The small dodecicosidodecahedron is the uniform polyhedron with Maeder index 33 (Maeder 1997), Wenninger index 72 (Wenninger
1989), Coxeter index 42 (Coxeter et al. 1954), and Har'El index 38 (Har'El
1993). It has Wythoff symbol 
and its faces are 
. It is a faceted
version of the small rhombicosidodecahedron.
The small dodecicosidodecahedron is implemented in the Wolfram Language as UniformPolyhedron[72],
UniformPolyhedron["SmallDodecicosidodecahedron"],
UniformPolyhedron[
"Coxeter",
42
],
UniformPolyhedron[
"Kaleido",
38
],
UniformPolyhedron[
"Uniform",
33
],
or UniformPolyhedron[
"Wenninger",
72
].
It is also implemented in the Wolfram
Language as PolyhedronData["SmallDodecicosidodecahedron"].
Its convex hull is the small rhombicosidodecahedron and its circumradius for unit edge lengths is
 |
The small dodecicosahedron appears on the cover of Maeder (1999).
Its dual polyhedron is the small dodecacronic hexecontahedron.
