More about the 52 four-dimensional parallelotopes
A parallelotope (in the sense of tilings) is a convex polytope filling the space by its translative copies without overlapping, i.e., a translative space-filler. The authors investigate the 52 types of four-dimensional parallelotopes. More precisely, they prove that there are exactly 17 four-dimensional unimodular vector systems, which yield precisely 17 types of zonotopal 4-parallelotopes. In addition it is shown that the remaining 35 types are: Schläfli's 24-cell, and 34 sums of the 24-cell and zonotopal parallelotopes. The constructions of these 34 types are described in detail.
scientific article; zbMATH DE number 5348116