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Bokowski-Schewe Configuration


The Bokowski-Schewe configuration is the term used in this work for the geometric 184 configuration constructed by Bokowski and Schewe (2005). It is the first of the two geometric 184 configurations classified by Bokowski and Pilaud (2014), is not combinatorially isomorphic to the Bokowski-Pilaud configuration, and 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-Schewe 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 48 (Bokowski and Pilaud 2014).

No geometric n4 configuration exists for n<=17, so it and the Bokowski-Pilaud configuration have the smallest possible order among geometric 4-configurations (Bokowski and Schewe 2005, Bokowski and Schewe 2013, Bokowski and Pilaud 2014).


See also

184 Configuration, Bokowski-Pilaud Configuration, Bokowski-Schewe Graph, 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. "There Are No Realizable 15_4- and 16_4-Configurations." Rev. Roumaine Math. Pures Appl. 50, 483-493, 2005.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-Schewe Configuration." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Bokowski-ScheweConfiguration.html

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