  We have investigated, by the Monte Carlo simulation, spin systems which
represent moments of arrayed magnetic nanoparticles interacting with each other
only by the dipole-dipole interaction. In the present paper we aim the
understanding of finite size effects on the magnetic nanoparticles arrayed in
hexagonal columns cut out from the close-packing structures or from those with
uniaxial compression. In columns with the genuine close-packing structures, we
observe a single vortex state which is also observed previously in finite
2-dimensional systems. On the other hand in the system with the inter-layer
distance set $1/\sqrt{2}$ times of the close-packing one, we found ground
states which depend on the number of layers. The dependence is induced by a
finite size effect and is related to a orientation transition in the
corresponding bulk system.
