A 15th way to Tile the Plane

How many shapes are able to “tile the plane” — meaning the shapes can fit together perfectly to cover any flat surface without overlapping or leaving any gaps. Mathematicians have proved that all triangles and quadrilaterals, or shapes with four sides, can tile the plane, and they have documented all of the convex hexagons that can do it. But it gets a lot more complicated when dealing with pentagons — specifically convex, or non regular pentagons with the angles pointing outward.

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Mon, Aug 24, 2015