![]() It also explains how they can be transformed using translation, rotation and glide reflection to create. Freeman 1990Ī unit cell or “tile” is the smallest region in the plane having the property that the set of all of its images will fill the plane. It shows a simple visual demonstration of tessellating triangles, squares and hexagons. Visions of Symmetry Doris Schattschneider W.H. ![]() Escher (1898-1972) was a master at constructing tessellations Mathematical Reference: “The Plane Symmetry Groups: Their Recognition and Notation” by Doris Schattschneider, The Mathematical Monthly, June-July, 1978 Artistic Source: Maurits C. P2gg p2mm p2mg p4mm p4gm p6mm p1 p4 p3m1 cm p6 p31m p2 c2mm p3 pm pg Journal of Chemical EducationĮscher’s Drawings of Alhambra Repeating PatternsĮscher Sketches of designs in the Alhambra and La Mezquita (Cordoba) P1 p2 pm pg cm p2mm pmg pgg c2mm p4 p4mm p4gm p3 p3m1 p31m p6 p6mm P1 p211 p1m1 pg c1m1 p2mm p2gg p4gm p2mg p4m c2mm p4 p3 p3m1 p6 p31m p6mm There are 17 “plane symmetry groups” or types of patterns.Įxamples of places where repeating patterns are found: Some examples of periodic or repeating patterns, sometimes called “wallpaper designs,” will be shown. Regular Hexagons Examples: Regular Polygons.Some examples of the 17 plane symmetry groups will be shown.Ī repeating pattern or a tessellation or a tiling of the plane is a covering of the plane by one or more figures with a repeating pattern of the figures that has no gaps and no overlapping of the figures. This PowerPoint aims to give a rough overview of Eschers graphic artistic style, help children understand what a tessellation is and then encourage them to have a go at creating their own. The way in which tessellations are classified will be illustrated using examples from Chinese Lattice Designs, The Alhambra, Hungarian Needlework, and M.Tanis Professor Emeritus of Mathematics Hope College March 2, 2006īIKE BOX CHECKBOOK DECKED HEED HIDE HEED HIDE BIKE BOX CHECKBOOK DECKED HEED HIDE BIKE BOX CHECKBOOK DECKED HEED HIDE BIKE BOX CHECKBOOK DECKED REFLECT ROTATE pĪ Computer Algebra System (CAS) such as MAPLE can be used to construct tessellations. Using MAPLE to Construct Repeating Patterns and Several Tessellations Inspired byM.
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