A catalogue of simplicial arrangements in the real projective plane

Branko Grünbaum

Abstract


An arrangement is the complex generated in the real projective plane by a finite family of straight lines that do not form a pencil. The faces of an arrangement are the connected components of the complement of the union of lines. An arrangement is simplicial if all its faces are simplices (triangles). The present paper updates the only previous catalogue of simplicial arrangements, published almost 40 years ago, and presented in a very condensed form. The simplicial arrangements often provide optimal solutions for various problems. A problem that seems very hard is to decide whether the collection presented here is a complete listing of simplicial arrangements.

Keywords


arrangement, simplicial, sporadic

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DOI: https://doi.org/10.26493/1855-3974.88.e12

ISSN: 1855-3974

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