Square-hexagonal duoantifastegiaprism

The square-hexagonal duoantifastegiaprism or shidafup, also known as the square-hexagonal duoantiwedge, is a convex scaliform polyteron and a member of the duoantifastegiaprism family. It consists of 2 square-hexagonal duoprisms, 8 hexagonal antifastegiums and 12 square antifastegiums. 1 square-hexagonal duoprism, 3 hexagonal antifastegiums, and 3 square antifastegiums join at each vertex.

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


 * $$\left(±\frac12,\,±\frac12,\,±1,\,0,\,\sqrt{\frac{-4+\sqrt2+2\sqrt3}{8}}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,±\frac{\sqrt3}{2},\,\sqrt{\frac{-4+\sqrt2+2\sqrt3}{8}}\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,0,\,0,\,±1,\,-\sqrt{\frac{-4+\sqrt2+2\sqrt3}{8}}\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,0,\,±\frac{\sqrt3}{2},\,±\frac12,\,-\sqrt{\frac{-4+\sqrt2+2\sqrt3}{8}}\right).$$
 * $$\left(0,\,±\frac{\sqrt2}{2},\,0,\,±1,\,-\sqrt{\frac{-4+\sqrt2+2\sqrt3}{8}}\right),$$
 * $$\left(0,\,±\frac{\sqrt2}{2},\,±\frac{\sqrt3}{2},\,±\frac12,\,-\sqrt{\frac{-4+\sqrt2+2\sqrt3}{8}}\right),$$