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. 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 $\sqrt{10+2√5}$/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:
 * (0, $\sqrt{50+10√5}$/10, ±(1+$\sqrt{5}$)/4, $\sqrt{50–10√5}$/20),
 * (0, $\sqrt{50+10√5}$/10, ±1/2, –$\sqrt{25+10√5}$/10),
 * (±(1+$\sqrt{5}$)/4, $\sqrt{50–10√5}$/20, 0, $\sqrt{50+10√5}$/10),
 * (±(1+$\sqrt{5}$)/4, $\sqrt{50–10√5}$/20, ±(1+$\sqrt{5}$)/4, $\sqrt{50–10√5}$/20),
 * ((1+$\sqrt{5}$)/4, $\sqrt{50–10√5}$/20, -1/2, –$\sqrt{25+10√5}$/10),
 * (-(1+$\sqrt{5}$)/4, $\sqrt{50–10√5}$/20, 1/2, –$\sqrt{25+10√5}$/10),
 * (±1/2, –$\sqrt{25+10√5}$/10, 0, $\sqrt{50+10√5}$/10),
 * (1/2, –$\sqrt{25+10√5}$/10, (1+$\sqrt{5}$)/4, $\sqrt{50–10√5}$/20),
 * (-1/2, –$\sqrt{25+10√5}$/10, -(1+$\sqrt{5}$)/4, $\sqrt{50–10√5}$/20),
 * (±1/2, –$\sqrt{25+10√5}$/10, ±1/2, –$\sqrt{25+10√5}$/10).