Questions we have:
-trapezoid tilability
--no T2-tilings for composite height?
--T2-tilling for height > 3 only some kind of composition of 2 and 3 cases?
-rhombus tilability
--T2-tiling only when side length is multiple of 6?
-hexagon tilability
-ditriangle tilability
-limit of tilability, like for a fractal
-number of tilings
-relation to cycle partitions problem?
--how hard is cycle partitioning problem?
-"moving between" tilings
--smallest T2-tilling "move"?

General tilability decider program
Data / Results / Etc
Trapezoid base cases work (nothing special)