An infinite class of movable 5-configurations

Abstract

A geometric 5-configuration is a collection of points and straight lines, typically in the Euclidean plane, in which every point has 5 lines passing through it and every line has 5 points lying on it; that is, it is an (n₅) configuration for some number n of points and lines. Using reduced Levi graphs and two elementary geometric lemmas, we develop a construction that produces infinitely many new 5-configurations which are movable; in particular, we produce infinitely many 5-configurations with one continuous degree of freedom, and we produce 5-configurations with k − 2 continuous degrees of freedom for all odd k > 2.