Title: Characterization of the Two-Dimensional Five-Fold Lattice 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 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.