Three planes through the center of a sphere. - By projection onto the enclosing sphere, the three planes produce each a complete great circle.
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One plane through the center of the sphere (PlaneA) and two planes parallel to this PlaneA. - By projection onto the enclosing sphere, only PlaneA produces a complete great circle - the other two planes produce just segments of piecewise different great circles.

Karl-Dietrich Neubert, July 2001
www.neubert.net