Mathematicians Discover 15th Pentagon That Can Tile the Plane

Posted on August 20, 2015

Pentagon is 15th to tile the plane

A new pentagon has been discovered that can cover the plane without gaps or overlaps. The Guardian reports that this is only the 15th known type of pentagon that can tile the plane. It is the first tile discovery in 30 years. The last pentagon that can tile the plane was discovered in 1985 by Rolf Stein.

The discovery was made by a research team at the University of Washington Bothell. The team includes mathematics associate professors and research co-directors Casey Mann and Jennifer McLoud-Mann. The discover was made using a computer program written by undergraduate researcher researcher David Von Derau.

Mann says in a statement, "Aside from the practical uses of this new knowledge, which would include a whole different way to tile a floor, the impact of this new tile moves us one step closer to having a complete understanding as to how shapes can fit together on a plane."

The discovery could lead to practical uses in many different fields from biochemistry to structural design. Mann told The Guardian, "Many structures that we see in nature, from crystals to viruses, are comprised of building blocks that are forced by geometry and other dynamics to fit together to form the larger scale structure."

NPR shows all 15 known pentagons that can tile the plane here.

Image: Casey Mann