The cubohemioctahedron is the uniform polyhedron with Maeder index 15 (Maeder 1997), Wenninger index 78 (Wenninger 1989), Coxeter
index 51 (Coxeter et al. 1954), and Har'El index 20 (Har'El 1993). It has
Wythoff symbol 
. Its faces are 
, making it a (non-regular) decahedron
with intersecting faces. It is a faceted version of
the cuboctahedron.
The cubohemioctahedron is implemented in the Wolfram Language as UniformPolyhedron[78],
UniformPolyhedron["Cubohemioctahedron"],
UniformPolyhedron[
"Coxeter", 51
], UniformPolyhedron[
"Kaleido", 20
], UniformPolyhedron[
"Uniform", 15
], or UniformPolyhedron[
"Wenninger", 78
]. It is also implemented in the Wolfram
Language as PolyhedronData["Cubohemioctahedron"].
Its skeleton is the cuboctahedral graph, illustrated above in a number of embeddings.
Its circumradius for unit edge length is 
.
Its dual is the hexahemioctacron.
