Geometric Constructions for Symmetric 6-Configurations
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A geometric k-configuration is a collection of points and lines, typically in the Euclidean plane, with k points on each line, k lines passing through each point, and non-trivial geometric symmetry; that is, it is a (n k ). configuration for some number n of points and lines. We say a k-configuration is symmetric if it has non-trivial geometric symmetry. While 3-configurations have been studied since the mid-1800s, and 4-configurations have been studied since 1990, little is known about more highly incident configurations, such as 5- or 6-configurations. This article surveys several known geometric construction techniques that produce highly symmetric 6-configurations.
KeywordsConfigurations Incidence geometry
Subject Classifications51E30 05E30
The author thanks Jill Faudree, University of Alaska Fairbanks, for many helpful discussions, and the anonymous referee for useful comments. As always, the author thanks Branko Grünbaum for inspiration.
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