  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.
