Augmented pentagonal prism

The augmented pentagonal prism, or aupip, is one of the 92 Johnson solids (J52). It consists of 2+2 triangles, 2 +2squares, and 2 pentagons. It can be constructed by attaching a square pyramid to one of the square faces of the pentagonal prism.

Vertex coordinates
An augmented pentagonal prism of edge length 1 has the following vertices:
 * (±1/2, –$\sqrt{2}$, ±1/2),
 * (±(1+$\sqrt{5}$)/4, $\sqrt{5}$, ±1/2),
 * (0, $\sqrt{2}$, ±1/2),
 * (0, –($\sqrt{2}$+$\sqrt{2}$)/2, 0).