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.

Vertex
Symbol
Wythoff
Symbol
No. of
Vertices
No. of
Edges
{3}
Faces
{4}
Faces
Symmetry
Group
Dual Polyhedron
3.4.4.4 3 4 | 2 24 48 8 6+12 S4×C2 Trapezoidal
Icositetrahedron

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.