Twelve resistances each of resistance R are connected in the circuit as shown in fig. Net resistance between points A and C would be

When a cell is connected across A and C, no current flows in the arms BG and ED due to symmetry in the arrangement. Then equivalent circuit will be as shown in Fig.(a) and (b). The effective resistance between A and C is
$\begin{array}{l}\frac{1}{{\mathrm{R}}_{\mathrm{eff} }}=\frac{1}{2\mathrm{R}}+\frac{1}{3\mathrm{R}}+\frac{1}{2\mathrm{R}}\\ =\frac{3+2+3}{6\mathrm{R}}=\frac{8}{6\mathrm{R}}=\frac{4}{3\mathrm{R}} \mathrm{or} {\mathrm{R}}_{\mathrm{eff} }=\frac{3\mathrm{R}}{4}\end{array}$