# Small rhombihexahedron

Small rhombihexahedron
Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymSroh
Elements
Faces12 squares, 6 octagons
Edges24+24
Vertices24
Vertex figureButterfly, edge lengths 2 and 2+2
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt{5+2\sqrt2}}{2} ≈ 1.39897}$
Dihedral angles8–4 #1: 90°
8–4 #2: 45°
Central densityodd
Number of pieces66
Level of complexity10
Related polytopes
ArmySirco
RegimentSirco
DualSmall rhombihexacron
ConjugateGreat rhombihexahedron
Convex coreCube
Abstract properties
Flag count192
Euler characteristic-6
Topological properties
OrientableNo
Genus8
Properties
SymmetryB3, order 48
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.