Biaugmented truncated cube

The biaugmented truncated cube, or bautic, is one of the 92 Johnson solids (J67). It consists of 8+8 triangles, 2+8 squares, and 4 octagons. It can be constructed by attaching square cupolas to two opposite octagonal faces of the truncated cube..

Vertex coordinates
A biaugmented 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).