Tilings - tilings because they use more than one shape...

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Tilings Slide 5-7: Pompeii Tiling with equilateral triangles Calter photo Tilings or tesselations refers to the complete covering of a plane surface by tiles. There are all sorts of tilings, some of which we'll cover later. For now, lets do the simplest kind, called a regular tiling, that is, tiling with regular polygons. This is opposed to semiregular tilings like the Getty pavement shown here. Slide 5-8: Getty Pavement Calter photo The equilateral triangle is one of the three regular polygons that tile a plane. the other two being the square and hexagon. Hexagon & Hexagram
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Slide 5-15: Plate with Star of David Keller, Sharon. The Jews: A Treasury of Art and Literature. NY: Levin Assoc. 1992 Hexagonal Tilings Our next polygon is the hexagon, closely related to the equilateral triangle The hexagon is a favorite shape for tilings, as in these Islamic designs, which are not regular
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Unformatted text preview: tilings, because they use more than one shape. Slide 5-9: Islamic Tiling Patterns El-Said, Issam, et al. Geometric Concepts in Islamic Art. Palo Alto: Seymour, 1976. p. 54 But, as we saw, the hexagon is one of the three regular polygons will make a regular tiling. An Illusion The hexagon is sometimes used to create the illusion of a cube by connecting every other vertex to the center, forming three diamonds, and shading each diamond differently. Slide 5-10: Basket Calter photo Slide 5-11: Pavement, Ducal Palace, Mantua Calter photo The Hexagon in Nature The hexagon is found in nature in the honeycomb, and some crystals such as basalt, and of course, in snowflakes. Slide 5-12: Snowflakes Bentley, W. A. Snow Crystals. NY: Dover, 1962....
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