Rectified hexacontatetrapeton

The rectified hexacontatetrapeton, or rag, also called the rectified 6-orthoplex, is a convex uniform polypeton. It consists of 12 regular triacontaditera and 64 rectified hexatera. Two triacontaditera and 16 rectified hexatera join at each hexadecachoric prismatic vertex. As the name suggests, it is the rectification of the hexacontatetrapeton.

The rectified hexacontatetrapeton contains the vertices of a square-hexadecachoric duoprism and octahedral duoprism.

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


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

Representations
A rectified hexacontatetrapeton has the following Coxeter diagrams:


 * o4o3o3o3x3o (full symmetry)
 * o3o3o *b3o3x3o (D6 symmetry)
 * ooo4ooo3ooo3oxo3xox&#xt (B5 axial, triacontaditeron-first)
 * ooo3ooo3ooo *b3oxo3xox&#xt (D5 symmetry, as above with half symmetry)
 * oxo3xoo3ooo3oox3oxo&#xt (A5 axial, rectified hexateron-first)
 * ooo4oox3oxo ooo4xoo3oxo&#zx (B3×B3 symmetry)