  Every body knows that identical regular triangles or squares can tile the
whole plane. Many people know that identical regular hexagons can tile the
plane properly as well. In fact, even the bees know and use this fact! Is there
any other convex domain which can tile the Euclidean plane? Yes, there is a
long list of them! To find the list and to show the completeness of the list is
a unique drama in mathematics, which has lasted for more than one century and
the completeness of the list has been mistakenly announced not only once! Up to
now, the list consists of triangles, quadrilaterals, three types of hexagons,
and fifteen types of pentagons. In 2017, Michael Rao announced a computer proof
for the completeness of the list. Meanwhile, Qi Yang and Chuanming Zong made a
series of unexpected discoveries in multiple tilings in the Euclidean plane.
For examples, besides parallelograms and centrally symmetric hexagons, there is
no other convex domain which can form any two-, three- or four-fold translative
tiling in the plane; there are only two types of octagons and one type of
decagons which can form five-fold translative tilings.
