# Small rhombihexahedron

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Small rhombihexahedron
Rank3
TypeUniform
Notation
Bowers style acronymSroh
Coxeter diagramx4x3/2x -8{6/2}
Elements
Faces12 squares, 6 octagons
Edges24+24
Vertices24
Vertex figureButterfly, edge lengths 2 and 2+2
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {5+2{\sqrt {2}}}}{2}}\approx 1.39897}$
Dihedral angles8–4 #1: 90°
8–4 #2: 45°
Central densityodd
Number of external pieces66
Level of complexity10
Related polytopes
ArmySirco
RegimentSirco
DualSmall rhombihexacron
ConjugateGreat rhombihexahedron
Convex coreCube
Abstract & topological properties
Flag count192
Euler characteristic-6
OrientableNo
Genus8
Properties
SymmetryB3, order 48
Flag orbits4
ConvexNo
NatureTame

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

It is a faceting of the small rhombicuboctahedron, using 12 of its squares, along with the 6 octagons of the small cubicuboctahedron.

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

## Vertex coordinates

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

## Related polyhedra

The rhombisnub hyperhombihedron is a uniform polyhedron compound composed of 5 small rhombihexahedra.