Triangular prismatic pyramid

The triangular prismatic pyramid, or trippy, is a CRF segmentochoron (designated K-4.7 on Richard Klitzing's list). It has It has 3 regular tetrahedra, 2 square pyramids, and 1 triangular prism as cells. As the name suggests, it is a pyramid based on the triangular prism.

The triangular prismatic pyramid can be viewed as the vertex pyramid of the rectified pentachoron, with the remainder of the original polychoron forming a triangular antifastegium.

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

Representations
A triangular prismatic pyramid has the following Coxeter diagrams:


 * ox ox3oo&#x (full symmetry)
 * oxx3ooo&#x (A2 symmetry, prism seen as frustum symmetry)
 * oox oxx&#x (A1×A1 symmetry, wedge pyramid)
 * oxxx&#x (bilateral symmetry only)