# 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.

 VertexSymbol WythoffSymbol No. ofVertices No. ofEdges {3}Faces {8}Faces SymmetryGroup Dual Polyhedron 3.8.8 2 3 | 4 24 36 8 6 S4×C2 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.