Great rhombic trisicositetrachoron

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Great rhombic trisicositetrachoron
Rank4
TypeUniform
Notation
Bowers style acronymGirti
Elements
Cells24 great rhombihexahedra, 24 great rhombicuboctahedra, 24 cuboctatruncated cuboctahedra
Faces288 squares, 192 hexagons, 144 octagons, 144 octagrams
Edges288+576+576
Vertices576
Vertex figureButterfly pyramid, base edge lengths 2–2, 2, 2–2, 2; lateral edge lengths 3, 3, 2+2, 2+2
Measures (edge length 1)
Circumradius
Dichoral anglesGroh–8/3–cotco: 135°
 Groh–4–girco: 90°
 Cotco–8–girco: 90°
 Cotco–6–girco: 60°
Related polytopes
ArmySemi-uniform Grico, edge lengths (truncated cubes), 1 (sides of triangular prisms)
RegimentDitdi
ConjugateSmall rhombic trisicositetrachoron
Abstract & topological properties
Flag count18432
Euler characteristic–168
OrientableNo
Properties
SymmetryF4, order 1152
ConvexNo
NatureTame

The great rhombic trisicositetrachoron, or girti, is a nonconvex uniform polychoron that consists of 24 great rhombihexahedra, 24 cuboctatruncated cuboctahedra, and 24 great rhombicuboctahedra. One great rhombihexahedron, two cuboctatruncated cuboctahedra, and two great rhombicuboctahedra join at each vertex.

It can be constructed as a blend of three tesseractihexadecatruncated prismatotesseractihexadecachora. In the process the truncated octahedra blend out, while the octagrammic prisms blend into great rhombihexahedra.

Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the disicositetratruncated disicositetrachoron.

External links[edit | edit source]