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 A5×C2 Hexakis Icosahedron

Edge ratios:

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.