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At a time only two, but in general, infinitely many.

If, for example, you consider the earth as a sphere, there are the Northern and Southern hemispheres, as well as the Eastern and Western hemispheres. But you could also have the Northeastern and Southwestern hemispheres with the dividing line being the equator rotated through 45% in a plane perpendicular to the Greenwich meridian. Any other angle would also do. And the equator could be rotated through all angles in a plane perpendicular to any meridian.

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Q: How many hemispheres can a sphere have?
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