Truncated cube

The truncated cube, the truncated hexahedron, or tic, is one of the 13 Archimedean solids. It consists of 8 triangles and 6 octagons. Each vertex joins one triangle and two octagons. As the name suggests, it can be obtained by truncation of the cube.

Vertex coordinates
A truncated cube of edge length 1 has vertex coordinates given by all permutations of:
 * (±(1+$\sqrt{7+4√2}$)/2, ±(1+$\sqrt{2}$)/2, ±1/2).

Representations
A truncated cube has the following Coxeter diagrams:


 * x4x3o (full symmetry)
 * xwwx4xoox&#xt (BC2 axial, octagon-first)
 * xwwxoo3ooxwwx&#xt (A2 axial, triangle-first)
 * wx3oo3xw&#zx (A3 subsymmetry, as hull of 2 small rhombitetratetrahedra)
 * wx xw4xo&#zx (BC2×A1 symmetry)
 * wwx wxw xww&#zx (A1×A1×A1 symmetry)
 * oxwUwxo xwwxwwx&#xt (A1×A1 axial)

Related polyhedra
A truncated cube can be augmented by attaching a square cupola to one of its octagonal faces, forming the augmented truncated cube. If a second square cupola is attached to the opposite octagonal face, the result is the biaugmented truncated cube.

The truncated rhombihedron is a uniform polyhedron compound composed of 5 truncated cubes.