# 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 | S_{4}×C_{2} |
Trapezoidal Icositetrahedron |

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.