Biaugmented pentagonal prism

The biaugmented pentagonal prism, or baupip, is one of the 92 Johnson solids (J53). It consists of 2+2+4 triangles, 1+2 squares, and 2 pentagons. It can be constructed by attaching square pyramids to two non-adjacent square faces of the pentagonal prism.

Vertex coordinates
A biaugmented 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),
 * (±(3+$\sqrt{2}$+2$\sqrt{2}$)/8, $\sqrt{25+10√5}$), 0).