Characterization of the Two-Dimensional Five-Fold Translative Tiles
Metric Geometry
2018-03-20 v4
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 two-, three- or four-fold translative tiling in the Euclidean plane, but there are centrally symmetric convex octagons and decagons which can form five-fold translative tilings. This paper characterizes all the convex domains which can form five-fold translative tilings of the Euclidean plane.
Keywords
Cite
@article{arxiv.1712.09732,
title = {Characterization of the Two-Dimensional Five-Fold Translative Tiles},
author = {Qi Yang and Chuanming Zong},
journal= {arXiv preprint arXiv:1712.09732},
year = {2018}
}
Comments
18 pages, 10 figures. arXiv admin note: substantial text overlap with arXiv:1711.02514, arXiv:1712.01122