Cubic pyramid

The cubical pyramid, or cubpy, is a CRF segmentochoron (designated K-4.26 on Richard Klitzing's list). It has 6 square pyramids and 1 cube as cells. As the name suggests, it is a pyramid based on the cube.

The cubic pyramid occurs as a vertex-first cap of the regular icositetrachoron.

A regular tesseract can be exactly decomposed into 8 CRF cubic pyramids.

Vertex coordinates
The vertices of a cubic pyramid of edge length 1 are given by:
 * $$\left(0,\,0,\,0,\,\frac12\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,0\right).$$

Representations
A cubic pyramid has the following Coxeter diagrams:


 * ox4oo3oo&#x (full symmetry)
 * ox ox4oo&#x (BC2×A1 base, square prismatic pyramid)
 * ox ox ox&#x (A1×A1×A1 base, cuboid pyramid)
 * oxx4ooo&#x (base square atop square)
 * oxx oxx&#x (*similar with rectangles)