Even Astral Configurations

Abstract

A configuration $(p_q, n_k)$ is a collection of $p$ points and $n$ straight lines in the Euclidean plane so that every point has $q$ straight lines passing through it and every line has $k$ points lying on it. A configuration is astral if it has precisely $\lfloor {q+1\over2} \rfloor$ symmetry classes (transitivity classes) of lines and $\lfloor{k+1\over2} \rfloor$ symmetry classes of points. An even astral configuration is an astral configuration configuration where $q$ and $k$ are both even. This paper completes the classification of all even astral configurations.