AbstractWe prove that there does not exist a tiling with Lee spheres of radius at least 2 in the 3-dimensional Euclidean space. In particular, this result verifies a conjecture of Golomb and Welch forn=3
AbstractIt is shown that any set of three lattice points in n-dimensional Euclidean space Rn tiles t...
AbstractIn this paper we survey recent results on the Golomb–Welch conjecture and its generalization...
The edge-to-edge tilings of the sphere by congruent quadrilaterals of Type $a^2bc$ are classified as...
AbstractWe prove that there does not exist a tiling of R3 with Lee spheres of radius greater than 0 ...
AbstractWe prove that there does not exist a tiling with Lee spheres of radius at least 2 in the 3-d...
AbstractGravier et al. proved [S. Gravier, M. Mollard, Ch. Payan, On the existence of three-dimensio...
The paper addresses the problem if the n-dimensional Euclidean space can be tiled with translated co...
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...
AbstractIn this paper we prove that one can only tile a triangle with tiles all congruent to each ot...
. O. H. Keller conjectured in 1930 that in any tiling of R n by unit n-cubes there exist two of t...
Objects with large symmetry groups have been an interest for many mathematicians. A classical questi...
AbstractLet T be a triangulation of a closed topological cube Q, and let V be the set of vertices of...
In 1976 Simmons conjectured that every coloring of a 2-dimensional sphere of radius strictly greater...
AbstractIn this paper it is shown that 3-space cannot be filled with cubes such that neighbouring cu...
AbstractIt is shown that any set of three lattice points in n-dimensional Euclidean space Rn tiles t...
AbstractIn this paper we survey recent results on the Golomb–Welch conjecture and its generalization...
The edge-to-edge tilings of the sphere by congruent quadrilaterals of Type $a^2bc$ are classified as...
AbstractWe prove that there does not exist a tiling of R3 with Lee spheres of radius greater than 0 ...
AbstractWe prove that there does not exist a tiling with Lee spheres of radius at least 2 in the 3-d...
AbstractGravier et al. proved [S. Gravier, M. Mollard, Ch. Payan, On the existence of three-dimensio...
The paper addresses the problem if the n-dimensional Euclidean space can be tiled with translated co...
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...
AbstractIn this paper we prove that one can only tile a triangle with tiles all congruent to each ot...
. O. H. Keller conjectured in 1930 that in any tiling of R n by unit n-cubes there exist two of t...
Objects with large symmetry groups have been an interest for many mathematicians. A classical questi...
AbstractLet T be a triangulation of a closed topological cube Q, and let V be the set of vertices of...
In 1976 Simmons conjectured that every coloring of a 2-dimensional sphere of radius strictly greater...
AbstractIn this paper it is shown that 3-space cannot be filled with cubes such that neighbouring cu...
AbstractIt is shown that any set of three lattice points in n-dimensional Euclidean space Rn tiles t...
AbstractIn this paper we survey recent results on the Golomb–Welch conjecture and its generalization...
The edge-to-edge tilings of the sphere by congruent quadrilaterals of Type $a^2bc$ are classified as...
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