Multiple Translative Tilings in Euclidean Spaces

Qi Yang; Chuanming Zong

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arXiv · 1711.02514

Multiple Translative Tilings in Euclidean Spaces

Qi Yang·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. This paper proves the following results: Besides parallelograms and centrally symmetric hexagons, there is no other convex domain which can form a two-, three- or four-fold translative tiling in the Euclidean plane. However, there are two-dimensional convex domains which is neither a parallelogram nor a centrally symmetric hexagon can form five-fold translative tilings.

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Qi Yang, Chuanming Zong. 2017-11-04. Multiple Translative Tilings in Euclidean Spaces. https://arxiv.org/abs/1711.02514

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