$\begin{array}{l}
ab + ac + bc = 1\\
G = \dfrac{{({a^2} + 2bc - 1)({b^2} + 2ac - 1)({c^2} + 2ab - 1)}}{{{{(a - b)}^2}{{(b - c)}^2}{{(c - a)}^2}}}\\
G = \dfrac{{({a^2} + 2bc - ab - ac - bc)({b^2} + 2ac - ab - ac - bc)({c^2} + 2ab - ab - ac - bc)}}{{{{(a - b)}^2}{{(b - c)}^2}{{(c - a)}^2}}}\\
G = \dfrac{{({a^2} + bc - ab - ac)({b^2} + ac - ab - bc)({c^2} + ab - ac - bc)}}{{{{(a - b)}^2}{{(b - c)}^2}{{(c - a)}^2}}}\\
G = \dfrac{{{{(a - b)}^2}{{(b - c)}^2}{{(c - a)}^2}}}{{{{(a - b)}^2}{{(b - c)}^2}{{(c - a)}^2}}}\\
G = 1\\
\sqrt[3]{{3G}} = 1.4422496
\end{array}$