# 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 | S_{4}×C_{2} |
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.