Rectified diacosipentacontahexazetton

The rectified diacosipentacontahexazetton, or rek, also called the rectified 8-orthoplex, is a convex uniform polyzetton. It consists of 16 regular hecatonicosoctaexa and 256 rectified octaexa. Two hecatonicosoctaexa and 64 rectified octaexa join at each hexacontatetrapetic prismatic vertex. As the name suggests, it is the rectification of the diacosipentacontahexazetton.

The rectified diacosipentacontahexazetton can be vertex-inscribed into the dischiliahecatonhexaconta-myriaheptachiliadiacosioctaconta-zetton (or 421 polytope).

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


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

Representations
A rectified diacosipentacontahexazetton has the following Coxeter diagrams:


 * o4o3o3o3o3o3x3o (full symmetry)
 * o3o3o *b3o3o3o3x3o (D8 symmetry)
 * ooo4ooo3ooo3ooo3ooo3oxo3xox&#xt (B7 axial, hecatonicosoctaexon-first)