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Bokowski-Pilaud Configuration


The Bokowski-Pilaud configuration is the term used in this work for the second of the two geometric 184 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. An affine chart is obtained by choosing a line at infinity; its complement is a real affine plane. A chosen chart may therefore place some configuration points at infinity. In the stricter usage that requires points and lines in the Euclidean plane, a projective collineation can be used to choose a line at infinity 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 n4 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

184 Configuration, Bokowski-Pilaud Graph, Bokowski-Schewe Configuration, Configuration, Geometric Realization, Grünbaum 204 Configuration, Levi Graph, n4 Configuration, 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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