Great rhombated order-5 cubic honeycomb

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Great rhombated order-5 cubic honeycomb
Rank4
TypeUniform, compact
SpaceHyperbolic
Notation
Bowers style acronymGripech
Coxeter diagramo5x3x4x ()
Elements
Cells12N pentagonal prisms, 2N truncated icosahedra, 5N great rhombicuboctahedra
Faces60N squares, 24N pentagons, 40N hexagons, 15N octagons
Edges60N+60N+120N
Vertices120N
Vertex figureSphenoid edge lengths 2 (2), (1+5)/2 (1), 3 (2), and 2+2 (1)
Measures (edge length 1)
Circumradius
Related polytopes
ArmyGripech
RegimentGripech
Abstract & topological properties
OrientableYes
Properties
Symmetry[5,3,4]
ConvexYes

The great rhombated order-5 cubic honeycomb, also called the cantitruncated order-5 cubic honeycomb, is a compact uniform tiling of 3D hyperbolic space. 2 pentagonal prisms, 1 truncated icosahedron, and 2 great rhombicuboctahedra meet at each vertex. As the name suggests, it can be derived by cantitruncation of the order-5 cubic honeycomb.

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