  It is known that a two dimensional dimerized Su-Schrieffer-Heeger model can
produce a nontrivial topological phase. It is a simple nearest-neighbor model
with either two or four lattice sites in in two dimensions.
Su-Schrieffer-Heeger model is easy to analyse but neglects important
interaction in physical systems. In this work, an extended version of this
model is proposed which includes all possible second nearest neighbor
interactions in order to make it more feasible to describe realistic systems.
The topological phases and properties of the model are characterized using a
polarization invariant. It is further shown that second nearest neighbor
interactions can be used to evoke a topological phase transition as well.
