Mathematicians and designers are rejoicing as the 15th pentagonal tile pattern has just been discovered.

Triangles and four-sided shapes can always tile a plane, meaning that they don't overlap or leave gaps in between each individual shape. Only 14 pentagonal tile patterns existed until this recent discovery, and the basic pentagon with all sides measuring the same length does not tile.

New tessellating pentagonal shape discovered. Image 1.

Image: Twitter

German mathematician Karl Reinhardt began to experiment with pentagons in 1918 and discovered five equations for shapes that tile the plane completely.

Since then, the remaining 11 tiles were discovered by R. B. Kershner, Richard James, Marjorie Rice, and Rolf Stein, with the latest discovery being in 1985.

It wasn't until just recently that Casey Mann, Jennifer McLoud, and David Von Derau of the University of Washington Bothell announced their new discovery.

New tessellating pentagonal shape discovered. Image 2.

Image: Casey Mann

The team used a computer with set parameters to discover the new formula.

Casey says, "The problem of classifying convex pentagons that tile the plane is a beautiful mathematical problem that is simple enough to state so that children can understand it, yet the solution to the problem has eluded us for over 100 years," said Casey. "The problem also has a rich history, connecting back to the 18th of David Hilbert’s famous 23 problems."

Facts about tessellations:

 Tessellations were first seen in Rome and early Islamic arts.

 M. C. Escher is a well-known Dutch artist famous for his experiments with tessellations.

 Tessellations appear in nature in the form of honeycombs, plant cells, turtle shells, and the structure of some viruses.

Cover image: Casey Mann