2023-08-30
The great ditrigonal icosidodecahedron is the uniform polyhedron with Maeder index 47 (Maeder 1997), Wenninger index 87 (Wenninger
1989), Coxeter index 58 (Coxeter et al. 1954), and Har'El index 51 (Har'El
1993). It has Wythoff symbol 
and its faces are 
, and
The great ditrigonal icosidodecahedron is implemented in the Wolfram Language as UniformPolyhedron[87],
UniformPolyhedron["GreatDitrigonal-Icosidodecahedron"],
UniformPolyhedron[
"Coxeter",
58
],
UniformPolyhedron[
"Kaleido",
51
],
UniformPolyhedron[
"Uniform",
47
],
or UniformPolyhedron[
"Wenninger",
87
].
It is also implemented in the Wolfram
Language as PolyhedronData["GreatDitrigonalIcosidodecahedron"].
Its circumradius for unit edge length is
 |
The convex hull of the great triambic icosahedron is a regular dodecahedron, whose dual is the icosahedron, so the dual of the great ditrigonal icosidodecahedron (the great triambic icosahedron) is one of the icosahedron stellations.
The cube 5-compound and tetrahedron 10-compound can be constructed from its vertices.
Its dual is the great triambic icosahedron.
