The (small) rhombicosidodecahedron (Cundy and Rowlett 1989, p. 111), sometimes simply called the rhombicosidodecahedron (Maeder 1997; Wenninger 1989, p. 27;
Conway et al. 1999; Maeder 1997), is the 62-faced Archimedean
solid with faces 
. It is also the uniform
polyhedron with Maeder index 10 (Maeder 1997), Wenninger index 13 (Wenninger
1989), Coxeter index 22 (Coxeter et al. 1954), and Har'El index 15 (Har'El
1993). It is illustrated above together with a wireframe version and a net
that can be used for its construction.
It has Schläfli symbol r
and Wythoff symbol 
.
The small dodecicosidodecahedron
and small rhombidodecahedron are faceted
versions.
Some symmetric projections of the small rhombicosidodecahedron are illustrated above.
It is implemented in the Wolfram Language as UniformPolyhedron["Rhombicosidodecahedron"]. Precomputed properties are available as PolyhedronData["SmallRhombicosidodecahedron", prop].
The small rhombicosidodecahedron is the convex hull of the small dodecicosidodecahedron, small rhombidodecahedron, and small stellated truncated dodecahedron.
The inradius 
of the dual, midradius 
of the solid and dual, and circumradius 
of the solid for 
are
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
The unit small rhombicosidodecahedron has surface area
 |
(4)
|
and volume
 |
(5)
|
The unit small rhombicosidodecahedron Dehn invariant
 |  |  |
(6)
|
 |  |  |
(7)
|
 |  |  |
(8)
|
(OEIS A377606), where the first expression uses the basis of Conway et al. (1999). It can be dissected into the metabigyrate rhombicosidodecahedron, parabigyrate rhombicosidodecahedron, and trigyrate rhombicosidodecahedron, from which it differs only by the relative rotations of three cupola.
The dual polyhedron of the small rhombicosidodecahedron is the deltoidal hexecontahedron, both of which are illustrated above together with their common midsphere.
The Minkowski sum of a unit regular dodecahedron and unit regular icosahedron in dual position is a small rhombicosidodecahedron.
." §3.7.11 in