# The Truncated Cube

A semi-regular polyhedron with two octagons and a triangle meeting at each vertex.

The truncated cube is one of the thirteen archimedian solids. 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 |
{3} Faces |
{8} Faces |
Symmetry Group |
Dual Polyhedron |

3.8.8 | 2 3 | 4 | 24 | 36 | 8 | 6 | S_{4}×C_{2} |
Triakis Octahedron |

Edge ratios:

- `e/rho = 2 - sqrt(2)`
- `e/R = (2 sqrt(7-4sqrt(2)))/sqrt(17)`
- `e/(e_6) = sqrt(2) - 1`
- `e/(e_8) = 3sqrt(2) - 4`

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.