Pentadiminished pentagonal duoprism

The pentadiminished pentagonal duoprism or pedpedip is a convex isogonal polychoron that consists of 5 tetragonal disphenoids and 10 parabidiminished pentagonal prisms. 1 tetragonal disphenoid and 4 parabidiminished pentagonal prisms join at each vertex. It was first found on December 5, 2020 by _Geometer.

It can be constructed by removing an inscribed pentachoron (considered as a 5-2 step prism) of edge length $$\sqrt{\frac{5+\sqrt5}{2}}$$ from a pentagonal duoprism.

The ratio between the longest and shortest edges is 1:$$\frac{1+\sqrt5}{2}$$ ≈ 1:1.61803.

Vertex coordinates
The vertices of a pentadiminished pentagonal duoprism, constructed from a pentagonal duoprism of edge length 1, centered at the origin, are given by:
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}}\right),$$
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,0,\,\sqrt{\frac{5+\sqrt5}{10}}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}}\right),$$
 * $$\left(\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,-\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}}\right),$$
 * $$\left(-\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}}\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,0,\,\sqrt{\frac{5+\sqrt5}{10}}\right),$$
 * $$\left(\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}}\right),$$
 * $$\left(-\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,-\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}}\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}}\right).$$