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.
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