The great icosihemidodecahedron is the uniform polyhedron with Maeder index 71 (Maeder 1997), Wenninger index 106 (Wenninger
1989), Coxeter index 85 (Coxeter et al. 1954), and Har'El index 76 (Har'El
1993). It has Wythoff symbol 
and its faces are 
.
The great icosihemidodecahedron is implemented in the Wolfram Language as UniformPolyhedron[106],
UniformPolyhedron["GreatIcosihemidodecahedron"],
UniformPolyhedron[
"Coxeter",
85
],
UniformPolyhedron[
"Kaleido",
76
],
UniformPolyhedron[
"Uniform",
71
],
or UniformPolyhedron[
"Wenninger",
106
].
It is also implemented in the Wolfram
Language as PolyhedronData["GreatIcosihemidodecahedron"].
Its convex hull is the regular icosidodecahedron, and its vertices are those of the octahedron 5-compound.
Its skeleton is the icosidodecahedral graph.
For unit edge length, its circumradius is
 |
where 
is the golden ratio.
Its dual is the great icosihemidodecacron.
