Constructions
There are many different Wythoff constructions of this honeycomb. The most symmetric form is regular, with Schläfli symbol {4,3,3,3,3,4}. Another form has two alternating 6-cube facets (like a checkerboard) with Schläfli symbol {4,3,3,3,31,1}. The lowest symmetry Wythoff construction has 64 types of facets around each vertex and a prismatic product Schläfli symbol {∞}6.
Read more about this topic: 6-cubic Honeycomb