Tessellations

Part 2: Practical Applications of Tessellations

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. This is an ancient technique that today 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 concentrate on the abstraction forms with a mathematical underlining.

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 apply tessellations in their work. These designs, which often contain representational elements, are often called diaper designs.

Although often considered an art or design application, tessellations can be found in nature, as in the patterns of snowflakes and in honeycombs. Scientists have determined that beehives are composed of hexagons because that is the most efficient shape for bees to build in.

Tessellations appear in various scientific and engineering disciplines. Chemical discoveries show that certain carbon molecules take the shape of a truncated isocahedren. Geodesic domes no longer are abstract shapes but can be actual built structures.

Next: Learn how to construct a Tessellation

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