  The influence of the geometry of a thin superconducting sample on the
penetration of the magnetic field lines and the arrangement of vortices are
investigated theoretically. We compare superconducting disks, squares and
triangles with the same surface area having nonzero thickness. The coupled
nonlinear Ginzburg-Landau equations are solved self-consistently and the
important demagnetization effects are taken into account. We calculate and
compare quantities like the free energy, the magnetization, the Cooper-pair
density, the magnetic field distribution and the superconducting current
density for the three geometries. For given vorticity the vortex lattice is
different for the three geometries, i.e. it tries to adapt to the geometry of
the sample. This also influences the stability range of the different vortex
states. For certain magnetic field ranges we found a coexistence of a giant
vortex placed in the center and single vortices toward the corners of the
sample. Also the H-T phase diagram is obtained.
