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 \(a + b + c + d^{}_{}\).

(第八届AIME1990 第12题)