Ising model across planar lattices

The Ising model on a two dimensional lattice with pentagon tiling and greater number of next to neighbours interaction is equivalent to the Ising model on the centered square lattice with nearest and next to nearest neighbour non-crossing interactions. We obtain exact expressions on calculation of critical temperature with ferromagnetic and anti-ferromagnetic interactions. A direct anti-ferromagnetic bond of strength alpha L can give rise to the transition temperatures for appropriate alpha. We apply the star-triangle mapping transformation technique and decorating transform to Ising model.