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3-D.S

3-dimensional.space · 834 words · saved by 1 readers

Space around us has a special kind of symmetry: it behaves the same at every point. (Of course this isn't strictly true as Einstein taught us, but it is a fantastically accurate idealization.) Generalizing this, mathematicians call a space homogeneous if there is a symmetry taking any point to any other point. The first thing one might ask following this definition is classification: how many possible types of geometry have rich symmetry like the euclidean space we live in? Given some reasonable constraints, it turns out there are eight homogeneous geometries in dimension three. These eight geometries are together called the Thurston Geometries in honor of William Thurston, who first realized their fundamental importance in three dimensional topology.

3-Dimensional Space 3-Dimensional space Explore Thurston's geometries Welcome! This project is joint work by Remi Coulon , Sabetta Matsumoto , Henry Segerman , and Steve Trettel to render accurate images of the eight Thurston geometries and their quotients. We are working hard to make a version of this software accessible to anyone who wants to explore, and encourage you to check out the GitHub repository and our papers on the topic (both technical and expository) for much more information. This website hosts various demonstrations we have created along the way, as well as tutorials and docume

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