Though the tiles fit neatly together and can cover an infinite plane, they are aperiodic, meaning they can’t form a pattern that repeats. With a periodic pattern, it’s possible to shift the ...

Infinitely many copies of a 13-sided shape can be arranged with no overlaps or gaps in a pattern ... tile is made up of eight kites, or four-sided polygons with two pairs of adjacent, equal-length ...

The swirling Arabesque ceramic tiles ... the same pattern until the early 1970s, when English mathematician Roger Penrose introduced his famous "Penrose" tiling system. The full study appears ...