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On a number of polyhex plane tilings. (Russian. English summary) Zbl 1395.52024
A polyhex is a strongly connected union of unit regular hexagons in the plane. A tiling is called a lattice tiling if there is a group of translations which acts transitively on the set of the tiles. In the paper the authors consider lattice tilings of the plane with polyhexes homeomorphic to disks. The lattice of the tiling is assumed to be a sublattice of the hexagonal lattice.
For the number of the lattice tilings of the plane with centrally symmetric polyhexes of given area, the lower and upper bounds are found in the paper.
52C20 Tilings in \(2\) dimensions (aspects of discrete geometry)
52C05 Lattices and convex bodies in \(2\) dimensions (aspects of discrete geometry)
Full Text: MNR
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