Don't resist it!

• Use the symmetry of the system to find the relationship between the different intensities.

• Calculate the voltage drop between $A$ and $B$ choosing any of the possible paths: $V=1\cdot I+1\cdot \frac{1}{2}I+1\cdot I=\frac{5}{2}I$

• The overall resistance is the quotient between this voltage and the total intensity, which is $3I$ :

$R=\dfrac{\frac{5}{2}I}{3I}=\boxed{\dfrac{5}{6}\,\Omega}$

Label the cube circuit as shown in the left figure. By symmetry, the three vertices adjacent to $A$ , $C'$ , $C''$ , and $C'''$ have the same voltage with respect to $A$ and $B$ . Therefore, $C'$ , $C''$ , and $C'''$ can be considered as a point $C$ . Similarly, the three vertices adjacent to $B$ , $D'$ , $D''$ , and $D'''$ can be considered as a point $D$ . Then the equivalent circuit of the cube circuit is as the right figure. And the resultant resistance between $A$ and $B$ is given by:

$\begin{aligned} R_{AB} & = 1||1||1+1||1||1||1||1||1 + 1||1||1 = \frac 13 + \frac 16 + \frac 13 = \frac 56 \approx \boxed{0.833}\ \Omega \end{aligned}$