Add to ORKGInternational audienceIn this paper, we study a class of polycubes that tile the space by translation in a non lattice periodic way. More precisely, we construct a family of tiles indexed by integers with the property that Tk is a tile having k ≥ 2 has anisohedral number. That is k copies of Tk are assembled by translation in order to form a metatile. We prove that this metatile is lattice periodic while Tk is not a lattice periodic tile
It has been proved that, among the polyominoes that tile the plane by translation, the so-called squ...
Brandolini et al. conjectured in (Preprint, 2019) that all concrete lattice polytopes can multitile ...
AbstractIt has been proved that, among the polyominoes that tile the plane by translation, the so-ca...
International audienceIn this paper, we study a class of polycubes that tile the space by translatio...
AbstractIn this paper, we study a class of polycubes that tile the space by translation in a non-lat...
International audienceWe construct a class of polycubes that tile the space by translation in a latt...
AbstractOn square or hexagonal lattices, tiles or polyominoes are coded by words. The polyominoes th...
We give a simple set of two tiles that can only tile aperiodically | that is no tiling with these ti...
The periodic tiling conjecture asserts that any finite subset of a lattice $\mathbb{Z}^d$ which tile...
AbstractWe give a simple set of two tiles that can only tile aperiodically—that is no tiling with th...
AbstractWe consider the tilings by translation of a single polyomino or tile on the square grid Z2. ...
AbstractWe give a set of only two tiles inEnfor eachn≥ 3; these sets of tiles admit only non-periodi...
We consider the tilings by translation of a single polyomino or tile on the square grid Z2 (Z exposa...
AbstractWe show that a single prototile can fill space uniformly but not admit a periodic tiling. A ...
AbstractThe definitions and lattice hierarchy previously established for tiling regions with individ...
It has been proved that, among the polyominoes that tile the plane by translation, the so-called squ...
Brandolini et al. conjectured in (Preprint, 2019) that all concrete lattice polytopes can multitile ...
AbstractIt has been proved that, among the polyominoes that tile the plane by translation, the so-ca...
International audienceIn this paper, we study a class of polycubes that tile the space by translatio...
AbstractIn this paper, we study a class of polycubes that tile the space by translation in a non-lat...
International audienceWe construct a class of polycubes that tile the space by translation in a latt...
AbstractOn square or hexagonal lattices, tiles or polyominoes are coded by words. The polyominoes th...
We give a simple set of two tiles that can only tile aperiodically | that is no tiling with these ti...
The periodic tiling conjecture asserts that any finite subset of a lattice $\mathbb{Z}^d$ which tile...
AbstractWe give a simple set of two tiles that can only tile aperiodically—that is no tiling with th...
AbstractWe consider the tilings by translation of a single polyomino or tile on the square grid Z2. ...
AbstractWe give a set of only two tiles inEnfor eachn≥ 3; these sets of tiles admit only non-periodi...
We consider the tilings by translation of a single polyomino or tile on the square grid Z2 (Z exposa...
AbstractWe show that a single prototile can fill space uniformly but not admit a periodic tiling. A ...
AbstractThe definitions and lattice hierarchy previously established for tiling regions with individ...
It has been proved that, among the polyominoes that tile the plane by translation, the so-called squ...
Brandolini et al. conjectured in (Preprint, 2019) that all concrete lattice polytopes can multitile ...
AbstractIt has been proved that, among the polyominoes that tile the plane by translation, the so-ca...