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applied to the pentagonal faces. In this construction, all the vertices are assumed to be the same distance from the center, while in general icosahedral symmetry can be maintained even with the 12 order-5 vertices at a different distance from the center as the other 30.
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of the icosidodecahedron, can be obtained by raising low pyramids on each equilateral triangular face on a pentakis icosidodecahedron. It has 120 isosceles triangle faces (2 types), 180 edges (3 types) and 62 vertices (3
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which has 60 isosceles triangle faces, 90 edges (2 types), and 32 vertices (2 types).
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439:, Proceedings of MOSAIC 2000, Seattle, WA, August, 2000, pp. 61–70
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Chapter 21: Naming the
Archimedean and Catalan polyhedra and Tilings (p 284)
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It represents the exterior envelope of a vertex-centered
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Its name comes from a topological construction from the
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looks like a pentakis icosidodecahedron with inverted
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241:It can also be topologically constructed from the
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437:Sculpture based on Propellorized Polyhedra
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447:, Heidi Burgiel, Chaim Goodman-Strauss,
392:3D model of a pentakis icosidodecahedron
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356:Tripentakis icosidodecahedron, the
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381:meeting at the polyhedron center.
215:truncated rhombic triacontahedron
16:Geodesic polyhedron with 80 faces
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375:small icosihemidodecahedron
551:
519:Conway polyhedron notation
476:Cambridge University Press
409:convex regular 4-polytopes
396:]]== Related polytopes ==
185:pentakis icosidodecahedron
22:Pentakis icosidodecahedron
515:VTML polyhedral generator
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26:
449:The Symmetries of Things
294:2-frequency subdivided
421:Tetrakis cuboctahedron
393:
340:is a slightly smaller
219:chamfered dodecahedron
190:subdivided icosahedron
146:Chamfered dodecahedron
411:, into 3 dimensions.
401:orthogonal projection
391:
338:Pentakis dodecahedron
91:Vertex configuration
379:pentagonal pyramids
197:with 80 triangular
40:Geodesic polyhedron
535:Geodesic polyhedra
394:
503:978-0-486-40921-4
485:978-0-521-29432-4
468:Wenninger, Magnus
457:978-1-56881-220-5
324:Icosidodecahedron
310:Related polyhedra
307:
306:
302:icosidodecahedron
231:icosidodecahedron
195:convex polyhedron
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472:Spherical Models
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141:Dual polyhedron
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110:k5aD = dcD = uI
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105:Conway notation
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509:External links
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445:John H. Conway
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373:The nonconvex
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75:120 (2 types)
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517:Try "k5aD" (
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235:kis operator
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225:Construction
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85:42 (2 types)
497:Dover 1999
296:icosahedron
243:icosahedron
122:Icosahedral
59:equilateral
427:References
209:. It is a
152:Properties
300:Pentakis
233:with the
205:, and 42
63:isosceles
54:triangles
529:Category
470:(1979),
415:See also
405:600-cell
358:Kleetope
247:coplanar
207:vertices
181:geometry
81:Vertices
494:0552023
403:of the
361:types).
267:(k5)aI
213:of the
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455:
451:2008,
272:Image
256:Conway
201:, 120
183:, the
156:convex
98:(30) 3
96:(12) 3
291:Form
203:edges
199:faces
193:is a
71:Edges
61:; 60
48:Faces
42:(2,0)
499:ISBN
480:ISBN
453:ISBN
211:dual
57:(20
36:Type
221:).
187:or
179:In
163:Net
52:80
531::
490:MR
488:,
478:,
474:,
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264:)I
260:(u
249:.
521:)
262:2
217:(
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131:h
127:I
124:(
65:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
