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Berman Configurations


BermanConfigurations

The Berman configurations are the terms used in this work for two geometric configurations due to Leah W. Berman. They are the Berman 48_5 configuration and Berman 96_6 configuration. Grünbaum (2009, p. 238) described the 48_5 configuration as the smallest known 5-configuration and credited it to Berman by private communication. Berman (2014) published the 96_6 construction, and Pegg (2023) described the 48_5 and 96_6 configurations as the first known geometric 5- and 6-configurations, respectively.

Both configurations have 12-fold rotational symmetry, making them 12-cyclic polycyclic configurations. The 48_5 configuration therefore has four point orbits and four line orbits, while the 96_6 configuration has eight of each. Both configurations are self-dual.

Their Levi graphs are the Berman graphs.


See also

Berman Graphs, Configuration, Polycyclic Configuration, Self-Dual

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References

Berman, L. W. "Geometric Constructions for Symmetric 6-Configurations." In Rigidity and Symmetry (Eds. R. Connelly, A. Ivić Weiss, and W. Whiteley). New York: Springer, pp. 61-85, 2014. https://doi.org/10.1007/978-1-4939-0781-6_4.Grünbaum, B. Configurations of Points and Lines. Providence, RI: Amer. Math. Soc., p. 238, 2009.Pegg, E., Jr. "Mathematical Games: Configurations." Dec. 2023. https://community.wolfram.com/groups/-/m/t/3089201.

Cite this as:

Weisstein, Eric W. "Berman Configurations." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BermanConfigurations.html

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