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:
 * $$\left(±\frac12,\,±\frac{\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(±1,\,0,\,±\frac12\right),$$
 * $$\left(0,\,\frac{\sqrt2+\sqrt3}{2},\,0\right).$$