Pentagonal duoantifastegium

The pentagonal duoantifastegium or piddaf, also known as the digonal-pentagonal duoantiwedge, is a convex scaliform polyteron and the third member of the duoantiwedge family. It consists of 4 pentagonal antifastegiums and 10 square scalenes, with 3 of each meeting at each vertex.

Vertex coordinates
A pentagonal duoantifastegium of edge length 1 has vertex coordinates given by:
 * $$\left(±\frac12,\,0,\,0,\,\sqrt{\frac{5+\sqrt5}{10}},\,\frac{1}{\sqrt[4]{20}}\right),$$
 * $$\left(0,\,±\frac12,\,0,\,-\sqrt{\frac{5+\sqrt5}{10}},\,-\frac{1}{\sqrt[4]{20}}\right),$$
 * $$\left(±\frac12,\,0,\,±\frac{1+\sqrt5}{4},\,\frac{\sqrt{5-\sqrt5}{40}},\,\frac{1}{\sqrt[4]{20}}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{1+\sqrt5}{4},\,-\frac{\sqrt{5-\sqrt5}{40}},\,-\frac{1}{\sqrt[4]{20}}\right),$$
 * $$\left(±\frac12,\,0,\,±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,\frac{1}{\sqrt[4]{20}}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac12,\,\sqrt{\frac{5+2\sqrt5}{20}},\,-\frac{1}{\sqrt[4]{20}}\right).$$