Let C be a compact subset of the Euclidean plane E whose boundary is a Jordan curve J. If C tiles the
plane, can J be such that it has a unique tangent line at each point and none of its sub-arcs is a
straight line segment with distinct end-points? If so, can you give an example? J does not need to be
convex and the tiling need not be regular. The only requirement is that the plane E be a countable union
of congruent copies of C, no two of which have a common interior point.