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Home > Chaim Goodman-Strauss :: Symmetries
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"Morning Glories 4_2 : 2," by Chaim Goodman-Strauss, University of Arkansas (

In addition to the thirty-five "prime", discrete symmetry types of three-dimensional Euclidean space, there are 184 "composite", types; these each can be projected down an axis to produce one of the 17 discrete symmetry types of the plane. This pattern in space, for example, with type 4_2 : 2, is a kind of attenuated planar pattern with type 4 * 2. This image is from "The Symmetries of Things", by John H. Conway, Heidi Burgiel and Chaim Goodman-Strauss (AK Peters, 2008).

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American Mathematical Society