Keller's Conjecture on the Existence of Columns in Cube Tilings of Rn
Abstract
It is shown that if n<7, then each tiling of Rn by translates of the unit cube [0,1)n contains a column; that is, a family of the form [0,1)n+(s+kei): k ∈ Z, where s ∈ Rn, ei is an element of the standard basis of Rn and Z is the set of integers.
0