Birectified penteractic pentacomb

The birectified penteractic pentacomb or brinoh, also called the birectified 5-cubic honeycomb, is a convex uniform pentacomb. 4 rectified triacontaditera and 8 penteractitriacontaditera join at each vertex of this tessellation. As the name suggests, it is the birectification of the penteractic pentacomb. It is also the rectified demipenteractic pentacomb.

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


 * $$\left(\sqrt2i,\,\sqrt2j,\,±\frac{\sqrt2}{2}+\sqrt2k,\,±\frac{\sqrt2}{2}+\sqrt2l,\,±\frac{\sqrt2}{2}+\sqrt2m\right),$$

where i, j, k, l, and m range over the integers.

Representations
A birectified penteractic pentacomb has the following Coxeter diagrams:


 * o4o3x3o3o4o (full symmetry)
 * o3o3o *b3x3o4o (half symmetry, penteractitriacontaditera of two types)
 * o3x3o *b3o3o4o (half symmetry, rectified triacontaditera of two types)
 * o3x3o o3o3o *b3*e (quarter symmetry)