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
Consider a tiling T of the two-dimensional Euclidean space made with copies up to translation of a f...
There is only one type of tilings of the sphere by 12 congruent pentagons. These tilings are isohedr...
The kissing number problem asks for the maximal number of non-overlapping unit balls in R^n that tou...
AbstractWe prove that there does not exist a tiling with Lee spheres of radius at least 2 in the 3-d...
AbstractWe prove that there does not exist a tiling of R3 with Lee spheres of radius greater than 0 ...
AbstractGravier et al. proved [S. Gravier, M. Mollard, Ch. Payan, On the existence of three-dimensio...
AbstractA family of n-dimensional Lee spheres L is a tiling of Rn, if ∪L=Rn and for every Lu,Lv∈L, t...
A family of ▫$n$▫-dimensional Lee spheres ▫$mathcal{L}$▫ is a tiling of ▫${mathbb{R}}^n$▫ if ▫$cupma...
AbstractIt is shown that any set of three lattice points in n-dimensional Euclidean space Rn tiles t...
AbstractStein (1990) discovered (n−1)! lattice tilings of Rn by translates of the notched n-cube whi...
Sommerville [10] and Davies [2] classified the spherical triangles that can tile the sphere in an ed...
AbstractAs shown by D. Barnette (1973, J. Combin. Theory Ser. A14, 37–53) there are precisely 39 sim...
There exist precisely 914, 58 and 46 equivariant types of tile-transitive tilings of 3-dimensional e...
It is proved that for no n can the Hamming space {0, 1}(n) be partitioned into three Hamming spheres...
Sommerville [10] and Davies [2] classified the spherical triangles that can tile the sphere in an ed...
Consider a tiling T of the two-dimensional Euclidean space made with copies up to translation of a f...
There is only one type of tilings of the sphere by 12 congruent pentagons. These tilings are isohedr...
The kissing number problem asks for the maximal number of non-overlapping unit balls in R^n that tou...
AbstractWe prove that there does not exist a tiling with Lee spheres of radius at least 2 in the 3-d...
AbstractWe prove that there does not exist a tiling of R3 with Lee spheres of radius greater than 0 ...
AbstractGravier et al. proved [S. Gravier, M. Mollard, Ch. Payan, On the existence of three-dimensio...
AbstractA family of n-dimensional Lee spheres L is a tiling of Rn, if ∪L=Rn and for every Lu,Lv∈L, t...
A family of ▫$n$▫-dimensional Lee spheres ▫$mathcal{L}$▫ is a tiling of ▫${mathbb{R}}^n$▫ if ▫$cupma...
AbstractIt is shown that any set of three lattice points in n-dimensional Euclidean space Rn tiles t...
AbstractStein (1990) discovered (n−1)! lattice tilings of Rn by translates of the notched n-cube whi...
Sommerville [10] and Davies [2] classified the spherical triangles that can tile the sphere in an ed...
AbstractAs shown by D. Barnette (1973, J. Combin. Theory Ser. A14, 37–53) there are precisely 39 sim...
There exist precisely 914, 58 and 46 equivariant types of tile-transitive tilings of 3-dimensional e...
It is proved that for no n can the Hamming space {0, 1}(n) be partitioned into three Hamming spheres...
Sommerville [10] and Davies [2] classified the spherical triangles that can tile the sphere in an ed...
Consider a tiling T of the two-dimensional Euclidean space made with copies up to translation of a f...
There is only one type of tilings of the sphere by 12 congruent pentagons. These tilings are isohedr...
The kissing number problem asks for the maximal number of non-overlapping unit balls in R^n that tou...