An infinite class of movable 5-configurations - Berman, Leah (Ars mathematica contemporanea, 2016)
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 ?$(n_5)$? 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 ?$k > 2$?.
Keywords: configurations; incidence geometry; incidenčna geometrija; konfiguracije