Keller`s Conjecture Revisited

Authors : Peter HORAK, Dongryul KİM

Pages : 175-177

Doi:10.36890/iejg.984269

View : 19 | Download : 6

Publication Date : 2022-10-31

Article Type : Research Paper

Abstract :In 1930, Keller conjectured that every tiling of R n Rn by unit cubes contains a pair of cubes sharing a complete insert ignore into journalissuearticles values( n − 1 ); insert ignore into journalissuearticles values(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