Small complex rhombicosidodecahedron
( p q 2 ) Parent Truncated Rectified Bitruncated Birectified ( dual ) Cantellated Omnitruncated ( Cantitruncated ) Snub
Wythoff symbol q | p 2 2 q | p 2 | p q 2 p | q p | q 2 p q | 2 p q 2 | | p q 2
Schläfli symbol t 0 { p , q } t 0,1 { p , q } t 1 { p , q } t 1,2 { p , q } t 2 { p , q } t 0,2 { p , q } t 0,1,2 { p , q } s { p , q }
Vertex figure p q.2p.2p p.q.p.q p.2q.2q q p.4.q.4 4.2p.2q 3.3.p.3.q
Icosahedral ( ​ ⁄ 2 3 2 ) { 3 , ​ ⁄ 2 } ​ ⁄ 2 .6.6 ( 3.​ ⁄ 2 ) 3.​ ⁄ 2 .​ ⁄ 2 { ​ ⁄ 2 ,3 } 3.4.​ ⁄ 2 .4 4.​ ⁄ 2 .6 3.3.3.3.​ ⁄ 2
As a cantellation
It can also be seen as a cantellation of the great icosahedron ( or , equivalently , of the great stellated dodecahedron ) .
In geometry, the small complex rhombicosidodecahedron (also known as the small complex ditrigonal rhombicosidodecahedron) is a degenerate uniform star polyhedron. It has 62 faces (20 triangles, 12 pentagrams and 30 squares), 120 (doubled) edges and 20 vertices. All edges are doubled (making it degenerate), sharing 4 faces, but are considered as two overlapping edges as a topological polyhedron. It can be constructed from the vertex figure 3(/.4.3.4), 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{5/2,3} or t{5/2,3}.