The great ditrigonal dodecicosidodecahedron is the uniform polyhedron with Maeder index 42 (Maeder 1997), Wenninger index 81 (Wenninger
1989), Coxeter index 54 (Coxeter et al. 1954), and Har'El index 47 (Har'El
1993). It has Wythoff symbol 
. Its faces are 
.
The great ditrigonal dodecicosidodecahedron is implemented in the Wolfram Language as UniformPolyhedron[81],
UniformPolyhedron["GreatDitrigonalDodecicosidodecahedron"],
UniformPolyhedron[
"Coxeter",
54
], UniformPolyhedron[
"Kaleido",
47
], UniformPolyhedron[
"Uniform",
42
], or UniformPolyhedron[
"Wenninger",
81
]. It is also implemented in the Wolfram
Language as PolyhedronData["GreatDitrigonalDodecicosidodecahedron"].
Its skeleton is the dodecicosahedral graph, illustrated above in a few embeddings.
Its convex hull is a truncated dodecahedron and its circumradius for unit edge length is
 |
The convex hull of the great ditrigonal dodecicosidodecahedron is a truncated dodecahedron, whose dual is the triakis icosahedron, so the dual of the great ditrigonal dodecicosidodecahedron (the great triambic icosahedron) is a stellation of the triakis icosahedron (Wenninger 1983, p. 42).
Its dual is the great ditrigonal dodecacronic hexecontahedron.
