Perhaps the most celebrated style of tessellations can be found in Islamic art and architecture. While the Sumerians of 5th and 6th BCE used tiles to decorate their homes and temples, other civilizations around the world adapted tessellations to fit their culture and traditions the Egyptians, Persians, Romans, Greeks, Arabs, Japanese, Chinese, and the Moors all embraced repeating patterns in their decorative arts. Tessellations in Ancient Islamic Art and ArchitectureĬeramic tile tessellations in Marrakech, Morocco (Photo: Wikimedia Commons, (CC BY-SA 3.0)) Now that we’ve covered the basic math of tessellations, read on to learn about how they were used throughout history. Each vertex is surrounded by the same polygons arranged in the same recurring order. Semi-regular tessellations occur when two or more types of regular polygons are arranged in a way that every vertex point is identical. A checkerboard is the simplest example of this: It comprises square tiles in two contrasting colors (usually black and white) that could repeat forever.

Regular periodic tiling involves creating a repeating pattern from polygonal shapes, each one meeting vertex to vertex (the point of intersection of three or more bordering tiles). The most common configurations are regular tessellations and semi-regular tessellations. There are many types of tessellations, all of which can be classified as those that repeat, are non-periodic, quasi-periodic, and those that are fractals.

An example of semi-regular tessellation (Photo: Wikimedia Commons, (CC BY-SA 3.0))

Tessellation drawing