The small rhombihexahedron is the uniform polyhedron with Maeder index 18 (Maeder 1997), Wenninger index 86 (Wenninger 1989), Coxeter
index 60 (Coxeter et al. 1954), and Har'El index 23 (Har'El 1993). It has
Wythoff symbol 
and its faces are 
. It is a faceted version
of the small rhombicuboctahedron.
The small rhombihexahedron is implemented in the Wolfram Language as UniformPolyhedron[86],
UniformPolyhedron["SmallRhombihexahedron"],
UniformPolyhedron[
"Coxeter", 60
], UniformPolyhedron[
"Kaleido", 23 
], UniformPolyhedron[
"Uniform", 18
], or UniformPolyhedron[
"Wenninger", 86
].
It is also implemented in the Wolfram
Language as PolyhedronData["SmallRhombihexahedron"].
Its skeleton is the small rhombicuboctahedral graph, illustrated above.
Its circumradius for unit edge lengths is
 |
Its dual polyhedron is the small rhombihexacron.
The convex hull of the small rhombihexahedron is the Archimedean small rhombicuboctahedron 
,
whose dual is the deltoidal icositetrahedron,
so the dual of the small rhombihexahedron (i.e., the small
rhombihexacron) is one of the stellations of the deltoidal
icositetrahedron (Wenninger 1971, p. 57).
