Decagonal antifastegium

The decagonal antifastegium, or daf, is a CRF segmentochoron (designated K-4.93 on Richard Klitzing's list). It consists of 1 decagonal prism, 2 decagonal antiprisms, 10 tetrahedra, and 10 square pyramids. It is a member of the infinite family of polygonal antifastegiums.

It is a segmentochoron between a decagon and a decagonal antiprism or between a decagon and a gyro decagonal prism.

Vertex coordinates
The vertices of a decagonal antifastegium of edge length 1 are given by:
 * $$\left(±\frac12,\,±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,0\right),$$
 * $$\left(±\frac{3+\sqrt5}4,\,±\sqrt{\frac{5+\sqrt5}8},\,±\frac12,\,0\right),$$
 * $$\left(±\frac{1+\sqrt5}2,\,0,\,±\frac12,\,0\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,0,\,\frac{\sqrt{2\sqrt{50+22\sqrt5}-4\sqrt5-9}}2\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,0,\,\frac{\sqrt{2\sqrt{50+22\sqrt5}-4\sqrt5-9}}2\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}2,\,0,\,\frac{\sqrt{2\sqrt{50+22\sqrt5}-4\sqrt5-9}}2\right).$$

Representations
The decagonal antifastegium can be represented by the following Coxeter diagrams:
 * ox xo10ox&#x
 * xoo10oxx&#x