In analogy to omittable lines in the plane, we study omittable planes in 3-space. Given a collection of n planes in real projective 3-space, a plane P is said to be omittable if P is free of ordinary lines of intersection – in other words, if all the lines of intersection of P with other planes from the collection come at the intersection of three or more planes. Several different general constructions yielding omittable planes are described, together with a few sporadic examples.

By: Branko Grünbaum, Jonathan Lenchner

Published in: RC25041 in 2010


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