Small tetrisicositetrachoron

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Small tetrisicositetrachoron
Rank4
TypeUniform
Notation
Bowers style acronymSuti
Coxeter diagramx3o4x3x4/3*a ()
Elements
Cells24 truncated octahedra, 24 quasitruncated hexahedra, 24 small rhombicuboctahedra, 24 quasitruncated cuboctahedra
Faces192 triangles, 144+288 squares, 192 hexagons, 144 octagrams
Edges288+576+576
Vertices576
Vertex figureIsosceles trapezoidal pyramid, base edge lengths 1, 2, 2, 2; lateral edge lengths 3, 3, 2–2, 2–2
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesQuith–8/3–quitco: 135°
 Toe–6–quitco: 120°
 Sirco–3–quith: 120°
 Sirco–4–quitco: 90°
 Sirco–4–toe: 45°
Related polytopes
ArmySemi-uniform Prico, edge lengths (small rhombicuboctahedra), (sides of triangular prisms)
RegimentSuti
ConjugateGreat tetrisicositetrachoron
Abstract & topological properties
Flag count18432
Euler characteristic0
OrientableYes
Properties
SymmetryF4, order 1152
ConvexNo
NatureTame

The small tetrisicositetrachoron, or suti, is a nonconvex uniform polychoron that consists of 24 truncated octahedra, 24 quasitruncated hexahedra, 24 small rhombicuboctahedra, and 24 quasitruncated cuboctahedra. 1 quasitruncated hexahedron, 1 truncated octahedron, 1 small rhombicuboctahedron, and 2 quasitruncated cuboctahedra join at each vertex.

The small tetrisicositetrachoron contains the vertices of a tesseractihexadecaquasitruncated prismatotesseractihexadecachoron.

Cross-sections[edit | edit source]

Vertex coordinates[edit | edit source]

The vertices of a small tetrisicositetrachoron of edge length 1 are given by all permutations of:

The second set of vertices are identical to the vertices of an inscribed tesseractihexadecaquasitruncated prismatotesseractihexadecachoron.

Related polychora[edit | edit source]

The small tetrisicositetrachoron is the colonel of a 3-member regiment that also includes the disicositetraquasitruncated disicositetrachoron and small rhombic trisicositetrachoron.

External links[edit | edit source]