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+$\sqrt{3(25+10√5)}$)/4, $\sqrt{3}$),
 * (0, $\sqrt{(5+√5)/10}$/3, ±1/2, –$\sqrt{3}$),
 * (±1/2, –$\sqrt{5}$/6, 0, $\sqrt{(5-√5)/40}$),
 * (±1/2, –$\sqrt{3}$/6, ±(1+$\sqrt{(5+2√5)/20}$)/4, $\sqrt{3}$),
 * (±1/2, –$\sqrt{(5+√5)/10}$/6, ±1/2, –$\sqrt{3}$).

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)