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Bokowski-Pilaud Configuration

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The Bokowski-Pilaud configuration is the term used in this work for the second of the two geometric 18_4 configurations classified by Bokowski and Pilaud (2014). It first appeared in that paper and is not combinatorially isomorphic to the Bokowski-Schewe configuration. It is self-dual.

Here "geometric" means realizable by points and straight lines in the real projective plane, so a chosen affine drawing may contain points at infinity. In the stricter usage that requires points and lines in the Euclidean plane, a projective collineation can be used to choose an affine chart avoiding the finitely many configuration points.

The Bokowski-Pilaud graph, or Levi graph of the configuration, is a connected quartic graph and bipartite graph on 36 vertices and 72 edges. Its automorphism group has order 4 (Bokowski and Pilaud 2014).

No geometric n_4 configuration exists for n<=17, so it and the Bokowski-Schewe configuration have the smallest possible order among geometric 4-configurations (Bokowski and Schewe 2013, Bokowski and Pilaud 2014).

See also

Bokowski-Pilaud Graph, Bokowski-Schewe Configuration, Configuration, Geometric Realization, Grünbaum 204 Configuration, Levi Graph, Point at Infinity

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References

Bokowski, J. and Pilaud, V. "Enumerating Topological (n_k)-Configurations." Comput. Geom. 47, 175-186, 2014. https://doi.org/10.1016/j.comgeo.2012.10.002.Bokowski, J. and Schewe, L. "On the Finite Set of Missing Geometric Configurations (n_4)." Comput. Geom. 46, 532-540, 2013. https://doi.org/10.1016/j.comgeo.2011.11.001.

Cite this as:

Weisstein, Eric W. "Bokowski-Pilaud Configuration." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Bokowski-PilaudConfiguration.html

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