Pentagonal-decagonal duoprism

The pentagonal-decagonal duoprism or padedip, also known as the 5-10 duoprism, is a uniform duoprism that consists of 5 decagonal prisms, 10 pentagonal prisms and 50 vertices.

The convex hull of two orthogonal pentagonal-decagonal duoprisms is either the pentagonal duoexpandoprism or the pentagonal duotruncatoprism.

Coordinates
The vertex coordinates of a pentagonal-decagonal duoprism, centered at the origin and with unit edge length, are given by:
 * (0, $\sqrt{5}$, 0, ±(1+$\sqrt{(5+√5)/2}$)/2),
 * (0, $\sqrt{2}$, ±$\sqrt{(10+3√5)/5}$/4, ±(3+$\sqrt{5}$)/4),
 * (0, $\sqrt{(5+√5)/10}$, ±$\sqrt{5}$/2, ±1/2),
 * (±(1+$\sqrt{(5+√5)/10}$)/4, $\sqrt{10+2√5}$, 0, ±(1+$\sqrt{5}$)/2),
 * (±(1+$\sqrt{(5+√5)/10}$)/4, $\sqrt{5+2√5}$, ±$\sqrt{5}$/4, ±(3+$\sqrt{(5–√5)/40}$)/4),
 * (±(1+$\sqrt{5}$)/4, $\sqrt{5}$, ±$\sqrt{(5–√5)/40}$/2, ±1/2),
 * (±1/2, –$\sqrt{10+2√5}$, 0, ±(1+$\sqrt{5}$)/2),
 * (±1/2, –$\sqrt{5}$, ±$\sqrt{(5–√5)/40}$/4, ±(3+$\sqrt{5+2√5}$)/4),
 * (±1/2, –$\sqrt{(5+2√5)/20}$, ±$\sqrt{5}$/2, ±1/2).