This further inspired Escher, who began exploring deeply intricate interlocking tessellations of animals, people and plants.Īccording to Escher, "Crystallographers have … ascertained which and how many ways there are of dividing a plane in a regular manner. His brother directed him to a 1924 scientific paper by George Pólya that illustrated the 17 ways a pattern can be categorized by its various symmetries. According to James Case, a book reviewer for the Society for Industrial and Applied Mathematics (SIAM), in 1937, Escher shared with his brother sketches from his fascination with 11 th- and 12 th-century Islamic artwork of the Iberian Peninsula. The most famous practitioner of this is 20 th-century artist M.C. These tessellations work because all the properties of a tessellation are present.A unique art form is enabled by modifying monohedral tessellations. Both tessellations will fill the plane, there are no gaps, the sum of the interior angle meeting at the vertex is 360 ∘, 360 ∘, and both are achieved by translation transformations. The interior angle of a hexagon is 120 ∘, 120 ∘, and the sum of three interior angles is 360 ∘. There are three hexagons meeting at each vertex. An interior angle of a square is 90 ∘Figure 10.103, the tessellation is made up of regular hexagons. There are four squares meeting at a vertex. In Figure 10.102, the tessellation is made up of squares.
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