# 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.

 VertexSymbol WythoffSymbol No. ofVertices No. ofEdges {4}Faces {6}Faces {8}Faces SymmetryGroup Dual Polyhedron 4.6.8 2 3 4 | 48 72 12 8 6 S4×C2 Hexakis Octahedron

Edge ratios:

• e/rho = sqrt(6-3sqrt(2))/3
• e/R = (2sqrt(13-6sqrt(2)))/sqrt(97)
• e/(e_6) = (2sqrt(2)-1)/7
• e/(e_8) = (2-sqrt(2))/3
• e/(d_12) = (3-sqrt(2))/7

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.