Omittable planes (Q640430)

An aggregate of planes is a family of planes in 3-dimensional real projective space, not all of which have a point in common, together with all the lines and points that are determined by their intersections. An ordinary line of an aggregate is a line that is contained in precisely two of the planes. A plane of an aggregate is omittable if it contains no ordinary line. This paper discusses omittable planes in the aggregates of planes in 3-dimensional space. Two infinite families of planes yielding omittable planes in either a pencil or near-pencil are given. Examples, called sporadic, which do not fit into either of the two infinite families, having between three and seven omittable planes are also explored.