The quasirhombicosidodecahedron is the uniform polyhedron with Maeder index 67 (Maeder 1997), Wenninger index 105 (Wenninger
1989), Coxeter index 84 (Coxeter et al. 1954), and Har'El index 72 (Har'El
1993). It has Schläfli symbol r'
and Wythoff symbol 
.
Its faces are 
.
Unfortunately, some authors (e.g., Maeder 1997, Model 67) use the term "great rhombicosidodecahedron" to refer to this solid, despite the fact that the same term is commonly used (e.g., Cundy and Rowlett 1989, pp. 112-113) to refer to a distinct Archimedean solid.
The quasirhombicosidodecahedron is implemented in the Wolfram Language as UniformPolyhedron[105],
UniformPolyhedron["GreatRhombicosidodecahedron"],
UniformPolyhedron[
"Coxeter",
84
],
UniformPolyhedron[
"Kaleido",
72
],
UniformPolyhedron[
"Uniform",
67
],
or UniformPolyhedron[
"Wenninger",
105
].
It is also implemented in the Wolfram
Language as PolyhedronData["Quasirhombicosidodecahedron"].
Its skeleton is the small rhombicosidodecahedral graph, illustrated above in a few embeddings.
Its dual is the great deltoidal hexecontahedron.
For unit edge length, its circumradius is
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." §3.7.12 in