  We show that minimizers of the Heitmann-Radin energy (R. C. Heitmann, C.
Radin, J. Stat. Phys. 22, 281-287, 1980) are unique if and only if the particle
number N belongs to an infinite sequence whose first thirty-five elements are
1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 19, 21, 24, 27, 30, 33, 37, 40, 44, 48,
52, 56, 61, 65, 70, 75, 80, 85, 91, 96, 102, 108, 114, 120 (see the paper for a
closed-form description of this sequence). The proof relies on the discrete
differential geometry techniques introduced in (L. De Luca, G. Friesecke,
preprint).
