What is a Tessellation?

A tessellation is any repeating pattern of interlocking distinct shapes.  Tessellations fill the plane they are created on  without any overlaps or gaps. There are also different types of tessellations some of them are known as regular, semiregular, edge-to-edge, irregular, ect.   

Regular Tessellations

A regular tessellation is a highly symmetric tessellation made up of congruent regular polygons. Only three types of regular tessellations exist: those made up of equilateral triangles, squares, or hexagons. Only three exist because there are only three polygons whose interior angles divide evenly into 360 degrees.

Semiregular Tessellations

A semiregular tessellation uses a variety of regular polygons, there are eight of these. The arrangement of the polygons at every vertex is the same.

Edge-To-Edge Tessellations

Edge-to-edge tessellations are not regular. The only requirement is that adjacent tiles only share full sides, no tile shares a partial side with any other tile.