  In (the surface of) a convex polytope P^3 in R^4, an area-minimizing surface
avoids the vertices of P and crosses the edges orthogonally.
  In a smooth Riemannian manifold M with a group of isometries G, an
area-minimizing G-invariant oriented hypersurface is smooth (except for a very
small singular set in high dimensions). Already in 3D, area-minimizing
G-invariant unoriented surfaces can have certain singularities, such as three
orthogonal sheets meeting at a point. We also treat other categories of
surfaces such as rectifiable currents modulo nu and soap films.
