Question

Given a square piece of paper, describe how you can cut a portion out of the paper and reattach it in a different location to produce an irregular polygon that tessellates

Answer 1

Cut from 1/3 of the way along one side to 2/3 of the way along the opposite side. Joining the pieces at either of the matching sets of short sides produces a tessellating shape.

Joining the 2S/3 sides produces a pentagon with a base of length S and two sides of length S/3 perpendicular to it.

Joining the S/3 sides produces a pentagon, also, but this one is concave. It still tessellates.