Parabiaugmented hexagonal prism

The parabiaugmented hexagonal prism is one of the 92 Johnson solids (J55). It consists of 4+4 triangles, 4 squares, and 2 hexagons. It can be constructed by attaching square pyramids to two opposite square faces of the hexagonal prism.

Vertex coordinates
A parabiaugmented hexagonal prism of edge length 1 has the following vertices:
 * $$\left(±\frac12,\,±\frac{\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(±1,\,0,\,±\frac12\right),$$
 * $$\left(0,\,±\frac{\sqrt2+\sqrt3}{2},\,0\right).$$