Last month, Michaël Rao posted a preprint on his webpage claiming that there are no other pentagonal tilings. It's a pretty technical paper, but I'll try to outline the basic idea. Given a convex ...

TOM M. CAVALIER, HANIF D. SHERALI, Euclidean Distance Location-Allocation Problems with Uniform Demands over Convex Polygons, Transportation Science, Vol. 20, No. 2 (May 1986), pp. 107-116 ...