Penrose tiling

These shapes were designed by Robert Fathauer. Here is how an arrangement might start.
Roger Penrose stands in front of his invention, in a bathroom in Philadelphia, USA.
A Penrose tiling built with rhombi.

In a Penrose tiling, named after Roger Penrose, a set of shapes can cover a perfectly flat surface without ever repeating. Many artists have drawn several sets of shapes that never repeat, and most of them are built around pentagons.

History

A non-Penrose tiling by pentagons and thin rhombs in the early 18th-century Pilgrimage Church of Saint John of Nepomuk at Zelená hora, Czech Republic
A 15th century shrine in Isfahan has a tiling that is very similar to a Penrose tiling

Penrose did most of his research in the 1970s. The idea of the tiling is older though; there was a shrine in Isfahan, Iran that uses tilings that are very similar. The shrine was built in the 15th century.


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