Multilaterals in configurations
We investigate the existence of g-laterals in geometric and combinatorial configurations. First we can show that within a special family of configurations any of the eight possible combinations of the existence or non-existence of g-laterals for 3 ≤ g ≤ 5 may arise. Moreover, this is true for arbitrarily large configurations belonging to this family. We also present geometric realizations of the two smallest trilateral-, quadrilateral- and pentalateral-free (v 3) configurations (generalized hexagons). Finally, we consider (v 4) configurations and present the smallest-known geometric trilateral-free (v 4) configuration.