# 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.

 VertexSymbol WythoffSymbol No. ofVertices No. ofEdges {4}Faces {6}Faces {10}Faces SymmetryGroup Dual Polyhedron 4.6.10 2 3 5 | 120 180 30 20 12 A5×C2 Hexakis Icosahedron

Edge ratios:

• e/rho = sqrt(2)tan(18^@)/sqrt(3) = 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.