Multilaterals in configurations
Tomaž Pisanski, Marko Boben and Branko Grünbaum
Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry 2011. ISSN 0138-4821

Abstract

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.

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