Hexadecachoric pyramid

The hexadecachoric pyramid, is a CRF segmentoteron. It has 8 regular pentachora and 1 regular hexadecachoron as cells. It is a pyramid based on the hexadecachoron.

Two hexadecachoric pyramids can be attached at their bases to form a regular triacontaditeron. An octahedral pyramid can be further cut in half to produce two octahedral scalenes.

Apart from being a point atop hexadecachoron, it has an alternate segmentochoron representation as a tetrahedron atop gyro pentachoron seen as a tetrahedral pyramid.

Vertex coordinates
The vertices of a hexadecachoric pyramid of edge length 1 are given by: with all permutations of the first 4 coordinates of:
 * $$\left(0,\,0,\,0,\,0,\,\frac{\sqrt2}{2}\right),$$
 * $$\left(0,\,0,\,0,\,±\frac{\sqrt2}{2},\,0\right).$$