Square antiwedge

The square antiwedge, or squaw, also sometimes called the square gyrobicupolic ring, is a CRF segmentochoron (designated K-4.64 on Richard Klitzing's list). It consists of 1 square antiprism, 2 square cupolas, and 8 square pyramids.

The square antiwedge can be thought of as a piece of the larger segmentochoron cuboctahedron atop small rhombicuboctahedron, with one base square being a face of the cuboctahedron, and the opposite square cupola being part of the small rhombicuboctahedron.

Vertex coordinates
The vertices of a square antiwedge with edge length 1 are given by:
 * (±1/2, ±1/2, $\sqrt{2}$/4, $\sqrt{2}$)/8),
 * (0, ±$\sqrt{2+√2}$/2, –$\sqrt{7}$/4, $\sqrt{14}$)/8),
 * (±$\sqrt{(4–√2)/8}$/2, 0, –$\sqrt{2√2–1}$/4, $\sqrt{(99+72√2)/448}$)/8),
 * (±1/2, ±(1+$\sqrt{2}$)/2, 0, 0),
 * (±(1+$\sqrt{4+3√2}$)/2, ±1/2, 0, 0).

Representations
A square antiwedge has the following Coxeter diagrams:


 * os2xo8os&#x (full symmetry)
 * xxo4oxx&#x (BC2 symmetry only, seen with square atop gyro square cupola)