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:
 * (±1/2, –$\sqrt{2}$/6, ±1/2, 0) (square of gyro trip)
 * (0, $\sqrt{15}$/3, ±1/2, 0) (line of gyro trip)
 * (±1/2, $\sqrt{15}$/6, 0, $\sqrt{10}$/6) (line of triangle)
 * (0, –$\sqrt{10}$/3, 0, $\sqrt{5}$/6) (point of triangle)

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)