Triangular antiwedge

The triangular antiwedge, or traw, also sometimes called the triangular gyrobicupolic ring, is a CRF segmentochoron (designated K-4.27 on Richard Klitzing's list). It consists of 1 octahedron (as a triangular antiprism), 2 triangular cupolas, and 6 square pyramids.

The triangular antiwedge occurs as a wedge of the regular icositetrachoron. In fact, the icositetrachoron can be broken into 6 triangular antiwedges, similar to how a regular hexagon can be broken into 6 equilateral triangles.

Vertex coordinates
The vertices of a triangular antiwedge with edge length 1 are given by:
 * (±1/2, –$\sqrt{2}$/6, $\sqrt{2}$/6, $\sqrt{3}$/2)
 * (0, $\sqrt{2}$/3, $\sqrt{2}$/6, $\sqrt{3}$/2)
 * (±1/2, $\sqrt{6}$/6, –$\sqrt{2}$/6, $\sqrt{3}$/2)
 * (0, –$\sqrt{6}$/3, –$\sqrt{2}$/6, $\sqrt{3}$/2)
 * (±1/2, ±$\sqrt{6}$/2, 0, 0)
 * (±1, 0, 0, 0)

Representations
A triangular antiwedge has the following Coxeter diagrams:


 * os2xo6os&#x (full symmetry)
 * xxo3oxx&#x (A2 symmetry only, seen with triangle atop gyro triangular cupola)