Milan Journal of Mathematics

, Volume 78, Issue 2, pp 643–682 | Cite as

Reflections on the Lemniscate of Bernoulli: The Forty-Eight Faces of a Mathematical Gem



Thirteen simple closed geodesics are found in the lemniscate. Among these are nine “mirrors”—geodesics of reflection symmetry—which generate the full octahedral group and determine a triangulation of the lemniscate as a disdyakis dodecahedron. New visualizations of the lemniscate are presented.


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© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Department of MathematicsCase Western Reserve UniversityClevelandUSA

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