Polycyclic Movable 4-Configurations are Plentiful.

A geometric 4 -configuration is a collection of points and straight lines with the property that every point lies on exactly four lines in the collection and every line passes through exactly four points in the collection. This paper describes a method for constructing a large number of new infinite families of rotationally symmetric geometric 4-configurations which are movable; that is, there is at least one continuous parameter which preserves the symmetry of the configuration. In fact, the configurations in this paper have 2 q continuous parameters for any integer $$q \ge 2$$ ; previously the known classes of movable 4-configurations had only one or two degrees of freedom. The construction is extended to produce movable 4-configurations with dihedral symmetry. The paper ends with a number of open questions. [ABSTRACT FROM AUTHOR]