  We study the effects of lattice type on polaron dynamics using a
continuous-time quantum Monte-Carlo approach. Holstein and screened Froehlich
polarons are simulated on a number of different Bravais lattices. The effective
mass, isotope coefficients, ground state energy and energy spectra, phonon
numbers, and density of states are calculated. In addition, the results are
compared with weak and strong coupling perturbation theory. For the Holstein
polaron, it is found that the crossover between weak and strong coupling
results becomes sharper as the coordination number is increased. In higher
dimensions, polarons are much less mobile at strong coupling, with more phonons
contributing to the polaron. The total energy decreases monotonically with
coupling. Spectral properties of the polaron depend on the lattice type
considered, with the dimensionality contributing to the shape and the
coordination number to the bandwidth. As the range of the electron-phonon
interaction is increased, the coordination number becomes less important, with
the dimensionality taking the leading role.
