  A growing or shrinking disc will adopt a conical shape, its intrinsic
geometry characterized by a surplus angle $se$ at the apex. If growth is slow,
the cone will find its equilibrium. Whereas this is trivial if $se <= 0$, the
disc can fold into one of a discrete infinite number of states if $se$ is
positive. We construct these states in the regime where bending dominates,
determine their energies and how stress is distributed in them. For each state
a critical value of $se$ is identified beyond which the cone touches itself.
Before this occurs, all states are stable; the ground state has two-fold
symmetry.
