Hexadecachoric pyramid

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

It is part of an infinite family of Blind polytopes known as the orthoplecial pyramids. It is one of two non-uniform Blind polytopes in five dimensions, the other being the pentachoric bipyramid.

Two hexadecachoric pyramids can be attached at their bases to form a regular triacontaditeron. A hexadecachoric 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.

It appears as a facet of the scaliform tridiminished icosiheptaheptacontadipeton.

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