A new pentagon shape could be used to form the exact pattern you have been looking for.
Have you been on the hunt for a unique tile product that will wow friends and family? Then the forthcoming math-lovers tile may be for you. The new pentagonal shape, 30 years in the making, is only the 15th type of nonregular pentagon in mathematical history that can tile the plane.
Tiling the plane refers to the ability to place tiles edge to edge on a flat surface — like a powder room floor or a kitchen backsplash — without leaving any gaps or overlapping. That’s why most tiles are triangular, quadrilateral or hexagonal. Because regular pentagons are made up of five equal sides, they cannot tessellate without adding another shape to fill in the spaces.
Only nonregular, or convex, pentagons can tile a plane.
“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,” Casey Mann, one of the University of Washington Bothell mathematicians who discovered the new type of pentagon, told The Guardian.
But it didn’t happen overnight.
“It had gotten to the point, where we hadn’t found anything. And I was starting to believe I just don’t know if we’re going to find anything,” researcher Jennifer McLoud-Mann, who is married to Mann, told NPR. But last week, after two years of sifting through data generated from a computer algorithm, they did find something.
The mathematicians explain that this shape is not just about solving a problem.
“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,” Mann noted.
In fact, the Manns say they may just tile a spot in their home with their new shape. No word on how soon it will be available to homeowners who want a bathroom that doesn’t look like everyone else’s. In the future, other convex pentagons may be discovered, providing inspiration for home-remodeling projects in the pipeline.