We numerically construct asymptotically AdS black brane solutions of $D=4$
Einstein-Maxwell theory coupled to a pseudoscalar. The solutions are
holographically dual to $d=3$ CFTs at finite chemical potential and in a
constant magnetic field, which spontaneously break translation invariance
leading to the spontaneous formation of abelian and momentum magnetisation
currents flowing around the plaquettes of a periodic Bravais lattice. We
analyse the three-dimensional moduli space of lattice solutions, which are
generically oblique, and show, for a specific value of the magnetic field, that
the free energy is minimised by the triangular lattice, associated with minimal
packing of circles in the plane. We show that the average stress tensor for the
thermodynamically preferred phase is that of a perfect fluid and that this
result applies more generally to spontaneously generated periodic phases. The
triangular structure persists at low temperatures indicating the existence of
novel crystalline ground states.