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Home > Chaim Goodman-Strauss :: Symmetries
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"Inverse Stereo," by Chaim Goodman-Strauss, University of Arkansas (

The pattern on this sphere is not a spherical pattern—that is, its symmetry is not a symmetry of the sphere itself. Symmetry is as much as anything a topological property; the pattern on the sphere is in fact a symmetry of the Euclidean plane, as shown by projecting it down to the plane below. Only seventeen types of symmetrical pattern can cover the Euclidean plane; this one has type 4*2. This image is on the cover of "The Symmetries of Things", by John H. Conway, Heidi Burgiel and Chaim Goodman-Strauss (AK Peters, 2008).

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American Mathematical Society