The dodecadodecahedron is the uniform polyhedron with Maeder index 36 (Maeder 1997), Wenninger index 73 (Wenninger 1989), Coxeter
index 45 (Coxeter et al. 1954), and Har'El index 41 (Har'El 1993). The dodecadodecahedron
has Schläfli symbol 
and Wythoff symbol 
. Its faces are 
.
It can be obtained by truncating a great dodecahedron or faceting a icosidodecahedron with pentagons and covering remaining open spaces with pentagrams (Holden 1991, p. 103).
The dodecadodecahedron is implemented in the Wolfram Language as UniformPolyhedron[73],
UniformPolyhedron["Dodecadodecahedron"],
UniformPolyhedron[
"Coxeter", 45
], UniformPolyhedron[
"Kaleido", 41
], UniformPolyhedron[
"Uniform", 35
], or UniformPolyhedron[
"Wenninger", 73
]. It is also implemented in the Wolfram
Language as PolyhedronData["Dodecadodecahedron"].
Its vertices correspond to those of the octahedron 5-compound.
Its skeleton is the dodecadodecahedral graph, illustrated above in a number of bilateral LCF embeddings.
Its circumradius for unit edge length is
 |
A faceted version is the great dodecahemicosahedron. The convex hull of the dodecadodecahedron is an icosidodecahedron and the dual of the icosidodecahedron is the rhombic triacontahedron, so the dual of the dodecadodecahedron is one of the rhombic triacontahedron stellations (Wenninger 1983, p. 41).
Its dual polyhedron is the medial rhombic triacontahedron.
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