Turtle shells, honeycombs, raspberries, quilts, fish scales and the art of M.C. Escher are just a few examples of real-life tessellations. Tessellations are patterns that repeat over and over without overlapping or leaving any gaps. Additional examples are snake skins, pineapples, origami and tile floors.
Many examples of tessellations can be found in Islamic architecture because the architects are not allowed to use human or animal figures, so they use a variety of different shapes arranged in patterns. Some of these shapes may be geometric, floral or calligraphic.
Tessellations can be regular, semi-regular or irregular. Equilateral triangles, squares and hexagons are regular polygons that easily tessellate because they are both regular and congruent. A soccer ball is a regular tessellation of hexagons. Semi-regular tessellations are formed when two or more regular polygons are arranged so every vertex is identical. Some tile floor patterns that use a smaller tile set between a repeating pattern of larger tiles are semi-regular tessellations. All tessellations that are not regular or semi-regular are considered irregular. A well-known painting by Escher depicts lizards in an irregular tessellation.
Tessellations also are known as tilings. In Latin, the word "tessera" means a small stone cube. In ancient Rome, the tessera were used to make tessellata, or mosaic pictures.