Elongated pentagonal gyrobirotunda

The elongated pentagonal gyrobirotunda, or epgybro, is one of the 92 Johnson solids (J43). It consists of 10+10 triangles, 5+5 squares, and 2+10 pentagons. It can be constructed by inserting a decagonal prism between the two halves of the icosidodecahedron, seen as a pentagonal gyrobirotunda.

Vertex coordinates
An elongated pentagonal gyrobirotunda of edge length 1 has the following vertices:
 * (±1/2, ±$\sqrt{5}$/2, ±1/2),
 * (±(3+$\sqrt{5}$)/4, ±$\sqrt{2}$, ±1/2),
 * (±(1+$\sqrt{2}$)/2, 0, ±1/2),
 * (±1/2, –$\sqrt{5}$, (1+2$\sqrt{5+2√5}$)/2),
 * (±(1+$\sqrt{2(5+√5)/15}$)/4, $\sqrt{5}$, (1+2$\sqrt{5+2√5)/15}$)/2),
 * (0, $\sqrt{(5+2√5)}$, (1+2$\sqrt{5}$)/2),
 * (±(1+$\sqrt{(5+√5)/8}$)/4, $\sqrt{5}$, (1+2$\sqrt{(5+2√5)/20}$)/2),
 * (±(3+$\sqrt{(5+2√5)/5}$)/4, –$\sqrt{5}$, (1+2$\sqrt{(5+√5)/40}$)/2),
 * (0, –$\sqrt{(5+2√5)/5}$, (1+2$\sqrt{(5+√5)/10}$)/2),
 * (±1/2, $\sqrt{(5+2√5)/5}$, –(1+2$\sqrt{5}$)/2),
 * (±(1+$\sqrt{(25+11√5)/40}$)/4, –$\sqrt{(5+√5)/10}$, –(1+2$\sqrt{5}$)/2),
 * (0, –$\sqrt{(5+√5)/40}$, –(1+2$\sqrt{(5+√5)/10}$)/2),
 * (±(1+$\sqrt{(5+2√5)/5}$)/4, –$\sqrt{(5+√5)/10}$, –(1+2$\sqrt{(5+2√5)/20}$)/2),
 * (±(3+$\sqrt{(5+2√5)/5}$)/4, $\sqrt{5}$, –(1+2$\sqrt{(5+√5)/40}$)/2),
 * (0, $\sqrt{(5+2√5)/5}$, –(1+2$\sqrt{(5+√5)/10}$)/2).