  We study geometrical confinement effects in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8
+\delta}$ mesoscopic vortex-matter with edge-to-surface ratio of $7-12$%.
Samples have in-plane square and circular edges, 30\,$\mu$m widths, and $\sim
2\,\mu$m thickness. Direct vortex imaging reveals the compact planes of the
structure align with the sample edge by introducing topological defects. The
defects density is larger for circular than for square edges. Molecular
dynamics simulations suggest this density is not an out-of-equilibrium property
but rather determined by the geometrical confinement.

Superconductivity