  We show that a magnetic vortex is the ground state of an array of magnetic
particles shaped as a hexagonal fragment of a triangular lattice, even for an
small number of particles in the array $N \leq 100$. The vortex core appears
and the symmetry of the vortex state changes with the increase of the intrinsic
magnetic anisotropy of the particle $\beta$; the further increase of $\beta$
leads to the destruction of the vortex state. Such vortices can be present in
arrays as small in size as dozen of nanometers.
