# The Small Rhombicosidodecahedron

A semi-regular polyhedron with (in order) a triangle, a square, a pentagon, and another square surrounding each vertex.

The small rhombicosidodecahedron is one of the thirteen archimedian solids. Each of its faces belongs to one of three circubscribing solids: the dodecahedron, the icosahedron, and the rhombic triacontahedron.

Vertex Symbol |
Wythoff Symbol |
No. of Vertices |
No. of Edges |
{3} Faces |
{4} Faces |
{5} Faces |
Symmetry Group |
Dual Polyhedron |

3.4.5.4 | 3 5 | 2 | 60 | 120 | 20 | 30 | 12 | A_{5}×C_{2} |
Trapezoidal Hexecontahedron |

Edge ratios:

- `e/rho = sqrt(2)tan(18^@) = sqrt((10-4sqrt(5))/5)`
- `e/R = 2sqrt((11-4sqrt(5))/41)`
- `e/(e_12) = (1+sqrt(5))/6`
- `e/(e_20) = (1+3sqrt(5))/22`
- `e/(d_30) = (3-sqrt(5))/2`

where `e` is the edge length, `rho` is the inter-radius, `R` is the circum-radius, `e_12` is the edge of the circumscribing dodecahedron, `e_20` is the edge of the circumscribing icosahedron, and `d_30` is the long face diagonal of the circumscribing rhombic triacontahedron.