Great quasirhombated small stellated hecatonicosachoron

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Great quasirhombated small stellated hecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymGaqrisashi
Coxeter diagramx5/3x5x3o ()
Elements
Cells1200 triangular prisms, 120 truncated dodecahedra, 120 quasitruncated dodecadodecahedra
Faces2400 triangles, 3600 squares, 1440 decagons, 720 decagrams
Edges3600+3600+7200
Vertices7200
Vertex figureSphenoid, edge lengths 1 (1), 2 (2), (5+5)/2 (2), and (5–5)/2 (1)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesQuitdid–4–trip:
 Quitdid–10/3–quitdid: 144°
 Quitdid–10–tid: 36°
 Tid–3–trip: 30°
Number of external pieces20640
Level of complexity89
Related polytopes
ArmySemi-uniform Grahi, edge lengths (decagons), (triangles)
RegimentGaqrisashi
ConjugateGreat quasirhombated great grand hecatonicosachoron
Convex coreHecatonicosachoron
Abstract & topological properties
Flag count172800
Euler characteristic–480
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The great quasirhombated small stellated hecatonicosachoron, or gaqrisashi, is a nonconvex uniform polychoron that consists of 1200 triangular prisms, 120 truncated dodecahedra, and 120 quasitruncated dodecadodecahedra. 1 triangular prism, 1 truncated dodecahedron, and 2 quasitruncated dodecadodecahedra join at each vertex. As the name suggests, it can be obtained by quasicantitruncating the small stellated hecatonicosachoron.

Cross-sections[edit | edit source]

Vertex coordinates[edit | edit source]

The vertices of a great quasirhombated small stellated hecatonicosachoron of edge length 1 are given by all permutations of:

plus all even permutations of:

External links[edit | edit source]