The most symmetric form is regular, with Schläfli symbol {4,36,4}.
Another form has two alternating hypercube facets (like a checkerboard) with Schläfli symbol {4,35,31,1}.
The lowest symmetry Wythoff construction has 256 types of facets around each vertex and a prismatic product Schläfli symbol {∞}(8).
The [4,36,4], , Coxeter group generates 511 permutations of uniform tessellations, 271 with unique symmetry and 270 with unique geometry.
A quadrirectified 8-cubic honeycomb, , contains all trirectified 8-orthoplex facets and is the Voronoi tessellation of the D8* lattice.