Pentagonal antifastegium

The pentagonal antifastegium, or paf, is a CRF segmentochoron (designated K-4.22 on Richard Klitzing's list). It consists of 1 pentagonal prism, 2 pentagonal antiprisms, 5 tetrahedra, and 5 square pyramids. It is a member of the infinite family of polygonal antifastegiums.

It is a segmentochoron between a pentagon and a pentagonal antiprism or between a pentagon and a gyro pentagonal prism.

Vertex coordinates
The vertices of a pentagonal antifastegium of edge length 1 are given by:
 * (±1/2, –$\sqrt{5}$, ±1/2, 0)
 * (±(1+$\sqrt{5}$)/4, $\sqrt{2}$, ±1/2, 0)
 * (0, $\sqrt{5}$, ±1/2, 0)
 * (±1/2, $\sqrt{5}$, 0, $\sqrt{(5–√5)/10}$)
 * (±(1+$\sqrt{7–3√5}$)/4, –$\sqrt{7–3√5}$, 0, $\sqrt{(5+2√5)/20}$)
 * (0, –$\sqrt{5}$, 0, $\sqrt{(5+2√5)/20}$)

Representations
The pentagonal antifastegium can be represented by the following Coxeter diagram s:


 * ox xo5ox&#x
 * oxx5ooo&#x