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Home > Chaim Goodman-Strauss :: Symmetries
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"The Hexacosm," by Chaim Goodman-Strauss, University of Arkansas (

This spaceship is flying about in the universal cover of the hexacosm, one of the ten, closed, flat three-manifolds. Equivalently, the pattern is one of the ten discrete co-compact symmetry types of Euclidean space that does not have any fixed points. The type here is (6_1 3_1 2_1) in the Thurston-Conway fibrefold notation. 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