Decagonal-pentagonal antiprismatic duoprism

The decagonal-pentagonal antiprismatic duoprism or dapap is a convex uniform duoprism that consists of 10 pentagonal antiprismatic prisms, 2 pentagonal-decagonal duoprisms and 10 triangular-decagonal duoprisms. Each vertex joins 2 pentagonal antiprismatic prisms, 3 triangular-decagonal duoprisms, and 1 pentagonal-decagonal duoprism.

Vertex coordinates
The vertices of a decagonal-pentagonal antiprismatic duoprism of edge length 1 are given by all central inversions of the last three coordinates of:
 * (0, ±(1+$\sqrt{34+10√5}$)/2, 0, $\sqrt{5}$/10, $\sqrt{(5+√5)/2}$/20)
 * (0, ±(1+$\sqrt{2}$)/2, ±(1+$\sqrt{5}$)/4, $\sqrt{50+10√5}$/20, $\sqrt{50+10√5}$/20)
 * (0, ±(1+$\sqrt{5}$)/2, ±1/2, –$\sqrt{5}$/10, $\sqrt{50–10√5}$/20)
 * (±$\sqrt{50+10√5}$/4, ±(3+$\sqrt{5}$)/4, 0, $\sqrt{25+10√5}$/10, $\sqrt{50+10√5}$/20)
 * (±$\sqrt{10+2√5}$/4, ±(3+$\sqrt{5}$)/4, ±(1+$\sqrt{50+10√5}$)/4, $\sqrt{50+10√5}$/20, $\sqrt{10+2√5}$/20)
 * (±$\sqrt{5}$/4, ±(3+$\sqrt{5}$)/4, ±1/2, –$\sqrt{50–10√5}$/10, $\sqrt{50+10√5}$/20)
 * (±$\sqrt{10+2√5}$/2, ±1/2, 0, $\sqrt{5}$/10, $\sqrt{25+10√5}$/20)
 * (±$\sqrt{50+10√5}$/2, ±1/2, ±(1+$\sqrt{5+2√5}$)/4, $\sqrt{50+10√5}$/20, $\sqrt{50+10√5}$/20)
 * (±$\sqrt{5+2√5}$/2, ±1/2, ±1/2, –$\sqrt{5}$/10, $\sqrt{50–10√5}$/20)

The vertices of a decagonal-pentagonal antiprismatic duoprism of edge length 1 are given by all central inversions of the last three coordinates of:
 * $$\left(0,\,±\frac{1+\sqrt5}2,\,0,\,\sqrt{\frac{5+\sqrt5}{10}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,0,\,\sqrt{\frac{5+\sqrt5}{10}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,0,\,\sqrt{\frac{5+\sqrt5}{10}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}2,\,±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}2,\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}},\,\sqrt{\frac{5+\sqrt5}{40}}\right).$$

Representations
A decagonal-pentagonal antiprismatic duoprism has the following Coxeter diagrams:
 * x10o s2s10o (full symmetry; pentagonal antiprisms as alternated decagonal prisms)
 * x10o s2s5s (pentagonal antiprisms as alternated dipentagonal prisms)
 * x5x s2s10o (decagons as dipentagons)
 * x5x s2s5s