Augmented truncated cube

The augmented truncated cube, or autic, is one of the 92 Johnson solids (J66). It consists of 4+4+4 triangles, 1+4 squares, and 1+4 octagons. It can be constructed by attaching a square cupola to one of the octagonal faces of the truncated cube..

Vertex coordinates
An augmented truncated cube of edge length 1 has vertices given by all permutations of: Plus the following additional vertices:
 * (±(1+$\sqrt{2}$)/2, ±(1+$\sqrt{2}$)/2, ±1/2),
 * (±$\sqrt{2}$/2, 0, (1+2$\sqrt{2}$)/2),
 * (0, ±$\sqrt{2+√2}$/2, (1+2$\sqrt{2+√2}$)/2).