Tridiminished icosiheptaheptacontadipeton

The tridiminished icosiheptaheptacontadipeton, or tedjak, also known as the hexadecachoric gyrotrigonism or hexadecachoric triorthowedge, is a convex scaliform polypeton that consists of 3 demipenteracts, 24 hexadecachoric pyramids, and 24 hexatera. Two demipenteracts, nine hexadecachoric pyramids, and six hexatera meet at its 24 bidiminished demipenteractic vertices.

As the name suggests, it can be obtained by removing 3 vertices from the icosiheptaheptacontadipeton, specifically 3 vertices forming an equilateral triangle of edge length $$\sqrt2$$. Each diminishing reveals one demipenteractic facet, while removing some of the hexateron facets entirely. Al the hexadecachoric pyramid facets correspond to triacontaditera in the full icosiheptaheptacontadipeton.

It is also a quotient prism based on the stellated icositetrachoron.

Vertex coordinates
The vertices of a tridiminished icosiheptaheptacontadipeton of edge length 1 are given by all permutations and even sign changes of the first four coordinates of:
 * $$\left(0,\,0,\,0,\,\frac{\sqrt2}{2},\,0,\,\frac{\sqrt6}{6}\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,-\frac{\sqrt6}{12}\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,-\frac{\sqrt2}{4},\,-\frac{\sqrt2}{4},\,-\frac{\sqrt6}{12}\right).$$