Great rhombihexahedron

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Great rhombihexahedron
Rank3
TypeUniform
Notation
Bowers style acronymGroh
Elements
Faces12 squares, 6 octagrams
Edges24+24
Vertices24
Vertex figureButterfly, edge lengths 2 and 2–2
Measures (edge length 1)
Circumradius
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
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[edit | edit source]

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

Related polyhedra[edit | edit source]

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

External links[edit | edit source]