A convex polyhedron \(P\) has 26 vertices, 60 edges, and 36 faces, 24 of which are triangular, and 12 of which are quadrilaterals. A space diagonal is a line segment connecting two non-adjacent vertices that do not belong to the same face. How many space diagonals does \(P\) have?

(第二十二届AIME1 2004 第3题)