2000006510

The bases of the prism shown in the figure are regular hexagons $ABCDEF$ and $A^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }{E}^{\prime }{F}^{\prime }$. The side edges are perpendicular to the bases. Let $k$ be a line through the points $A$ and $C$ (see the picture). How many diagonals of the prism are parallel to the line $k$?