Highly Influential

@article{Langer2010WhenIA, title={When Is a Curve an Octahedron?}, author={Joel Langer and David A. Singer}, journal={The American Mathematical Monthly}, year={2010}, volume={117}, pages={889-902} }

- Published 2010 in The American Mathematical Monthly
DOI:10.4169/000298910X523371

We consider complex curves of genus zero and answer the above riddle. Namely, the lemniscate of Bernoulli, which has obvious four-fold symmetry, actually has the octahedral group as its symmetry group, and may in fact be characterized by this symmetry.