64 intersections.

There are 64 squares on the chess board. Each square is an intersection of invisible lines: the lines of the pieces' movements. Here you can see how many other squares each square on the board is connected to by the movement lines of the pieces (horizontal, vertical, diagonal, knight-move). The central squares are connected to the most other squares. I guess that is why the books recommend control and occupation of the center. This allows you something positionally/materially.

You can also show it like this. Horizontals and verticals are colored red here. Diagonals are blue, and squares involving knights moves are colored yellow. Hmmm...the board would seem to not just be made up of 64 squares, but 64 connected and overlapping sub-boards. Interesting.

This image shows all of the possible connections between squares (moves) all at once. These are the lines along which the pieces move. Different pieces use different lines. Anything that happens on the chessboard involves these lines. Interesting.