The small icosihemidodecahedron is the uniform polyhedron with Maeder index 49 (Maeder 1997), Wenninger index 89 (Wenninger
1989), Coxeter index 63 (Coxeter et al. 1954), and Har'El index 54 (Har'El
1993). It has Wythoff symbol 
and its faces are 
. It is a faceted version
of the icosidodecahedron.
The small icosihemidodecahedron is implemented in the Wolfram Language as UniformPolyhedron[89],
UniformPolyhedron["Icosihemidodecahedron"],
UniformPolyhedron[
"Coxeter",
63
],
UniformPolyhedron[
"Kaleido",
54
],
UniformPolyhedron[
"Uniform",
49
],
or UniformPolyhedron[
"Wenninger",
89
].
It is also implemented in the Wolfram
Language as PolyhedronData["Icosihemidodecahedron"].
Its skeleton is the icosidodecahedral graph, illustrated above in a few embeddings.
Its circumradius for unit edge lengths is
 |
Its convex hull is a regular icosidodecahedron and an octahedron 5-compound can be constructed from its vertices.
Its dual polyhedron is the small icosihemidodecacron.
