Birectified hexacontatetrapeton

The birectified hexacontatetrapeton, or brag, also called the birectified 6-orthoplex, is a convex uniform polypeton. It consists of 12 rectified triacontaditera and 64 dodecatera. 3 rectified triacontaditera and 8 dodecatera join at each triangular-octahedral duoprismatic vertex. As the name suggests, it is the birectification of the hexacontatetrapeton.

The birectified hexacontatetrapeton can fill 6-space in the trirectified hexeractic hexacomb.

The birectified hexacontatetrapeton contains the vertices of a hexeract, square-icositetrachoric duoprism, and octahedral-cuboctahedral duoprism.

Vertex coordinates
The vertices of a birectified hexacontatetrapeton of edge length 1 are given by all permutations of:


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

Representations
A birectified hexacontatetrapeton has the following Coxeter diagrams:


 * o4o3o3x3o3o (full symmetry)
 * o3o3o *b3x3o3o (D6 symmetry)
 * ooo4ooo3oxo3xox3ooo&#xt (B5 axial, rectified triacontaditeron-first)
 * ooo3oxo3ooo *b3xox3ooo&#xt (D5 symmetry, same as above with half symmetry)
 * oxoo3ooxo3xoox3oxoo3ooxo&#x (A5 axial, dodecateron-first)