Tessellations

1. Tessellations

2. A tessellation is created when a shape is repeated over and over again covering a plane without any gaps or overlaps. Another word for a tessellation is a tiling. A regular polygon has 3 or 4 or 5 or more sides and angles, all equal. A regular tessellation means a tessellation made up of congruent regular polygons. [Remember: Regular means that the sides and angles of the polygon are all equivalent (i.e., the polygon is both equiangular and equilateral). Congruent means that the polygons that you put together are all the same size and shape.] Only three regular polygons tessellate in the Euclidean plane: triangles, squares or hexagons. Here are examples of a tessellation of triangles a tessellation of squares a tessellation of hexagons

3. Regular and semi-regular tessellations Hexagonal tessellation of a floor A regular tessellation is a highly symmetric tessellation made up of congruent regular polygons. Only three regular tessellations exist: those made up of equilateral triangles, squares, or hexagons. A semi regular tessellation uses a variety of regular polygons; there are eight of these. The arrangement of polygons at every vertex point is identical. An edge-to-edge tessellation is even less regular: the only requirement is that adjacent tiles only share full sides, i.e. no tile shares a partial side with any other tile.

4. Here are some examples of semi-regular tessellations: