A solid S has square base ABCD ,two trapezoid faces ABFE and DCFE (with EF//AB//CD) ,and two triangular races AED and BFC. If AB=AE=ED=BF=FC=\(6\sqrt{2}\) and EF=\(12\sqrt{2}\), what is the volume of S?

(第一届AIME1983 第十一题)