Small tritrigonary hexacositrishecatonicosachoron

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Small tritrigonary hexacositrishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymStut xethi
Coxeter diagramx3o3/2o3/2x5*a5*c
Elements
Cells600 tetrahedra, 120 great ditrigonary icosidodecahedra, 120 truncated dodecahedra, 120 small dodecicosidodecahedra
Faces2400+2400 triangles, 1440 pentagons, 1440 decagons
Edges3600+7200
Vertices2400
Vertex figureCrossed retrotriangular cupola, edge lengths 1 (top triangle and 3 edges of base tripod), (1+5)/2 (remaining base edges), and (5+5)/2 (side edges)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesGidtid–5–saddid: 144°
 Tet–3–saddid:
 Gidtid–3–tid: 120°
 Saddid–10–tid: 108°
Related polytopes
ArmySemi-uniform sidpixhi, edge lengths (dodecahedra), 1 (tetrahedra)
RegimentStut phiddix
ConjugateGreat tritrigonary hexacositrishecatonicosachoron
Abstract & topological properties
Flag count144000
Euler characteristic–1680
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The small tritrigonary hexacositrishecatonicosachoron, or stut xethi, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 truncated dodecahedra, 120 small dodecicosidodecahedra, and 120 great ditrigonary icosidodecahedra. 1 tetrahedron, 3 truncated dodecahedra, 3 small dodecicosidodecahedra, and 1 great ditrigonary icosidodecahedron join at each vertex.

Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the small tritrigonary prismatohecatonicosidishexacosichoron.

External links[edit | edit source]