Hi,
As a rule, this kind of circuits can be methodically solved with the bisection theorem.
In this case it is like this:
Imagine a voltage V symmetrically applied between the terminals A and B, i.e. V/2 at A and -V/2 at B, and split the two vertical resistors as the series of two R/2.
Take the central horizontal line that is the symmetry axis of the circuit.
By symmetry, all the points cut by this line are at the same voltage (0) and they can be virtually short-circuited to ground. So, calling Req the total equivalent resistance, we have
Req/2 = (1 || 1/2) || (1 + (1 || 1/2)) * R
Of course, the result is the same as obtained with Eduardo's method.
Regards
Z