Pentagonal duoantifastegiaprism

The pentagonal duoantifastegiaprism or pedafup, also known as the pentagonal duoantiwedge, is a convex scaliform polyteron and a member of the duoantifastegiaprism family. It consists of 2 pentagonal duoprisms and 20 pentagonal antifastegiums. 1 pentagonal duoprism and 6 pentagonal antifastegiums join at each vertex.

Vertex coordinates
A pentagonal duoantifastegiaprism of edge length 1 has verex coordinates given by:


 * $$±\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,0,\,\sqrt{\frac{5+\sqrt5}{10}},\,\frac{1}{\sqrt[4]{80}}\right),$$
 * $$±\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,\frac{1}{\sqrt[4]{80}}\right),$$
 * $$±\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,\frac{1}{\sqrt[4]{80}}\right),$$
 * $$±\left(±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,0,\,\sqrt{\frac{5+\sqrt5}{10}},\,\frac{1}{\sqrt[4]{80}}\right),$$
 * $$±\left(±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,\frac{1}{\sqrt[4]{80}}\right),$$
 * $$±\left(±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,\frac{1}{\sqrt[4]{80}}\right),$$
 * $$±\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,0,\,\sqrt{\frac{5+\sqrt5}{10}},\,\frac{1}{\sqrt[4]{80}}\right),$$
 * $$±\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,\frac{1}{\sqrt[4]{80}}\right),$$
 * $$±\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,\frac{1}{\sqrt[4]{80}}\right).$$