When Is a Curve an Octahedron?

When Is a Curve an Octahedron?

We consider complex curves of genus 0 and answer the above riddle. Namely, the lemniscate of Bernoulli, which has obvious fourfold symmetry, actually has the octahedral group as its symmetry group, and may in fact be characterized by this symmetry. [PUBLICATION ABSTRACT]

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Veröffentlicht in:The American mathematical monthly 2010-12, Vol.117 (10), p.1
Hauptverfasser: Langer, Joel C, Singer, David A
Format: Artikel
Sprache:eng
Schlagworte:
Geometry
Mathematical analysis
Mathematical problems
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Zusammenfassung:We consider complex curves of genus 0 and answer the above riddle. Namely, the lemniscate of Bernoulli, which has obvious fourfold symmetry, actually has the octahedral group as its symmetry group, and may in fact be characterized by this symmetry. [PUBLICATION ABSTRACT]
ISSN:0002-9890
1930-0972