# Great rhombihexahedral prism

Great rhombihexahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymGrohp
Elements
Cells12 cubes, 6 octagrammic prisms, 2 great rhombihexahedra
Faces24+24+24 squares, 12 octagrams
Edges24+48+48
Vertices48
Vertex figureButterfly pyramid, edge lengths 2, 2–2, 2, 2–2 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {3-{\sqrt {2}}}{2}}}\approx 0.89045}$
Dichoral anglesGroh–4–cube: 90°
Groh–8/3–stop: 90°
Cube–4–stop #1: 90°
Cube–4–stop #2: 45°
Height1
Number of external pieces200
Related polytopes
ArmySemi-uniform Ticcup, edge lengths ${\displaystyle {\sqrt {2}}-1}$ (base), 1 (sides)
RegimentGoccope
DualGreat rhombihexacronic tegum
ConjugateSmall rhombihexahedral prism
Abstract & topological properties
Flag count1536
Euler characteristic–8
OrientableNo
Properties
SymmetryB3×A1, order 96
ConvexNo
NatureTame

The great rhombihexahedral prism or grohp is a prismatic uniform polychoron that consists of 2 great rhombihexahedra, 12 cubes, and 6 octagrammic prisms. Each vertex joins 1 great rhombihexahedron, 2 cubes, and 2 octagrammic prisms. As the name suggests, it is a prism based on the great rhombihexahedron.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the great cubicuboctahedral prism.