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 ...

The Penrose tiling pattern is a type of quasicrystal, which means that it has an ordered yet never-repeating structure. The pattern, composed of two shapes, is a 2D projection of a 5D square lattice.

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 ...