Exercise 345
Solution
- A plane of symmetry of a cube must pass through its center.
- There are $3$ planes parallel to a pair of opposite faces (each through the midpoints of $4$ parallel edges).
- There are $6$ planes through a pair of opposite edges (each also containing two face diagonals); one for each of the $6$ pairs of opposite edges.
- The total is $3+6=\boxed{9}$.
