how how will the minimal triangulation of a torus look like?
Let $\omega = e^{2 \pi i/3}$. Let $L$ be the planar lattice generated by $1$ and $\omega$. Let $M$ be the sublattice generated by $2\omega$ and $\omega (2  \omega)$. Tile $\mathbb{R}^2$ by equilateral triangles with vertices at $L$, and quotient by $M$. This is a triangulation of the torus with $7$ vertices (exercise!). It is minimal because any triangulation of the torus must have a vertex of degree $6$, so you can't get use fewer vertices. 

