A convex polyhedron $\mathcal{P}$ has 26 vertices, 60 edges, and 36 faces. 24 faces are triangular and 12 are quadrilaterals. A spatial diagonal is a line segment connecting two vertices not belonging to the same face. How many spatial diagonals does $\mathcal{P}$ have?
The 26 vertices determine exactly $\binom{26}{2}=26 \times 25 / 2=$ 325 segments. Of these segments, 60 are edges and since each quadrilateral has two diagonals, we have $12 \times 2=24$ diagonals that are not spatial.

Therefore, the number of spatial diagonals is $325-60-24=241$.