Elongated pentagonal bipyramid

The elongated pentagonal bipyramid is one of the 92 Johnson solids (J16). It consists of 10 triangles and 5 squares. It can be constructed by inserting a pentagonal prism between the halves of the pentagonal bipyramid.

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