The Bipyramid

Consider $12$ resistors arranged symmetrically in a shape of bipyramid $ABCDEF$ . Here $ABCD$ is a square. Point $E$ , point $F$ and the center of the square are in the same straight line perpendicular to the plane of square. The resistance of each resistor is $R$ . The sum of effective resistance between $E-F$ , $A-C$ and $A-B$ is $\frac{x}{y}$ ( $R$ ) , where $x$ and $y$ are coprime integers, find $x+y$ .