We address a particular set of extended Su-Schrieffer-Heeger models with $2n$ sites in the unit cell [SSH($2n$)], that we designate by Sine-Cosine [SC$(n)$], hopping terms defined as sequence $n$ sine-cosine pairs form $\{\sin(\theta_j),\cos(\theta_j)\}$, $j=1, \cdots,n$. These models, when squared, generate block-diagonal matrix representation one blocks corresponding to chain uniform local po...