From the BAMA website:
"In the 1870s, 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 rules are key for understanding the physic of foams, but were not given a mathematical proof until the 1970s. This 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 show how these eight candidates arise from the eight possible polyhedra whose faces are equilateral triangles (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."
For more information, see the BAMA website.