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Polygons and PolyhedraPenrose

Penrose Tilings

All the tessellations we saw so far have one thing in common: they are periodic. That means they consist of a regular pattern that is repeated again and again. They can continue forever in all directions and they will look the same everywhere.

In the 1970s, the British mathematician and physicist Roger Penrose

Sir Roger Penrose (born 1931) is a British mathematician and physicist who is known for his groundbreaking work in general relativity and cosmology. He also discovered Penrose Tilings: self-similar, non-periodic tessellations using only two different tiles.

In 1988, he shared the Wolf Prize with Stephen Hawking, and in 2020, he received the Nobel Prize in physics for discoveries about the formation of black holes.

Timeline

discovered non-periodic tessellations – they still continue infinitely in all directions, but never look exactly the same. These are called Penrose tilings, and you only need a few different kinds of polygons to create one:

Move the slider to reveal the underlying structure of this tessellation. Notice how the same patterns appear at various scales: the yellow pentagons, blue stars, purple rhombi and green ‘ships’ appear in their original size, in a slightly larger size and an even larger size. This self-similarity can be used to prove that a Penrose tiling is always non-periodic.

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