# Soap Film Cones

If one magnifies a point of a soap film, one gets
a *tangent cone*. Recall that a *cone*
is composed of rays emanating from a point. At
*regular points* the tangent cone is just a plane.
At a *singular point* (a non-regular point), the
tangent cone must be three half-planes meeting at
120 degrees, or a cone over the edges of a polyhedron.
For such a polyhedral cone, the cone is made of flat
sheets meeting along triple lines. There are only eight
polyhedra that satisfy this condition. But only one gives
a true minimal cone, since the other seven cones can
be deformed to soap films of less area.
In the examples below, clicking on the small image will get
a full-screen version the image. You can get a 3D version
by clicking on the VRML tag below a picture, if you have
a VRML2 viewer.

These images were generated with my
Surface Evolver program. The Evolver datafile names are in
parentheses. The datafiles contain commands to evolve the surfaces
shown here. The VRML files were generated by the Evolver using
my vrml2.cmd script.

## Candidate cones:

## Triple junction
(ycone.fe)

### Reference:

Jean E. Taylor, "The structure of singularities in soap-bubble-like and
soap-film-like minimal surfaces," *Annals of Mathematics*** 103**
(1976), 489-539.

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