Constructing $5$-Configurations with Chiral Symmetry

Abstract

A $5$-configuration is a collection of points and straight lines in the Euclidean plane so that each point lies on five lines and each line passes through five points. We describe how to construct the first known family of $5$-configurations with chiral (that is, only rotational) symmetry, and prove that the construction works; in addition, the construction technique produces the smallest known geometric 5-configuration.