Just came across news of the discovery of a new pentagonal shape that can tile the plane.
Tiling the plane means that you can cover a flat surface using only identical copies of the same shape leaving neither gaps nor overlaps. It is known that any triangle can tile the plane, as does every quadrilateral (a four-sided shape). Tiling using (convex) pentagonal shapes is an interesting problem whose history goes all the way back to 1918. Prior to the latest discovery, there were only 14 distinct tiling patterns. This newly discovered pentagonal tiling is the first discovery since 1985. The three mathematicians who discovered this new pattern are Casey Mann, Jennifer McLoud and David Von Derau of the University of Washington at Bothell. They made the discovery after an exhaustive computer search through a large but finite set of possibilities. No one know if there are more distinct pentagonal shapes that can tile the plane. This piece from the Guardian gives a good background to this problem.
The following is a picture of the 15 distinct pentagonal tiling patterns (the new one is on the bottom right).
Source: Wikimedia Commons