would a basketball be considered having rotational symmetry?

Question

where would the axis be?

what kind of ball would have rotational symmetry?

Answer 1

yes, if the axis was the center of the ball.

Answer 2

No. The ball has a pinhole for inflation and markings that destroy rotational symmetry. If there was an axis of rotational symmetry, it would be the line passing through the center of the ball and the pinhole. Now consider rotating the ball about that axis and determine whether the ball looks exactly the same for all angles of rotation. You will find that the lines move, so there is no axis of rotational symmetry. The ball does have functional rotational symmetry if the rotation is fast. Suppose that you spin the ball on an arbitrary axis at 600 rpm and expose film for 1 second. The lines will be indistinguishable on the film. This situation occurs in molecular spectroscopy. A methyl group (CH3) has exact C3v symmetry, and follows C3v selection rules at low temperature, but may rotate fast enough to give effective rotational symmetry at higher temperature so that the selection rules are relaxed.