## Soap-Bubble Singularities and Deltahedra |

**John Sullivan**

University of Illinois

May 7, 2001

7:30 pm

Bailey Hall 201

Over 120 years ago, Plateau observed the geometric structure of soap froths: at any corner where bubbles meet, there are exactly four bubbles, in a tetrahedral pattern. Plateau's rule was not proved until the 1970s; the proof relies on ruling out seven other possibilities. For instance, when we dip a wire frame cube into soapy water, the resulting soap film has four Plateau corners instead of one of a new type. We will examine how these eight candidates arise from the eight polyhedra with equilateral-triangle faces (including Platonic solids as well as less familiar ones.) Similar ideas can also be extended to higher dimensions, where there would be more possibilities for singularities in soap films.

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