# Small tetrisicositetrachoron

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${\displaystyle {\sqrt {4-{\sqrt {2}}}}\approx 1.60804}$
Hypervolume${\displaystyle 13+48{\sqrt {2}}\approx 80.88225}$
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 ${\displaystyle {\sqrt {2}}-1}$ (small rhombicuboctahedra), ${\displaystyle 2-{\sqrt {2}}}$ (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.

## Vertex coordinates

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

• ${\displaystyle \left(\pm {\frac {2-{\sqrt {2}}}{2}},\,\pm {\sqrt {2}},\,\pm {\frac {\sqrt {2}}{2}},\,0\right),}$
• ${\displaystyle \left(\pm {\frac {2{\sqrt {2}}-1}{2}},\,\pm {\frac {{\sqrt {2}}-1}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}}\right).}$

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

## Related polychora

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