A plane tiling consisting of congruent copies of a shape is isohedral provided that for any pair of copies, there exists a symmetry of the tiling mapping one copy to the other. We give a $O(n\log^2{ n})$-time algorithm for deciding if a polyomino with $n$ edges can tile the plane isohedrally. This improves on the $O(n^{ 18})$-time algorithm of Keating and Vince and generalizes recent work by Brlek, Proven\c{ c}al, F\'{ e}dou, and the second author.
Categories: cs.CG