In geometry, a pentagon tiling is a tiling of the plane by pentagons. A regular pentagonal tiling on the Euclidean plane is impossible because the internal angle of a regular pentagon, 3π/5, is not a divisor of 2π. Fourteen types of tiling by convex pentagons are known as of 2012, and it is not known whether this list is complete.
Read more about Pentagon Tiling: History, Non-convex Pentagons, Dual Uniform Tilings, Regular Pentagonal Tilings in Non-Euclidean Geometry, Irregular Hyperbolic Plane Pentagonal Tilings