Disicositetraquasitruncated disicositetrachoron

The disicositetraquasitruncated disicositetrachoron, or diquitdi, is a nonconvex uniform polychoron that consists of 24 truncated octahedra, 24 quasitruncated hexahedra, 24 small cubicuboctahedra, and 24 cuboctatruncated cuboctahedra. 1 quasitruncated hexahedron, 1 truncated octahedron, 1 small cubicuboctahedron, and 2 cuboctatruncated cuboctahedra join at each vertex.

Disicositetraquasitruncated disicositetrachoron
Rank4
TypeUniform
Notation
Bowers style acronymDiquitdi
Coxeter diagramx3x4/3x3o4/3*a4*c ()
Elements
Cells24 truncated octahedra, 24 quasitruncated hexahedra, 24 small cubicuboctahedra, 24 cuboctatruncated cuboctahedra
Faces192 triangles, 144 squares, 192 hexagons, 144 octagons, 144 octagrams
Edges288+576+576
Vertices576
Vertex figureCrossed isosceles trapezoidal pyramid, base edge lengths 1, 2+2, 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${\displaystyle 168{\sqrt {2}}-139\approx 98.58788}$
Dichoral anglesSocco–8–cotco: 135°
Socco–3–quith: 120°
Toe–6–cotco: 120°
Socco–4–toe: 45°
Quith–8/3–cotco: 45°
Central density19
Related polytopes
ArmySemi-uniform Prico, edge lengths ${\displaystyle {\sqrt {2}}-1}$ (small rhombicuboctahedra), ${\displaystyle 2-{\sqrt {2}}}$ (sides of triangular prisms)
RegimentSuti
ConjugateDisicositetratruncated disicositetrachoron
Abstract & topological properties
Flag count18432
Euler characteristic–144
OrientableYes
Properties
SymmetryF4, order 1152
ConvexNo
NatureTame

Vertex coordinates

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