Triangular antifastegium

The triangular antifastegium, or traf, is a CRF segmentochoron (designated K-4.6 on Richard Klitzing's list). It consists of 1 triangular prism, 2 octahedra, 3 tetrahedra, and 3 square pyramids. It is a member of the infinite family of polygonal antifastegiums, consisting of a prism joined to two antiprisms, with a ring of square pyramids and tetrahedra in between.

The triangular antifastegium can be viewed as a vertex-diminished rectified pentachoron, where a triangular prismatic pyramid is removed.

Vertex coordinates
The vertices of a triangular antifastegium with edge length 1 are given by:
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12,\,0\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac12,\,0\right),$$
 * $$\left(±\frac12,\,\frac{\sqrt3}{6},\,0,\,\frac{\sqrt{15}}{6}\right),$$
 * $$\left(0,\,-\frac{\sqrt3}{3},\,0,\,\frac{\sqrt{15}}{6}\right).$$

Representations
A triangular antifastegium has the following Coxeter diagrams:


 * ox xo3ox&#x (full symmetry)
 * xoo3oxx&#x (A2 symmetry, triangle atop octahedron)
 * xoxoxo&#xr (bilateral symmetry only)
 * ooxx oxox&#xr (A1×A1 symmetry)