Small hecatonicosihecatonicosachoron

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Small hecatonicosihecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymShihi
Coxeter diagramo5/2x5x3o ()
Elements
Cells120 truncated dodecahedra, 120 truncated great dodecahedra
Faces1200 triangles, 720 pentagrams, 1440 decagons
Edges3600+3600
Vertices3600
Vertex figureDigonal disphenoid, edge lengths 1 (base 1), (5–1)/2 (base 2) and (5+5)/2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesTigid–5/2–tigid: 144°
 Tigid–10–tid: 144°
 Tid–3–tid: 120°
Central density4
Number of external pieces2520
Level of complexity17
Related polytopes
ArmySemi-uniform Xhi, edge lengths (pentagons), 1 (triangles)
RegimentShihi
ConjugateGreat hecatonicosihecatonicosachoron
Convex coreHecatonicosachoron
Abstract & topological properties
Flag count86400
Euler characteristic–480
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The small hecatonicosihecatonicosachoron, or shihi, is a nonconvex uniform polychoron that consists of 120 truncated dodecahedra and 120 truncated great dodecahedra. 2 of each join at each vertex.

It is the medial stage of the truncation series between a faceted hexacosichoron and its dual small stellated hecatonicosachoron, which makes it the bitruncation of both of these polychora.

Gallery[edit | edit source]

Card with cell counts, vertex figure, and cross-sections.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a small hecatonicosihecatonicosachoron of edge length 1 are given by all permutations of:

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together with all even permutations of:

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External links[edit | edit source]