  A flat elastic sheet may contain pointlike conical singularities that carry a
metrical "charge" of Gaussian curvature. Adding such elementary defects to a
sheet allows one to make many shapes, in a manner broadly analogous to the
familiar multipole construction in electrostatics. However, here the underlying
field theory is non-linear, and superposition of intrinsic defects is
non-trivial as it must respect the immersion of the resulting surface in three
dimensions. We consider a "charge-neutral" dipole composed of two conical
singularities of opposite sign. Unlike the relatively simple electrostatic
case, here there are two distinct stable minima and an infinity of unstable
equilibria. We determine the shapes of the minima and evaluate their energies
in the thin-sheet regime where bending dominates over stretching. Our
predictions are in surprisingly good agreement with experiments on paper
sheets.
