The small cubicuboctahedron is the uniform polyhedron with Maeder index 13 (Maeder 1997), Wenninger index 69 (Wenninger 1989), Coxeter
index 38 (Coxeter et al. 1954), and Har'El index 18 (Har'El 1993). Its faces
are 
and it has Wythoff symbol 
.
Its dual polyhedron is the small hexacronic icositetrahedron.
The small cubicuboctahedron is implemented in the Wolfram Language as UniformPolyhedron[69],
UniformPolyhedron["SmallCubicuboctahedron"],
UniformPolyhedron[
"Coxeter",
38
],
UniformPolyhedron[
"Kaleido",
18
],
UniformPolyhedron[
"Uniform",
13
],
or UniformPolyhedron[
"Wenninger",
69
].
It is also implemented in the Wolfram
Language as PolyhedronData["SmallCubicuboctahedron"].
The circumradius for the solid with unit edge length is
 |
Faceted versions include the uniform great rhombicuboctahedron and small rhombihexahedron.
The skeleton of the small cubicuboctahedron is the small rhombicuboctahedral graph, illustrated above.
The convex hull of the small cubicuboctahedron is the Archimedean small rhombicuboctahedron 
,
whose dual is the deltoidal icositetrahedron,
so the dual of the small cubicuboctahedron (i.e., the small
hexacronic icositetrahedron) is one of the stellations of the deltoidal
icositetrahedron (Wenninger 1983, p. 57).
