It is analogous to the square tiling of the plane and to the cubic honeycomb of 3-space.
The most symmetric form is regular, with Schläfli symbol {4,34,4}.
Another form has two alternating 6-cube facets (like a checkerboard) with Schläfli symbol {4,33,31,1}.
The lowest symmetry Wythoff construction has 64 types of facets around each vertex and a prismatic product Schläfli symbol {∞}(6).
A trirectified 6-cubic honeycomb, , contains all birectified 6-orthoplex facets and is the Voronoi tessellation of the D6* lattice.