Minimal surfaces, crystals, shortest networks, and undergraduate research (Q1200117)

The minimal surface on a tetrahedral frame consists of 6 triangular pieces which stretch from the 6 edges of the tetrahedron to its centre. The author gives a simple direct proof, which can be generalized to the \(n\)-simplex. Realizations by soap films, energy problems, relations to the shape of crystals and in particular applications to length-minimizing networks are discussed. Finally the author describes his stimulating and active undergraduate research project.