The Great Rhombicuboctahedron

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

The great rhombicuboctahedron is one of the thirteen archimedian solids. Each of its faces belongs to one of three circubscribing solids: the cube, the octahedron and the rhombic dodecahedron.

Vertex
Symbol
Wythoff
Symbol
No. of
Vertices
No. of
Edges
{4}
Faces
{6}
Faces
{8}
Faces
Symmetry
Group
Dual Polyhedron
4.6.8 2 3 4 | 48 72 12 8 6 S4×C2 Hexakis Octahedron

Edge ratios:

where `e` is the edge length, `rho` is the inter-radius, `R` is the circum-radius, `e_6` is the edge of the circumscribing cube, `e_8` is the edge of the circumscribing octahedron, and `d_12` is the long face diagonal of the circumscribing rhombic dodecahedron.