Pentagonal-hexagonal duoantifastegiaprism

The pentagonal-hexagonal duoantifastegiaprism or phidafup, also known as the pentagonal-hexagonal duoantiwedge, is a convex scaliform polyteron and a member of the duoantifastegiaprism family. It consists of 2 pentagonal-hexagonal duoprisms, 10 hexagonal antifastegiums and 12 pentagonal antifastegiums. 1 pentagonal-hexagonal duoprism, 3 hexagonal antifastegiums, and 3 pentagonal antifastegiums join at each vertex.

Vertex coordinates
The vertices of a pentagonal-hexagonal duoantifastegiaprism of edge length 1 are given by:


 * $$\left(±1,\,0,\,0,\,\sqrt{\frac{5+\sqrt5}{10}},\,\sqrt{\frac{9+2\sqrt3+\sqrt5}{8}}\right),$$
 * $$\left(±1,\,0,\,±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,\sqrt{\frac{9+2\sqrt3+\sqrt5}{8}}\right),$$
 * $$\left(±1,\,0,\,±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,\sqrt{\frac{9+2\sqrt3+\sqrt5}{8}}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt3}{2},\,0,\,\sqrt{\frac{5+\sqrt5}{10}},\,\sqrt{\frac{9+2\sqrt3+\sqrt5}{8}}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt3}{2},\,±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,\sqrt{\frac{9+2\sqrt3+\sqrt5}{8}}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt3}{2},\,±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,\sqrt{\frac{9+2\sqrt3+\sqrt5}{8}}\right),$$
 * $$\left(0,\,±1,\,0,\,-\sqrt{\frac{5+\sqrt5}{10}},\,-\sqrt{\frac{9+2\sqrt3+\sqrt5}{8}}\right),$$
 * $$\left(0,\,±1,\,±\frac{1+\sqrt5}{4},\,-\sqrt{\frac{5-\sqrt5}{40}},\,-\sqrt{\frac{9+2\sqrt3+\sqrt5}{8}}\right),$$
 * $$\left(0,\,±1,\,±\frac12,\,\sqrt{\frac{5+2\sqrt5}{20}},\,-\sqrt{\frac{9+2\sqrt3+\sqrt5}{8}}\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,0,\,-\sqrt{\frac{5+\sqrt5}{10}},\,-\sqrt{\frac{9+2\sqrt3+\sqrt5}{8}}\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,±\frac12,\,±\frac{1+\sqrt5}{4},\,-\sqrt{\frac{5-\sqrt5}{40}},\,-\sqrt{\frac{9+2\sqrt3+\sqrt5}{8}}\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,±\frac12,\,\sqrt{\frac{5+2\sqrt5}{20}},\,-\sqrt{\frac{9+2\sqrt3+\sqrt5}{8}}\right),$$