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Grünbaum 20_4 Configuration

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The Grünbaum 20_4 configuration is the term used in this work for the geometric 20_4 configuration constructed by Grünbaum (2008) and denoted G(20_4) by Berman et al. (2024). It consists of 20 points and 20 lines, with four points on each line and four lines through each point. Its construction disproved the conjecture of Grünbaum and Rigby (1990) that no geometric n_4 configuration exists for n<21.

The Grünbaum 204 graph, or Levi graph of the configuration, has 40 vertices and 80 edges and is a quartic graph and a bipartite graph.

See also

Berman-Gévay-Pisanski Configuration, Bokowski-Pilaud Configuration, Bokowski-Schewe Configuration, Configuration, Grünbaum 204 Graph, Grünbaum-Rigby Configuration, Levi Graph

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References

Berman, L. W.; Gévay, G.; and Pisanski, T. "On a New (21_4) Polycyclic Configuration." Electron. J. Combin. 31, #P4.54, 2024. https://doi.org/10.37236/12405.Grünbaum, B. "Musings on an Example of Danzer's." Europ. J. Combin. 29, 1910-1918, 2008. https://doi.org/10.1016/j.ejc.2008.01.004.Grünbaum, B. and Rigby, J. F. "The Real Configuration (21_4)." J. London Math. Soc. 41, 336-346, 1990. https://doi.org/10.1112/jlms/s2-41.2.336.

Cite this as:

Weisstein, Eric W. "Grünbaum 20_4 Configuration." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Gruenbaum20-4Configuration.html

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