Icosahedral pyramid

The icosahedral pyramid, or ikepy, is a CRF segmentochoron (designated K-4.84 on Richard Klitzing's list). It has 20 regular tetrahedra and 1 regular icosahedron as cells. As the name suggests, it is a pyramid based on the icosahedron.

It is also the first segment of the hexacosichoron in vertex-first orientation.

Vertex coordinates
The vertices of an icosahedral pyramid of edge length 1 are given by:
 * (0, 0, 0, ($\sqrt{5}$–1)/4)
 * (±(1+$\sqrt{5}$)/2, ±1/2, 0, 0) and all permutations of first three coordinates