Small complex rhombicosidodecahedron


In geometry, the small complex rhombicosidodecahedron is a degenerate uniform star polyhedron. It has 62 faces, 120 edges and 20 vertices. All edges are doubled, sharing 4 faces, but are considered as two overlapping edges as a topological polyhedron.
It can be constructed from the vertex figure 3, thus making it also a cantellated great icosahedron. The "3" in front of this vertex figure indicates that each vertex in this degenerate polyhedron is in fact three coincident vertices. It may also be given the Schläfli symbol rr or t0,2.

As a compound

It can be seen as a compound of the small ditrigonal icosidodecahedron, U30, and the compound of five cubes. It is also a facetting of the dodecahedron.
Small ditrigonal icosidodecahedronCompound of five cubesCompound

As a cantellation

It can also be seen as a cantellation of the great icosahedron.
Fund.
triangle		ParentTruncatedRectifiedBitruncatedBirectified
CantellatedOmnitruncated
Snub
Wythoff symbolq | p 22 q | p2 | p q2 p | qp | q 2p q | 2p q 2 || p q 2
Schläfli symbolt0t0,1t1t1,2t2t0,2t0,1,2s
Coxeter–Dynkin diagram
Vertex figurepqq.2p.2pp.q.p.qp.2q.2qqpp.4.q.44.2p.2q3.3.p.3.q
Icosahedral
Great icosahedron|
.6.6
2
3..
Great stellated dodecahedron|
3.4..4
4..6
3.3.3.3.

Related degenerate uniform polyhedra

Two other degenerate uniform polyhedra are also facettings of the dodecahedron. They are the complex rhombidodecadodecahedron with vertex figure /3 and the great complex rhombicosidodecahedron with vertex figure /3. All three degenerate uniform polyhedra have each vertex in fact being three coincident vertices and each edge in fact being two coincident edges.
They can all be constructed by cantellating regular polyhedra. The complex rhombidodecadodecahedron may be given the Schläfli symbol rr or t0,2, while the great complex rhombicosidodecahedron may be given the Schläfli symbol rr or t0,2.