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, cutting off two square antiprismatic pyramids.

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

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)