:{\displaystyle S={\frac {1291}{210\cdot {\sqrt {3}}}}\approx 3.5493}
416:
148:
18:
531:
Skilling, John (1976). "Uniform
Compounds of Uniform Polyhedra".
155:
3D model of a compound of four tetrahedra or digonal antiprisms.
533:
Mathematical
Proceedings of the Cambridge Philosophical Society
253:
plane of symmetry, with one pair of tetrahedra shifted
449:. This particular model was built by Robert Webb using
469:
427:
340:
259:
202:
302:
414:, in 2004, following studies of polyhedron models:
242:This compound can also be seen as two compounds of
506:
441:
354:
273:
216:
177:in a number of different symmetry positions.
196:(that is the middle of an edge) in multiples of
453:, a computer software for generating polyhedra.
334:Four tetrahedra that are not spread equally in
369:can still hold uniform symmetry when allowed
293:= 2 is a digonal antiprism, or tetrahedron.
8:
21:
287:prismatic compound of antiprisms
27:
488:
476:
468:
431:
426:
344:
339:
263:
258:
206:
201:
517:This compound is self-dual, meaning its
26:
642:(nonuniform) with adjustable angles at
421:Compound of four tetrahedra rotated by
457:With edge-length as a unit, it has a
7:
289:, where in this case the component
14:
521:is the same compound polyhedron.
22:Compound of 4 digonal antiprisms
316:
309:
117:
101:
93:
85:
74:
62:
45:
35:
1:
584:Symmetry: Culture and Science
618:Compound of three tetrahedra
315:
308:
281:. It is a special case of a
224:. It has dihedral symmetry,
623:Compound of five tetrahedra
173:can be constructed by four
690:
628:Compound of six tetrahedra
545:10.1017/S0305004100052440
600:"Tetrahedron 4-Compound"
592:(Figure 6.a "Compounds")
246:fit evenly on the same
640:Tetrahedron 4-Compound
508:
454:
443:
442:{\displaystyle \pi /3}
356:
355:{\displaystyle \pi /4}
275:
274:{\displaystyle \pi /4}
218:
217:{\displaystyle \pi /4}
156:
66:4 digonal antiprisms (
578:Webb, Robert (2002).
509:
444:
420:
357:
276:
219:
154:
674:Polyhedral compounds
467:
425:
338:
257:
200:
598:Weisstein, Eric W.
305:
298:regular tetrahedron
121:restricting to one
16:Polyhedral compound
504:
455:
439:
387:, with parameters
371:rotational freedom
352:
303:
271:
233:vertex arrangement
214:
157:
496:
493:
332:
331:
244:stella octangulae
181:Uniform compounds
147:
146:
681:
653:
607:
606:. Wolfram Alpha.
591:
572:
513:
511:
510:
505:
497:
495:
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477:
448:
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445:
440:
435:
361:
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320:
313:
306:
280:
278:
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231:, and the same
223:
221:
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210:
187:uniform compound
153:
123:stella octangula
57:(n=4, p=2, q=1)
40:Uniform compound
31:
19:
689:
688:
684:
683:
682:
680:
679:
678:
664:
663:
651:
636:
614:
597:
590:(3–4): 391–399.
580:"Stella Models"
577:
530:
527:
519:dual polyhedron
481:
465:
464:
423:
422:
401:
399:Other compounds
385:
379:
368:
336:
335:
255:
254:
251:
237:octagonal prism
230:
198:
197:
194:
183:
149:
142:
136:
133:
112:
56:
54:
17:
12:
11:
5:
687:
685:
677:
676:
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665:
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661:
660:
659:
652:Rotating model
635:
634:External links
632:
631:
630:
625:
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613:
610:
609:
608:
594:
593:
574:
573:
539:(3): 453–454.
526:
523:
503:
500:
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487:
484:
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475:
472:
438:
434:
430:
400:
397:
383:
377:
366:
351:
347:
343:
330:
329:
326:
322:
321:
314:
270:
266:
262:
249:
235:as the convex
228:
213:
209:
205:
192:
182:
179:
145:
144:
140:
131:
125:
115:
114:
110:
105:
103:Symmetry group
99:
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87:
83:
82:
76:
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64:
60:
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52:
47:
43:
42:
37:
33:
32:
24:
23:
15:
13:
10:
9:
6:
4:
3:
2:
686:
675:
672:
671:
669:
658:
654:
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633:
629:
626:
624:
621:
619:
616:
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611:
605:
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581:
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570:
566:
562:
558:
554:
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546:
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534:
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528:
524:
522:
520:
515:
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498:
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485:
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473:
470:
462:
460:
452:
436:
432:
428:
419:
415:
413:
408:
406:
398:
396:
395:= 4 as well.
394:
390:
386:
376:
372:
365:
349:
345:
341:
327:
324:
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319:
312:
307:
304:Perspectives
301:
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294:
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109:
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77:
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69:
65:
61:
58:
55:
48:
44:
41:
38:
34:
30:
25:
20:
643:
603:
587:
583:
536:
532:
516:
463:
459:surface area
456:
450:
409:
404:
402:
392:
388:
374:
363:
362:angles over
333:
295:
290:
282:
247:
241:
225:
190:
184:
164:
158:
137:
128:
107:
49:
143:, order 16
113:, order 32
569:0322.50007
525:References
405:nonuniform
328:Side view
175:tetrahedra
170:tetrahedra
135:, order 48
68:tetrahedra
604:MathWorld
561:123279687
499:≈
486:⋅
461:equal to
429:π
342:π
325:Top view
261:π
204:π
80:triangles
63:Polyhedra
668:Category
645:GeoGebra
612:See also
391:= 2 and
168:of four
166:compound
161:geometry
119:Subgroup
94:Vertices
657:YouTube
553:0397554
285:-gonal
567:
559:
551:
502:3.5493
451:Stella
412:Stella
557:S2CID
86:Edges
75:Faces
46:Index
479:1291
239:.
163:, a
36:Type
655:on
565:Zbl
541:doi
483:210
389:p/q
291:p/q
283:p/q
159:In
97:16
89:32
78:16
670::
602:.
588:13
586:.
582:.
563:.
555:.
549:MR
547:.
537:79
535:.
514:.
403:A
384:22
382:UC
300::
229:8h
185:A
141:4h
111:8h
70:)
53:23
51:UC
571:.
543::
491:3
474:=
471:S
437:3
433:/
393:n
378:2
375:C
367:2
364:C
350:4
346:/
269:4
265:/
250:2
248:C
226:D
212:4
208:/
193:2
191:C
138:D
132:h
129:O
108:D
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