Tessellations have practical applications in many realms, from art and architecture to science, technology, and production.
In design and architecture, tessellation refers to the paving of walls, floors, or other surfaces with a pattern of small tiles (tesserae) made of ceramics, glass, metal leaf, stone, or other materials. These tesserae normally are cut into geometric shapes that fit together perfectly in either simple or complex designs in a seemingly infinite pattern while providing continous surface coverage. This is an ancient technique that you can see in buildings and wall murals in Greece, Italy, Turkey, India, and many other countries. Tessellations are particularly prominent in Islamic art, which forbids representational images of God; therefore, its designs favor abstract forms with mathematical underpinnings.
Although tesserae often consist of abstract shapes, primarily symmetrical rectangles, hexagons, octagons, and other polygons, they also can consist of figurative elements, as in the work of artists like Kolomon Moser (1868-1918) and M.C. Escher (1898-1972). Escher is famed for his tessellations composed of horses, butterflies, birds, and imaginary creatures (which in the 1990s formed the basis of a popular line of upholstery fabrics!). Many of his designs “morph” different shapes, such as hexagons evolving into creatures.
Many contemporary artists and craftspeople apply tessellations in their work. These designs, which can contain representational elements, are often called diaper designs. Those with a 3D aspect often incorporate principles of origami.
Although often considered an art or design application, tessellations can be found in nature, as in the patterns of snowflakes, honeycombs, and cracks in dry earth. Scientists have determined that beehives are composed of hexagons because that is the most efficient way for bees to construct their homes.
Tessellations appear in various scientific and engineering disciplines. Chemical discoveries show that certain carbon molecules take the shape of a truncated isocahedren. Geodesic domes are both theoretical 3D geometric constructs and built structures. The mathematics of various tessellation types underscore efficiency-focused processes of machining and manufacturing.