Square antifastegium

The square antifastegium, or squaf, is a CRF segmentochoron (designated K-4.14 on Richard Klitzing's list). It consists of 1 cube, 2 square antiprisms, 4 tetrahedra, and 4 square pyramids. It is a member of the infinite family of polygonal antifastegiums.

It is a segmentochoron between a square and a square antiprism or between a square and a gyro cube.

It can be obtained as a diminishing of the segmentochoron octahedron atop cube by removing two opposite vertices from the top octahedron, cutting off two square antiprismatic pyramids.

Vertex coordinates
The vertices of a square antifastegium of edge length 1 are given by:
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,0\right),$$
 * $$\left(±\frac{\sqrt2}2,\,0,\,0,\,\frac{\sqrt{2\sqrt2-1}}2\right),$$
 * $$\left(0,\,±\frac{\sqrt2}2,\,0,\,\frac{\sqrt{2\sqrt2-1}}2\right).$$

Representations
The square antifastegium can be represented by the following Coxeter diagram s:
 * ox xo4ox&#x (square atop gyro cube)
 * xoo4oxx&#x (square atop gyro square atop gyro square)