Can't resist this

We note that the circuit can be simplified as the left circuit in the figure below.

Due to symmetry, we note that the potentials of $C$ , $D$ , $E$ and $F$ with respect to $A$ and $B$ are the same. Therefore, there is no current flowing through the eight resistors between the four points. The eight resistors are equivalent to open circuits, therefore the right circuit in the figure is the final equivalent circuit. Then the equivalent resistance is:

$\begin{aligned} R_{AB} & = (4+4)||(4+4)||(4+4)||(4+4) = 8||8||8||8 \\ & = \frac{1} {\frac{1}{8} + \frac{1}{8} + \frac{1}{8} + \frac{1}{8}} = \frac{1}{\frac{1}{2}} = \boxed{2} \end{aligned}$

Diagram is really nice!