Small tripesic hecatonicosachoron

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Small tripesic hecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymSitphi
Coxeter diagram(o5/2x5x5/2o)/2 (/2)
Elements
Cells120 truncated great dodecahedra
Faces
Edges3600
Vertices1800 (as 600 fissary)
Vertex figureCompound of 3 tetragonal disphenoids, edge lengths (5–1)/2 (base) and (5+5)/2 (sides)
Measures (edge length 1)
Circumradius
Inradius
Hypervolume
Dichoral angleTigid–10–tigid: 108°
Tigid–5/2–tigid: 72°
Related polytopes
ArmyHi
RegimentSidtaxhi
ConjugateGreat tripesic hecatonicosachoron
Abstract & topological properties
Flag count43200
OrientableYes
Properties
SymmetryH4, order 14400
Flag orbits3
ConvexNo
NatureTame

The small tripesic hecatonicosachoron, or sitphi, is a nonconvex noble fissary uniform polychoron that consists of 120 truncated great dodecahedra as cells. 12 cells join at each vertex.

It is fissary due to having a compound vertex figure, specifically a compound of three disphenoids. It shares its edges with the small ditetrahedronary hexacosihecatonicosachoron.

A double cover of this polychoron can be seen as the bitruncated grand stellated hecatonicosachoron.

Cross sections[edit | edit source]

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


Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the small ditetrahedronary hexacosihecatonicosachoron.

External links[edit | edit source]