  We study the competition between the Wigner crystal and the Laughlin liquid
states in an ultracold quasi two-dimensional rapidly rotating polarized
fermionic dipolar gas, and find that the Wigner crystal has a lower energy
below a critical filling factor. We examine the quantum crystal to liquid
transition for different confinements in the third direction. Our analysis of
the phonon spectra of the Wigner crystal with the account of phonon-phonon
interactions also shows the stability of the Wigner crystal for sufficiently
low filling factors (\nu <1/7).
