  Electrons on liquid helium can form different phases depending on density,
and temperature. Also the electron-ripplon coupling strength influences the
phase diagram, through the formation of so-called "ripplonic polarons", that
change how electrons are localized, and that shifts the transition between the
Wigner solid and the liquid phase. We use an all-coupling, finite-temperature
variational method to study the formation of a ripplopolaron Wigner solid on a
liquid helium film for different regimes of the electron-ripplon coupling
strength. In addition to the three known phases of the ripplopolaron system
(electron Wigner solid, polaron Wigner solid, and electron fluid), we define
and identify a fourth distinct phase, the ripplopolaron liquid. We analyse the
transitions between these four phases and calculate the corresponding phase
diagrams. This reveals a reentrant melting of the electron solid as a function
of temperature. The calculated regions of existence of the Wigner solid are in
agreement with recent experimental data.
