Four 5-cubes meet at each cubic cell, and it is more explicitly called an order-4 penteractic honeycomb.
The most symmetric form is regular, with Schläfli symbol {4,33,4}.
Another form has two alternating 5-cube facets (like a checkerboard) with Schläfli symbol {4,3,3,31,1}.
The lowest symmetry Wythoff construction has 32 types of facets around each vertex and a prismatic product Schläfli symbol {∞}(5).
The vertices correspond to points in the 5-dimensional cubic lattice, and the tiles are formed by connecting points in a predefined manner.
[1] A tritruncated 5-cubic honeycomb, , contains all bitruncated 5-orthoplex facets and is the Voronoi tessellation of the D5* lattice.