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:
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac12\right),$$
 * $$\left(0,\,±\sqrt{\frac{5+\sqrt5}{10}},\,±\frac12\right),$$
 * $$\left(0,\,-\frac{\sqrt2+\sqrt{\frac{5+2\sqrt5}{5}}}{2},\,0\right).$$