Trirectified diacosipentacontahexazetton

The trirectified diacosipentacontahexazetton, or tark, also called the trirectified 8-orthoplex, is a convex uniform polyzetton. It consists of 16 birectified hecatonicosoctaexa and 256 hexadecaexa. 4 birectified hecatonicosoctaexa and 16 hexadecaexa join at each tetrahedral-hexadecachoric duoprismatic vertex. As the name suggests, it is the trirectification of the diacosipentacontahexazetton.

The trirectified diacosipentacontahexazetton can be vertex-inscribed into the diacositetraconta-myriaheptachiliadiacosioctaconta-zetton (better known as the 241 polytope).

Vertex coordinates
The vertices of a trirectified diacosipentacontahexazetton of edge length 1 are given by all permutations of:


 * $$\left(±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0,\,0,\,0,\,0\right).$$

Representations
A trirectified diacosipentacontahexazetton has the following Coxeter diagrams:


 * o4o3o3o3x3o3o3o (full symmetry)
 * o3o3o *b3o3x3o3o3o (D8 symmetry)
 * ooo4ooo3ooo3oxo3xox3ooo3ooo&#xt (B7 axial, birectified hecatonicosoctaexon-first)