Hat tessellation

A tessellation is a way of filling a plane by repeating a set of figures, called tesserae, infinitely. Normally the tessellations are periodic, that is, they are repeated over and over again.

The hat tiling is the first non-periodic tiling in the plane with a single tile. The tile has been discovered in March 2023 and has been a mathematical achievement of the first order.

Below you can see the tessellation of the hat made with a single tesserae.

Teselado sombrero

Tessellation with hat tesserae. The red tesserae are arranged face down, as in a mirror image, with respect to the others.

Hat tessellation. PDF format.


Print the following document showing hat tesserae. Place the tesserae on a plane so that they form a non-periodic tessellation. Color the tesserae with four different colors, so that no two of the same colors touch.