Soap Films on an Octahedral Frame

A simple octahedral wire frame bounds five stable soap films. These are pictured below, along with a couple of unstable films. The images were made with the Surface Evolver program. The Surface Evolver datafiles for each can be downloaded by clicking on the filenames (ending in .fe) under each image.
The conical film on an octahedral frame is unstable because it has four films meeting along the lines from the corners to the center. There are six non-equivalent ways to resolve the six quadruple lines into pairs of triple lines, giving the six other films on this page.

This film is at equilibrium and satisfies all the criteria for soap film singularities (three films meeting along a line, four triple lines meeting at a point), yet it is unstable. Two "diamonds" or "kites" meet at the center, and if the film is perturbed and allowed to evolve, one kite will grow at the expense of the other, winding up with the pentagonal center film.
Stable film with a central hexagon.
Stable film with a central pentagon.
Stable film with a central quadrilateral.
Stable film with a central square.
Stable film with a central tetrahedral film. All surfaces are flat. This film has the least area of all those on this page.

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