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We compute the finite-size corrections to the free energy, internal energyand specific heat of the critical two-dimensional spin-1/2 Ising model on atriangular and hexagonal lattices wrapped on a torus. We find the general formof the finite-size corrections to these quantities, as well as explicitformulas for the first coefficients of each expansion. We analyze theimplications of these findings on the renormalization-group description of themodel.Comment: 45 pages (LaTeX2e). Self-unpacking file containing the tex file and  three macros (indent.sty, eqsection.sty, subeqnarray.sty). Paper I  corresponds to cond-mat/0009054. Final versio

Exact finite-size-scaling corrections to the critical two-dimensional Ising model on a torus: II. Triangular and hexagonal lattices