Small hecatonicosintercepted hecatonicosachoron

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Small hecatonicosintercepted hecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymShinhi
Elements
Cells
Faces
Edges3600
Vertices1200
Vertex figureTriangular toroprism, edge lengths 1 (base edges), (1+5)/2 (side edges of rectangles), and (5+5)/2 (side edges of triangles)
Edge figureid 5 id 3 tid 10 tid 10 tid 3
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesId–5–id: 144°
 Id–3–tid: 120°
 Tid–10–tid: 72°
Number of external pieces2520
Level of complexity6
Related polytopes
ArmyRahi
RegimentRahi
ConjugateGreat hecatonicosintercepted hecatonicosachoron
Convex coreHecatonicosachoron
Abstract & topological properties
Flag count72000
Euler characteristic1200
OrientableYes
Properties
SymmetryH4, order 14400
Flag orbits5
ConvexNo
NatureWild

The small hecatonicosintercepted hecatonicosachoron, or shinhi, is a nonconvex uniform polychoron that consists of 120 icosidodecahedra and 120 truncated dodecahedra. 3 icosidodecahedra and 6 truncated dodecahedra join at each vertex.

It is wild because it has icosidodecahedra intercepted by decagons.

Gallery[edit | edit source]

Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the rectified hecatonicosachoron.

External links[edit | edit source]