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 {4,35,4}.
Another form has two alternating 7-cube facets (like a checkerboard) with Schläfli symbol {4,34,31,1}.
The lowest symmetry Wythoff construction has 128 types of facets around each vertex and a prismatic product Schläfli symbol {∞}(7).
A quadritruncated 7-cubic honeycomb, , contains all tritruncated 7-orthoplex facets and is the Voronoi tessellation of the D7* lattice.