Number of reflection symmetries of a basketball 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)?


Maybe there are different versions, but from this "basketball sewing pattern"  it looks as if the noncircular line is not two dijoint "ellipses" but rather a singl ezig-zag line - as on the tennis ball.
