Elongated pentagonal pyramid

The elongated pentagonal pyramid, or epeppy, is one of the 92 Johnson solids (J9). It consists of 5 triangles, 5 squares, and 1 pentagon. It can be constructed by attaching a pentagonal prism to the base of the pentagonal pyramid..

If a second pyramid is attached to the other base of the pentagonal prism, the result is the elongated pentagonal bipyramid.

Vertex coordinates
An elongated pentagonal pyramid of edge length 1 has the following vertices:
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac12\right),$$
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac12\right),$$
 * $$\left(0,\,0,\,\frac{1+2\sqrt{\frac{5-\sqrt5}{10}}}{2}\right).$$