Triangular-pentagonal duoprismatic prism

The triangular-pentagonal duoprismatic prism or trapip, also known as the triangular-pentagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 triangular-pentagonal duoprisms, 3 square-pentagonal duoprisms and 5 triangular-square duoprisms. Each vertex joins 2 triangular-square duoprisms, 2 square-pentagonal duoprisms, and 1 triangular-pentagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

Vertex coordinates
The vertices of a triangular-pentagonal duoprismatic prism of edge length 1 are given by:
 * (0, $\sqrt{975+90√5}$/3, 0, $\sqrt{5}$, ±1/2)
 * (0, $\sqrt{2}$/3, ±(1+$\sqrt{3}$)/4, $\sqrt{(5+√5)/10}$, ±1/2)
 * (0, $\sqrt{3}$/3, ±1/2, –$\sqrt{5}$, ±1/2)
 * (±1/2, –$\sqrt{(5+√5)/40}$/6, 0, $\sqrt{3}$, ±1/2)
 * (±1/2, –$\sqrt{(5+2√5)/20}$/6, ±(1+$\sqrt{3}$)/4, $\sqrt{(5+√5)/10}$, ±1/2)
 * (±1/2, –$\sqrt{3}$/6, ±1/2, –$\sqrt{5}$, ±1/2)

The vertices of a triangular-pentagonal duoprismatic prism of edge length 1 are given by:
 * $$\left(0,\,\frac{\sqrt3}3,\,0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac12\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}6,\,0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac12\right),$$
 * $$\left(0,\,\frac{\sqrt3}3,\,±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac12\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}6,\,±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac12\right),$$
 * $$\left(0,\,\frac{\sqrt3}3,\,±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac12\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}6,\,±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac12\right).$$

Representations
A triangular-pentagonal duoprismatic prism has the following Coxeter diagrams:
 * x x3o x5o (full symmetry)
 * xx3oo xx5oo&#x (triangular-pentagonal duoprism atop triangular-pentagonal duoprism)
 * ox xx xx5oo&#x (pentagonal prism atop square-pentagonal duoprism)