Topological supermatter is given by ordinary topological matter constrained supersymmetry or graded supergroups such as OSP(2N|2N). Using results on super oscillators and lattice QFT$_{d}$, we construct a tight binding model hypercubic with supercharge $ \boldsymbol{Q}=\sum_{\mathbf{k}}\hat{F}_{\mathbf{k}}.\boldsymbol{q}_{\mathbf{k}}.\hat{B}_{\mathbf{k}}$. We first show that the algebraic tripl...