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Geometric Constructions for Symmetric 6-Configurations

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Rigidity and Symmetry

Part of the book series: Fields Institute Communications ((FIC,volume 70))

Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. University of Alaska Fairbanks, Fairbanks, AK, USA

    Leah Wrenn Berman

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  1. Leah Wrenn Berman
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Correspondence to Leah Wrenn Berman .

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Editors and Affiliations

  1. Department of Mathematics, Cornell University, Ithaca, New York, USA

    Robert Connelly

  2. Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada

    Asia Ivić Weiss

  3. Department of Mathematics & Statistics, York University, Toronto, Ontario, Canada

    Walter Whiteley

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Berman, L.W. (2014). Geometric Constructions for Symmetric 6-Configurations. In: Connelly, R., Ivić Weiss, A., Whiteley, W. (eds) Rigidity and Symmetry. Fields Institute Communications, vol 70. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0781-6_4

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