The original version of this story appeared in Quanta Magazine. If you want to tile a bathroom floor, square tiles are the simplest option—they fit together without any gaps in a grid pattern that can ...

Creatively tiling a bathroom floor isn’t just a stressful task for DIY home renovators. It is also one of the hardest problems in mathematics. For centuries, experts have been studying the special ...

Infinitely many copies of a 13-sided shape can be arranged with no overlaps or gaps in a pattern that never repeats. David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss (CC BY ...

The surprisingly simple tile is the first single, connected tile that can fill the entire plane in a pattern that never repeats — and can’t be made to fill it in a repeating way. In mid-November of ...

Ever wanted an actual one-of-a-kind bathroom or kitchen? Well, mathematicians have found the perfect tile for you. A team from the University of Arkansas have discovered the first shape that can cover ...

A new 13-sided shape is the first example of an elusive "einstein" — a single shape that can be tiled infinitely without repeating a pattern. When you purchase through links on our site, we may earn ...

A 13-sided shape known as “the hat” has mathematicians tipping their caps. It’s the first true example of an “einstein,” a single shape that forms a special tiling of a plane: Like bathroom floor tile ...

Mathematicians solved a decades-long mystery earlier this year when they discovered a shape that can cover a surface completely without ever creating a repeating pattern. But the breakthrough had come ...

For centuries, mathematicians and floor designers alike have been fascinated by the shapes that can tile a plane — in particular, those that do so without repetition. Now, a team of chemists has ...

If you want to tile a bathroom floor, square tiles are the simplest option — they fit together without any gaps in a grid pattern that can continue indefinitely. That square grid has a property shared ...