Generalized pentagonal geometries.

A pentagonal geometry PENT(k,r) is a partial linear space, where every line is incident with k points, every point is incident with r lines, and for each point x, there is a line incident with precisely those points that are not collinear with x. Here we generalize the concept by allowing the points not collinear with x to form the point set of a Steiner system S(2,k,w) whose blocks are lines of the geometry. [ABSTRACT FROM AUTHOR]