Augmented hexagonal prism

The augmented hexagonal prism, or auhip, is one of the 92 Johnson solids (J54). It consists of 2+2 triangles, 1+2+2 squares, and 2 hexagons. It can be constructed by attaching a square pyramid to one of the square faces of the hexagonal prism.

Vertex coordinates
An augmented hexagonal prism of edge length 1 has the following vertices:
 * (±1/2, ±$\sqrt{2}$/2, ±1/2),
 * (±1, 0, ±1/2).
 * (0, ($\sqrt{3}$+$\sqrt{5}$)/2, 0).