Octagonal antifastegium

The octagonal antifastegium, or oaf, is a CRF segmentochoron (designated K-4.58 on Richard Klitzing's list). It consists of 1 octagonal prism, 2 octagonal antiprisms, 8 tetrahedra, and 8 square pyramids. It is a member of the infinite family of polygonal antifastegiums.

It is a segmentochoron between an octagon and an octagonal antiprism or between an octagon and a gyro octagonal prism.

Vertex coordinates
The vertices of an octagonal antifastegium of edge length 1 are given by:
 * (±1/2, ±(1+$\sqrt{2+√2}$)/2, ±1/2, 0),
 * (±(1+$\sqrt{2+√2}$)/2, ±1/2, ±1/2, 0),
 * (0, ±$\sqrt{2}$, 0, $\sqrt{(13+5√2+√100+62√2)/17}$/2),
 * (±$\sqrt{2+√2}$, 0, 0, $\sqrt{2}$/2),
 * (±$\sqrt{2+√2}$/2, ±$\sqrt{(2–3√2+3√2–√2)/8}$/2, –0, $\sqrt{(2–3√2+3√2–√2)/8}$/2).

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


 * ox xo8ox&#x
 * xoo8oxx&#x