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arXiv · 1712.01122

Characterization of the Two-Dimensional Five-Fold Lattice Tiles

Chuanming Zong
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Abstract

In 1885, Fedorov discovered that a convex domain can form a lattice tiling of the Euclidean plane if and only if it is a parallelogram or a centrally symmetric hexagon. It is known that there is no other convex domain which can form a two-, three- or four-fold lattice tiling in the Euclidean plane, but there is a centrally symmetric convex decagon which can form a five-fold lattice tiling. This paper characterizes all the convex domains which can form a five-fold lattice tiling of the Euclidean plane.

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Chuanming Zong. 2017-12-01. Characterization of the Two-Dimensional Five-Fold Lattice Tiles. https://arxiv.org/abs/1712.01122

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