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Swallowtail on the shore

Snapshots of modern mathematics from Oberwolfach

Swallowtail on the shore

Platonic solids, Felix Klein, H. S. M. Coxeter and a flap of a swallowtail: The five Platonic solids tetrahedron, cube, octahedron, icosahedron and dodecahedron have always attracted much curiosity from mathematicians, not only for their sheer beauty but also because of their many symmetry properties. In this snapshot we will start from these symmetries, move on to groups, singularities, and finally find the connection between a tetrahedron and a “swallowtail”. Our running example is the tetrahedron, but every construction can be carried out with any other of the Platonic solids.

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Mathematical subjects

Algebra and Number Theory
Geometry and Topology

Author(s)

Ragnar-Olaf Buchweitz, Eleonore Faber

License

DOI (Digital Object Identifier)

10.14760/SNAP-2014-007-EN

Download PDF

snapshot-2014-007.pdf

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