Plane tiling is a set of geometric shapes that do not have common internal points, but whose union makes up precisely the entire plane.

There are many different types of tiling: regular, Archimedean, Escher’s…

**Regular tiling** is a set of mutually congruent regular polygons set in a way that two polygons either do not touch or they have a common vertex or one common side. Think… how many are there?

**Archimedean tiling** is a union of sets of congruent regular polygons such that each node is a vertex of the same number of polygons and such that the sequence containing the number of sides of each polygon to which that node is a vertex (starting from the polygon with the smallest number of sides and going in the positive direction) is the same. Explore… how many are there?

Escher’s tilings

We have made unique „tiles“ with the help of GeoGebra. You can make your own…