Minimum degree of 4-connected toroidal graph

Question

Let $G$ be a 4-connected toroidal graph. Find the minimum degree $\delta(G)$ of $G$. It is known that cross product of two cycle of even length is toroidal graph and also 4-connected. Hence minimum degree of this graph is 4. If we can prove that $\delta(G) = 4$ explicitly without taking an example. Any hint or direction how to prove is appreciable. Thanks in advance.