Pentagrammic cuploid

The pentagrammic cuploid, also called the pentagrammic semicupola or stiscu, is an orbiform polyhedron. It consists of 5 triangles, 5 squares, and 1 pentagram. It is a cuploid based on the pentagram {5/2}, with a pseudo {10/2} base (corresponding to a doubled-up pentagon which is blended out).

Vertex coordinates
A retrograde pentagrammic cupola of edge length 1 has vertices given by the following coordinates:


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

Related polyhedra
The pentagrammic cuploid can be edge-inscribed into the small ditrigonary icosidodecahedron; it uses its triangles and pentagrams as well as squares of the rhombihedron, the inscribed compound of 5 cubes.