Triangular prismatic pyramid

The triangular prismatic pyramid, or trippy, is a CRF segmentochoron (designated K-4.7 on Richard Klitzing's list). Its cells are one triangular pyramid, and two triangular pyramids and three square pyramids that join at an external point.

The triangular prismatic pyramid can be viewed as the vertex pyramid of the rectified pentachoron.

Vertex coordinates
The vertices of an triangular prismatic pyramid of edge length 1 are given by:
 * (±1/2, -$\sqrt{3/5}$/6, ±1/2, 0) (a square side of the triangular prism),
 * (0, $\sqrt{5/12}$/3, ±1/2, 0) (the remaining line of the triangular prism),
 * (0, 0, 0, $\sqrt{5}$) (the pyramid's point).

Representations
A triangular prismatic pyramid has the following Coxeter diagrams:


 * ox ox3oo&#x (point atop triangular pyramid)
 * xox3ooo&#x (triangle atop tetrahedron)