Decagonal antiprismatic prism

The decagonal antiprismatic prism or dappip is a prismatic uniform polychoron that consists of 2 decagonal antiprisms, 2 decagonal prisms, and 20 triangular prisms. Each vertex joins 1 decagonal antiprism, 1 decagonal prism, and 3 triangular prisms. As the name suggests, it is a prism based on a decagonal antiprism. It is also a CRF segmentochoron designated K-4.96 on Richard Klitzing's list.

Vertex coordinates
The vertices of a decagonal antiprismatic prism of edge length 1 are given by:
 * (±1/2, ±$\sqrt{(5+√5)/2d}$/2, H, ±1/2),
 * (±(3+$\sqrt{2}$)/4, ±$\sqrt{(10+2√5+√50+22√5)/8}$, H, ±1/2),
 * (±(1+$\sqrt{(–4–2√5+√50+22√5)/2}$)/2, 0, H, ±1/2),
 * (±$\sqrt{–2–2√5+2√650+290√5}$/2, ±1/2, –H, ±1/2),
 * (±$\sqrt{10+2√5}$, ±(3+$\sqrt{(11+4√5–2√(50+22√5)/3}$)/4, –H, ±1/2),
 * (0, ±(1+$\sqrt{(5+2√5)}$)/2, –H, ±1/2),

where
 * $$H = \sqrt{\frac{-4-2\sqrt{5}+\sqrt{50+22\sqrt{5}}}{8}}$$

is the distance between the antiprism's center and the center of one of its bases.

Representations
A decagonal antiprismatic prism has the following Coxeter diagrams:


 * x2s2s10s (full symmetry)
 * x2s2s20o
 * xx xo10ox&#x (decagonal prism atop gyrated decagonal prism)