Keller's Conjecture Revisited
Authors : Peter Horak, Dongryul Kim
Pages : 175-177
Doi:10.36890/iejg.984269
View : 7 | Download : 3
Publication Date : 2022-10-31
Article Type : Research
Abstract :In 1930, Keller conjectured that every tiling of R n Rn by unit cubes contains a pair of cubes sharing a complete ( n − 1 ) (n−1) -dimensional face. Only 50 years later, Lagarias and Shor found a counterexample for all n ≥ 10 n≥10 . In this note we show that neither a modification of Keller's conjecture to tiles of more complex shape is true.Keywords : Tiling, tiling by unit cubes, Keller's conjecture