Excerpt from John Horton Conway, The Symmetries of Things, pg. 12.
Basketballs have two planes of reflective symmetry, as do tennis balls.
I read this sentence and it immediately struck me as incorrect: from my understanding of the pattern of lines on a basketball, there are three planes of reflective symmetry. Two correspond to the two distinct great circles in the pattern, and the third corresponds to the plane mutually perpendicular to these. I agree with the statement regarding tennis balls.
But J.H. Conway is such a respected (and far more brilliant and knowledgeable) mathematician that I could ever even hope to be, so despite my certainty I have literally spent the past 15 minutes trying to think of how I might have overlooked some detail. (I think it is safe to say we can ignore the branding/logo on the ball, as well as the pump hole.) Who is correct? If I am, is this error acknowledged somewhere (the book was published in 2008)?
In the basketball I hold in my hands just now, there really are just two planes of symmetry. The plane perpendicular to the two great circles is not a symmetry. This is because the lines which are not great circles intersect one of the great circles near one of the poles, but the other great circle near the other pole. This is not visible in the picture you made, and will be hard to visualize in a non-distorted fashion in any static image.
The correct place to look for errata would likely be http://www.mit.edu/~hlb/Symmetries_of_Things/SoTerrors.html, but this issue isn't reported there. Probably because there are more basketballs marked in the way I just descibed.