# The Small Rhombicuboctahedron

A semi-regular polyhedron with three squares and a triangle meeting at each vertex.

The small 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 {3}Faces {4}Faces SymmetryGroup Dual Polyhedron 3.4.4.4 3 4 | 2 24 48 8 6+12 S4×C2 TrapezoidalIcositetrahedron

Edge ratios:

• e/rho = sqrt(2-sqrt(2))
• e/R = (2sqrt(5-2sqrt(2)))/sqrt(17)
• e/(e_6) = sqrt(2)-1
• e/(e_8) = (3sqrt(2)-2)/7
• e/(d_12) = sqrt(2)-1

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.