# The Great Rhombicosidodecahedron

A semi-regular polyhedron with a square, a hexagon, and a decagon meeting at each vertex.

The great 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 |
{4} Faces |
{6} Faces |
{10} Faces |
Symmetry Group |
Dual Polyhedron |

4.6.10 | 2 3 5 | | 120 | 180 | 30 | 20 | 12 | A_{5}×C_{2} |
Hexakis Icosahedron |

Edge ratios:

- `e/rho = sqrt(2)/sqrt(3) tan(18^@) = sqrt((10-4sqrt(5))/15)`
- `e/R = 2sqrt((31-12sqrt(5))/241)`
- `e/(e_12) = (1+sqrt(5))/10`
- `e/(e_20) = (sqrt(5)-1)/6`
- `e/(d_30) = (7-sqrt(5))/22`

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.