Triangular-pentagonal duoprism

The triangular-pentagonal duoprism, also known as the 3-5 duoprism, is a uniform duoprism that consists of 3 pentagonal prisms and 5 triangular prisms, with two of each at each vertex.

It is also a CRF segmentochoron, as pentagon atop pentagonal prism. It is designated K-4.34 on Richard Klitzing's list.

Vertex coordinates
Coordinates for the vertices of a triangular-pentagonal duoprism with edge length 1 are given by:


 * $$\left(0,\,\frac{\sqrt3}{3},\,0,\,\sqrt{\frac{5+\sqrt5}{10}}\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}}\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,0,\,\sqrt{\frac{5+\sqrt5}{10}}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}}\right),$$

Representations
A triangular-pentagonal duoprism has the following Coxeter diagrams:


 * x3o x5o (full symmetry)
 * ox xx5oo&#x (pentagon atop pentagon prism)
 * ofx xxx3oooo&#xt (triangle-first)