AIME problem

A regular ${12}-gon$ is inscribed in a circle of radius ${12}$ . The sum of the lengths of all sides and diagonals of the ${12}-gon$ can be written in the form $a + b \sqrt{2} + c \sqrt{3} + d \sqrt{6},$ where $a^{}_{}$ , $b^{}_{}$ , $c^{}_{}$ , and $d^{}_{}$ are positive integers. Find $a + b + c + d^{}_{}$