  We present results for the solution of the large polaron Fr\"ohlich
Hamiltonian in 3-dimensions (3D) and 2-dimensions (2D) obtained via the
Diagrammatic Monte Carlo (DMC) method. Our implementation is based on the
approach by Mishchenko [A.S. Mishchenko et al., Phys. Rev. B 62, 6317 (2000)].
Polaron ground state energies and effective polaron masses are successfully
benchmarked with data obtained using Feynman's path integral formalism. By
comparing 3D and 2D data, we verify the analytically exact scaling relations
for energies and effective masses from 3D$\to$2D, which provides a stringent
test for the quality of DMC predictions. The accuracy of our results is further
proven by providing values for the exactly known coefficients in weak- and
strong coupling expansions. Moreover, we compute polaron dispersion curves
which are validated with analytically known lower and upper limits in the small
coupling regime and verify the first order expansion results for larger
couplings, thus disproving previous critiques on the apparent incompatibility
of DMC with analytical results and furnishing useful reference for a wide range
of coupling strengths.
