A catalogue of simplicial arrangements in the real projective plane

Abstract

An arrangement is the complex generated in the real projective plane by a family of straight lines that do not form a pencil. The faces of an arrangement are the connected components of the complement of the set of lines generating the arrangement. An arrangement is simplicial if all faces are triangles. Simplicial arrangements were first introduced by E. Melchior in 1941; the only existing extensive account appeared in a paper published by Grunbaum in 1971. The interest in these arrangements is due to their relevance to many extremal problems. The present paper is a complete and illustrated survey of the three known infinite families of simplicial arrangements, and the 90 known sporadic ones.