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If the shape is considered as a union of five cubes yielding a simple nonconvex solid without self-intersecting surfaces, then it has 360 faces (all
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281:(where pentagrams can be seen correlating to the pentagonal faces). Each cube represents a selection of 8 of the 20 vertices of the dodecahedron.
327:), 182 vertices (60 with degree 3, 30 with degree 4, 12 with degree 5, 60 with degree 8, and 20 with degree 12), and 540 edges, yielding an
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363:. With these, it can form polyhedral compounds that can also be considered as degenerate uniform star polyhedra; the
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is one of the five regular polyhedral compounds. It was first described by
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666:
Cundy, H. and
Rollett, A. "Five Cubes in a Dodecahedron." §3.10.6 in
672:, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 135–136, 1989.
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29:
622:
Skilling, John (1976), "Uniform
Compounds of Uniform Polyhedra",
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624:
Mathematical
Proceedings of the Cambridge Philosophical Society
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The 30 rhombic faces exist in the planes of the 5 cubes.
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474:(which share the same vertex arrangement of a cube).
377:
498:This compound can be formed as a stellation of the
317:Views from 2-fold, 5-fold and 3-fold symmetry axis
728:Steven Dutch: Uniform Polyhedra and Their Duals
716:MathWorld: Rhombic Triacontahedron Stellations
786:
492:The yellow area corresponds to one cube face.
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462:can be formed by taking each of these five
32:
793:
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600:: CS1 maint: location missing publisher (
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214:Model of the compound in a dodecahedron
684:, (3rd edition, 1973), Dover edition,
593:
7:
747:
745:
369:great complex rhombicosidodecahedron
365:small complex rhombicosidodecahedron
251:
399:Great ditrigonal icosidodecahedron
388:Small ditrigonal icosidodecahedron
357:great ditrigonal icosidodecahedron
353:small ditrigonal icosidodecahedron
25:
577:Regular polytopes, pp.49-50, p.98
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466:and replacing them with the two
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373:complex rhombidodecadodecahedron
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277:The compound is a faceting of a
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723:George Hart: Compounds of Cubes
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698:Stellating the Platonic solids
610:Harman, Michael G. (c. 1974),
191:restricting to one constituent
1:
410:Ditrigonal dodecadodecahedron
361:ditrigonal dodecadodecahedron
347:. It additionally shares its
765:. You can help Knowledge by
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586:Cromwell, Peter R. (1997),
555:Uniform polyhedron compound
247:of a regular dodecahedron.
838:
744:
711:MathWorld: Cube 5-Compound
694:The five regular compounds
535:Compound of five octahedra
460:compound of ten tetrahedra
241:compound of five octahedra
162:Compound of five octahedra
644:10.1017/S0305004100052440
316:
286:
616:, unpublished manuscript
331:of 182 − 540 + 360 = 2.
540:Compound of three cubes
500:rhombic triacontahedron
256:rhombic triacontahedron
84:rhombic triacontahedron
33:Compound of five cubes
761:-related article is a
545:Compound of four cubes
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526:compound of four cubes
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439:Compound of five cubes
243:. It can be seen as a
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812:Polyhedral stellation
550:Compound of six cubes
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489:
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817:Polyhedral compounds
613:Polyhedral Compounds
329:Euler characteristic
260:icosahedral symmetry
733:Klitzing, Richard.
669:Mathematical Models
636:1976MPCPS..79..447S
27:Polyhedral compound
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239:, and dual to the
235:It is one of five
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681:Regular Polytopes
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490:Stellation facets
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250:It is one of the
237:regular compounds
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16:(Redirected from
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822:Polyhedron stubs
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696:, pp.47-50, 6.2
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349:edge arrangement
335:Edge arrangement
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132:(visible as 360
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63:Regular compound
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18:Cube 5-compound
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630:(3): 447–457,
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767:expanding it
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423:Dodecahedron
345:dodecahedron
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279:dodecahedron
276:
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249:
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219:
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195:pyritohedral
177:
96:Dodecahedron
700:, pp.96-104
590:, Cambridge
427:convex hull
341:convex hull
252:stellations
230:Edmund Hess
174:icosahedral
91:Convex hull
806:Categories
759:polyhedron
565:References
468:tetrahedra
359:, and the
78:Stellation
660:123279687
588:Polyhedra
351:with the
325:triangles
258:. It has
232:in 1876.
134:triangles
113:Polyhedra
47:Animation
596:citation
512:See also
273:Geometry
245:faceting
223:of five
221:compound
189:Subgroup
150:Vertices
51:3D model
652:0397554
632:Bibcode
606:. p 360
470:of the
254:of the
129:squares
72:2{5,3}
692:, 3.6
688:
658:
650:
355:, the
757:This
656:S2CID
464:cubes
449:As a
225:cubes
142:Edges
124:Faces
118:cubes
102:Index
763:stub
686:ISBN
602:link
458:The
371:and
339:Its
218:The
158:Dual
80:core
59:Type
640:doi
269:).
153:20
145:60
127:30
808::
678:,
654:,
648:MR
646:,
638:,
628:79
626:,
598:}}
594:{{
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116:5
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