Some Results on Odd Astral Configurations

An astral configuration (pq, nk) is a collection of p points and n straight lines in the Euclidean plane where every point has q straight lines passing through it and every line has k points lying on it, with precisely b q+1 2 c symmetry classes (transitivity classes) of lines and bk+1 2 c symmetry classes of points. An odd astral configuration is an astral configuration where at least one of q and k is odd. This paper presents all known results in the classification of odd astral configurations where q and k are both at least 4.