Triangular antifastegium

The triangular antifastegium, or traf, is a CRF segmentochoron (designated K-4.6 on Richard Klitzing's list). Its cells are a triangular pyramid and 2 octahedra, with 3 tetrahedra and 3 square pyramids filling in the gaps between them.

The triangular antifastegium can be viewed as a vertex-diminished rectified pentachoron.

Vertex coordinates
The vertices of a triangular antifastegium with edge length 1 are given by:
 * (±1/2, -$\sqrt{3/5}$/6, ±1/2, 0) (square of gyro trip)
 * (0, $\sqrt{5/12}$/3, ±1/2, 0) (line of gyro trip)
 * (±1/2, $\sqrt{5/8}$/6, 0, $\sqrt{5/8}$) (line of triangle)
 * (0, -$\sqrt{1/6}$/3, 0, $\sqrt{3/8}$) (point of triangle)

Representations
A triangular antifastegium has the following Coxeter diagrams:


 * xo3ox ox&#x (triangle atop gyrated triangular prism)
 * xoo3oxx&#x (triangle atop gyrated triangle atop gyrated triangle)