  Recently it was shown that vacuum in a background of strong enough magnetic
field becomes an electromagnetic superconductor due to interplay between strong
and electromagnetic forces. The superconducting ground state of the vacuum is
associated with a spontaneous emergence of quark-antiquark condensates which
carry quantum numbers of charged rho mesons. The rho-meson condensate is an
inhomogeneous structure made of the so-called rho vortices, which are parallel
to the magnetic field axis. The condensation of the charged rho mesons induces
a (much weaker) superfluid-like condensate with quantum numbers of the neutral
rho mesons. In this paper we show that the vortices in the superconducting
condensate organize themselves in an equilateral triangular lattice similarly
to an ordinary type-II superconductor. We show that each of these
superconductor vortices is accompanied by three superfluid vortices and three
superfluid antivortices made of the neutral rho meson condensate. The
superconductor vortex overlaps with one of the superfluid vortices. The
superposition of the superconducting and superfluid vortex lattices has a
honeycomb pattern.
