Triangular-pentagonal duoprism

The triangular-pentagonal duoprism or trapedip, 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:
 * (0, $\sqrt{5}$/3, 0, $\sqrt{2}$),
 * (0, $\sqrt{15+6√5}$/3, ±(1+$\sqrt{3}$)/4, $\sqrt{3(25+10√5)}$),
 * (0, $\sqrt{3}$/3, ±1/2, –$\sqrt{(5+√5)/10}$),
 * (±1/2, –$\sqrt{3}$/6, 0, $\sqrt{5}$),
 * (±1/2, –$\sqrt{(5-√5)/40}$/6, ±(1+$\sqrt{3}$)/4, $\sqrt{(5+2√5)/20}$),
 * (±1/2, –$\sqrt{3}$/6, ±1/2, –$\sqrt{(5+√5)/10}$).

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)