  Charging of a clean two-dimensional island is studied in the regime of small
concentration of electrons when they form the Wigner crystal. The number of
electrons in the island is assumed to be not too big (N < 100). It is shown
that the total energy of the island as a function of N has a quasi-periodic
component of a universal shape, that is independent of the form of
electron-electron interactions. These oscillations are caused by the
combination of the geometric effects associated with packing of the triangular
lattice into the circular island. These effects are: the shell effect,
associated with starting a new crystalline row, and the so-called confinement
polaronic effect. In the presence of close metallic gates, which eliminate the
long-range part of the electron-electron interactions, the oscillations of the
energy bring about simultaneous entering of the dot by a few electrons.
