Square-pentagonal antiprismatic duoprism

The square-pentagonal antiprismatic duoprism or squapap is a convex uniform duoprism that consists of 4 pentagonal antiprismatic prisms, 2 square-pentagonal duoprisms, and 10 triangular-square duoprisms. Each vertex joins 2 pentagonal antiprismatic prisms, 3 triangular-square duoprisms, and 1 square-pentagonal duoprism. It is a duoprism based on a square and a pentagonal antiprism, which makes it a convex segmentoteron.

Vertex coordinates
The vertices of a square-pentagonal antiprismatic duoprism of edge length 1 are given by all central inversions of the last three coordinates of:
 * $$\left(±\frac12,\,±\frac12,\,0,\,\sqrt{\frac{5+\sqrt5}{10}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}},\,\sqrt{\frac{5+\sqrt5}{40}}\right).$$

Representations
A square-pentagonal antiprismatic duoprism has the following Coxeter diagrams:
 * x4o s2s10o (full symmetry; pentagonal antiprisms as alternated decagonal prisms)
 * x4o s2s5s (pentagonal antiprisms as alternated dipentagonal prisms)
 * x x s2s10o (pentagonal antiprismatic prismatic prism)
 * x x s2s5s