Attack on the Pentagon Results in Discovery of New Mathematical Tile
12th August 2015
If you can cover a flat surface using only identical copies of the same shape leaving neither gaps nor overlaps, then that shape is said to tile the plane.
Every triangle can tile the plane. Every four-sided shape can also tile the plane.
Things get interesting with pentagons. The regular pentagon cannot tile the plane. (A regular pentagon has equal side lengths and equal angles between sides, like, say, a cross section of okra, or, erm, the Pentagon). But some non-regular pentagons can.
If, of course, that’s what you want to do.