Highly Incident Configurations with Chiral Symmetry
A geometric -configuration is a collection of points and straight lines in the plane so that points lie on each line and lines pass through this point. We introduce a new construction method for constructing -configurations with non-trivial dihedral or chiral (i.e., purely rotational) symmetry, for any ; the configurations produced have symmetry classes of points and lines. The construction method produces the only known infinite class of symmetric geometric 7-configurations, the second known infinite class of symmetric geometric 6-configurations, and the only known 6-configurations with chiral symmetry.
configurations symmetry incidence geometry