# Great rhombihexahedron

(Redirected from Groh)
Great rhombihexahedron
Rank3
TypeUniform
Notation
Bowers style acronymGroh
Coxeter diagramx4/3x3/2x -8{6/2}
Elements
Faces12 squares, 6 octagrams
Edges24+24
Vertices24
Vertex figureButterfly, edge lengths 2 and 2–2
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {5-2{\sqrt {2}}}}{2}}\approx 0.73681}$
Dihedral angles8/3–4 #1: 90°
8/3–4 #2: 45°
Central densityodd
Number of external pieces366
Level of complexity56
Related polytopes
ArmyTic, edge length ${\displaystyle {\sqrt {2}}-1}$
RegimentGocco
DualGreat rhombihexacron
ConjugateSmall rhombihexahedron
Convex coreRhombic dodecahedron
Abstract & topological properties
Flag count192
Euler characteristic-6
OrientableNo
Genus8
Properties
SymmetryB3, order 48
Flag orbits4
ConvexNo
NatureTame

The great rhombihexahedron, or groh, is a uniform polyhedron. It consists of 12 squares and 6 octagrams. Two squares and two octagrams meet at each vertex. It also has 8 triangular pseudofaces and 6 square pseudofaces.

It is a faceting of the great cubicuboctahedron, using its 6 octagrams along with 12 squares of the quasirhombicuboctahedron.

It can be constructed as a blend of three orthogonal octagrammic prisms, with 6 pairs of coinciding square faces blending out.

## Vertex coordinates

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

## Related polyhedra

The rhombisnub quasihyperhombihedron is a uniform polyhedron compound composed of 5 great rhombihexahedra.