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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

Senior Editor:

Carla Cederbaum

Junior Editor:

Lea Renner

## License

## DOI (Digital Object Identifier)

10.14760/SNAP-2014-007-EN

## Download PDF

## snapshots: overview

## Mathematical subjects

Algebra and Number Theory

Analysis

Didactics and Education

Discrete Mathematics and Foundations

Geometry and Topology

Numerics and Scientific Computing

Probability Theory and Statistics

## Connections to other fields

Chemistry and Earth Science

Computer Science

Engineering and Technology

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Reflections on Mathematics