tiling by Lee spheres integer tiling lattice-like tiling exact cover problem
Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 40, No 1, (2014), 1p-12p
The paper addresses the problem if the n-dimensional Euclidean space can be tiled with translated copies of Lee spheres of not necessarily equal radii such that at least one of the Lee spheres has radius at least 2. It will be showed that for n = 3, 4 there is no such tiling. 2010 Mathematics Subject Classification: Primary 94B60; Secondary 05B45, 52C22.