# The Truncated Octahedron

A semi-regular polyhedron with two hexagons and a square meeting at each vertex.

The truncated icosahedron is one of the thirteen archimedian solids. It is also the unit cell for face centred cubic (FCC) packing. It can be created by slicing suitable sections off the vertices of either a cube or an octahedron and thus may be inscribed in either solid.

Vertex Symbol |
Wythoff Symbol |
No. of Vertices |
No. of Edges |
{4} Faces |
{6} Faces |
Symmetry Group |
Dual Polyhedron |

4.6.6 | 2 4 | 3 | 24 | 36 | 6 | 8 | S_{4}×C_{2} |
Tetrakis Hexahedron |

Edge ratios:

- `e/rho = 2/3`
- `e/R = sqrt(10)/5`
- `e/(e_6) = sqrt(2)/4`
- `e/(e_8) = 1/3`

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, and `e_8` is the edge of the circumscribing octahedron.