The octahemioctahedron, also called the octatetrahedron, is the uniform polyhedron with Maeder index 3 (Maeder 1997), Wenninger index 68 (Wenninger 1989),
Coxeter index 37 (Coxeter et al. 1954), and Har'El index 8 (Har'El 1993).
It has Wythoff symbol 
and its faces are 
. It is a dodecahedron
with intersecting faces, and its hull is a faceted cuboctahedron.
The octahemioctahedron is implemented in the Wolfram Language as UniformPolyhedron[68],
UniformPolyhedron["SmallDitrigonalIcosidodecahedron"],
UniformPolyhedron[
"Coxeter", 37
], UniformPolyhedron[
"Kaleido", 8
], UniformPolyhedron[
"Uniform", 3
], or UniformPolyhedron[
"Wenninger", 68
]. It is also implemented in the Wolfram
Language as PolyhedronData["Octahemioctahedron"].
Its skeleton is the cuboctahedral graph, illustrated above in a number of embeddings.
The convex hull of the octahemioctahedron is the cuboctahedron.
For unit edge lengths, its circumradius is
 |
Its dual polyhedron is the octahemioctacron.
