The great truncated icosidodecahedron, also called the great quasitruncated icosidodecahedron, is the uniform polyhedron with Maeder index 68 (Maeder 1997), Wenninger index 108 (Wenninger 1989), Coxeter index 87 (Coxeter et al. 1954), and Har'El index 73 (Har'El 1993). It has Schläfli symbol and Wythoff symbol . Its faces are .
The great truncated icosidodecahedron is implemented in the Wolfram Language as UniformPolyhedron[108], UniformPolyhedron["GreatTruncatedIcosidodecahedron"], UniformPolyhedron["Coxeter", 87], UniformPolyhedron["Kaleido", 73], UniformPolyhedron["Uniform", 68], or UniformPolyhedron["Wenninger", 108]. It is also implemented in the Wolfram Language as PolyhedronData["GreatTruncatedIcosidodecahedron"].
Its skeleton graph is the great rhombicosidodecahedral graph, illustrated above.
Its circumradius for unit edge length is
Its dual is the great disdyakis triacontahedron.