Great quasirhombated icositetrachoron

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Great quasirhombated icositetrachoron
Rank4
TypeUniform
Notation
Bowers style acronymGaqri
Coxeter diagramx3x4/3x3o ()
Elements
Cells96 triangular prisms, 24 quasitruncated hexahedra, 24 quasitruncated cuboctahedra
Faces192 triangles, 288 squares, 96 hexagons, 144 octagrams
Edges288+288+576
Vertices576
Vertex figureSphenoid edge lengths 1 (1), 2 (2), 3 (1), and 2–2 (2)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesQuitco–6–quitco: 120°
 Quitco–8/3–quith: 45°
 Quitco–4–trip:
 Quith–3–trip: 30°
Number of external pieces2856
Level of complexity105
Related polytopes
ArmySemi-uniform Prico, edge lengths (small rhombicuboctahedra), (bases of triangular prisms)
RegimentGaqri
ConjugateGreat rhombated icositetrachoron
Convex coreIcositetrachoron
Abstract & topological properties
Flag count13824
Euler characteristic0
OrientableYes
Properties
SymmetryF4, order 1152
ConvexNo
NatureTame

The great quasirhombated icositetrachoron, or gaqri, is a nonconvex uniform polychoron that consists of 96 triangular prisms, 24 quasitruncated hexahedra, and 24 quasitruncated cuboctahedra. 1 triangular prism, 1 quasitruncated hexahedron, and 2 quasitruncated cuboctahedra join at each vertex. As the name suggests, it can be obtained by quasicantitruncating the icositetrachoron.

Gallery[edit | edit source]

Vertex coordinates[edit | edit source]

The vertices of a great quasirhombated icositetrachoron of edge length 1 are given by all permutations of:

The quasicantitruncation of the dual icositetrachron has coordinates given by all permutations of:

External links[edit | edit source]