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If it is treated as a simple non-convex polyhedron without self-intersecting surfaces, it has 180 faces (120 triangles and 60 concave quadrilaterals), 122 vertices (60 with degree 3, 30 with degree 4, 12 with degree 5, and 20 with degree 12), and 300 edges, giving an
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represents two chiral halves of this compound (it can therefore be seen as a "compound of two compounds of five tetrahedra").
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on the cube's vertices (which results in a "compound of five compounds of two tetrahedra").
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can be seen on the compound where the pentagonal faces of the dodecahedron are positioned.
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is one of the five regular polyhedral compounds. This polyhedron can be seen as either a
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The stellation process on the icosahedron creates a number of related
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234:). It is one of five regular compounds constructed from identical
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447:; Du Val, P.; Flather, H. T.; Petrie, J. F. (1999).
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159:3D model of a compound of ten tetrahedra
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185:. This compound was first described by
483:, (3rd edition, 1973), Dover edition,
471:(1st Edn University of Toronto (1938))
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817:. You can help Knowledge (XXG) by
541:The Wolfram Demonstrations Project
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356:Ten tetrahedra in a dodecahedron.
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537:Compounds of 5 and 10 Tetrahedra
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445:Coxeter, Harold Scott MacDonald
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562:stellations of the icosahedron
497:Stellating the Platonic solids
429:. Cambridge University Press.
263:by replacing each cube with a
134:restricting to one constituent
1:
368:, as shown at left. Concave
620:Compound of five tetrahedra
605:Medial triambic icosahedron
395:Compound of five tetrahedra
254:compound of five tetrahedra
215:It can also be seen as the
196:of a regular dodecahedron.
22:Compound of ten tetrahedra
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625:Compound of ten tetrahedra
615:Compound of five octahedra
610:Great triambic icosahedron
600:Small triambic icosahedron
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493:The five regular compounds
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515:"Tetrahedron 10-Compound"
451:(3rd ed.). Tarquin.
449:The fifty-nine icosahedra
225:full icosahedral symmetry
289:Wenninger model index 25
259:It can be made from the
413:Regular polytopes, p.98
813:-related article is a
635:Excavated dodecahedron
376:As a simple polyhedron
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261:compound of five cubes
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864:Polyhedral stellation
385:of 122-300+180 = +2.
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869:Polyhedral compounds
786:icosahedral symmetry
595:(Convex) icosahedron
383:Euler characteristic
192:It can be seen as a
547:Klitzing, Richard.
241:It shares the same
16:Polyhedral compound
575:Uniform duals
512:Weisstein, Eric W.
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298:Stellation diagram
243:vertex arrangement
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792:
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630:Great icosahedron
580:Regular compounds
539:by Sándor Kabai,
480:Regular Polytopes
458:978-1-899618-32-3
427:Polyhedron Models
423:Wenninger, Magnus
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874:Polyhedron stubs
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640:Final stellation
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495:, pp.47-50, 6.2
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265:stella octangula
210:spherical tiling
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40:regular compound
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287:, and given as
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271:As a stellation
236:Platonic solids
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504:External links
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475:H.S.M. Coxeter
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348:As a facetting
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112:Symmetry group
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46:Coxeter symbol
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549:"3D compound"
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360:It is also a
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200:As a compound
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102:Dual compound
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49:2{5,3}2{3,5}
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819:expanding it
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585:Regular star
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366:dodecahedron
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340:Dodecahedron
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247:dodecahedron
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499:, pp.96-104
329:Icosahedron
309:Convex hull
285:icosahedron
187:Edmund Hess
179:icosahedron
141:tetrahedral
117:icosahedral
858:Categories
811:polyhedron
401:References
370:pentagrams
303:Stellation
281:stellation
277:polyhedron
221:tetrahedra
175:stellation
170:tetrahedra
106:Self-dual
81:tetrahedra
782:compounds
778:polyhedra
520:MathWorld
362:facetting
189:in 1876.
560:Notable
425:(1974).
389:See also
217:compound
194:faceting
183:compound
166:compound
132:Subgroup
73:Elements
589:Others
570:Regular
531:model:
467:0676126
364:of the
283:of the
219:of ten
177:of the
168:of ten
491:, 3.6
487:
465:
455:
433:
138:chiral
92:= 60,
88:= 40,
809:This
784:with
279:is a
275:This
245:as a
223:with
208:As a
181:or a
96:= 20
54:Index
815:stub
780:and
529:VRML
485:ISBN
453:ISBN
431:ISBN
305:core
252:The
163:The
36:Type
79:10
860::
788:.
517:.
477:,
463:MR
461:.
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126:)
65:25
61:,
57:UC
846:e
839:t
832:v
821:.
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232:h
229:I
227:(
145:T
143:(
124:h
121:I
119:(
94:V
90:E
86:F
83::
63:W
59:6
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