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 ...

It’s been just months since researchers reported the first “einstein” — a single tile that can cover an infinite plane, but only with a pattern that never repeats (SN: 3/24/23). Now, the same team has ...

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 ...

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 ...

Mathematicians have discovered a single shape that can be used to cover a surface completely without ever creating a repeating pattern. The long-sought shape is surprisingly simple but has taken ...

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 ...

Remember the graph paper you used at school, the kind that’s covered with tiny squares? It’s the perfect illustration of what mathematicians call a “periodic tiling of space”, with shapes covering an ...

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 ...