Pentagonal-hexagonal duoprism

The pentagonal-hexagonal duoprism or phiddip, also known as the 5-6 duoprism, is a uniform duoprism that consists of 5 hexagonal prisms and 6 pentagonal prisms, with two of each joining at each vertex.

Vertex coordinates
Coordinates for the vertices of a pentagonal-hexagonal duoprism with edge length 1 are given by:
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,0,\,±1\right),$$
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac{\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,0,\,±1\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac{\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,0,\,±1\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac{\sqrt3}{2},\,±\frac12\right).$$

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


 * x5o x6o (full symmetry)
 * x3x x5o (hexagons as ditrigons)
 * ofx xxx6ooo&#xt (hexagonal axial)


 * ofx xxx3xxx&#xt (ditrigonal axial)
 * xux xxx5ooo&#xt (pentagonal axial)