Characterization of the Two-Dimensional Five-Fold Translative Tiles

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.

18 pages, 10 figures. arXiv admin note: substantial text overlap with arXiv:1711.02514, arXiv:1712.01122

References in corpus (4)

• Exhaustive search of convex pentagons which tile the plane
• The complete classification of five-dimensional Dirichlet-Voronoi polyhedra of translational lattices
• Characterization of the Two-Dimensional Five-Fold Lattice Tiles
• Multiple Translative Tilings in Euclidean Spaces

Cited by in corpus (1)

• Can You Pave the Plane Nicely with Identical Tiles