This analysis reveals construction methods for astral (n4) configurations with dihedral symmetry and explores chiral symmetry implications.
An astral (n4) configuration of pseudolines is a collection in the Euclidean plane of n points and n pseudolines (that is, topological lines that have been modified in the Euclidean plane from straight lines only in a finite part, which cross each other only once, or have parallel infinite part and are disjoint), where each point lies on four pseudolines, each pseudoline contains four points, and the points and pseudolines form two symmetry (transitivity) classes each. We describe how to construct astral (n4) pseudoline configurations with dihedral symmetry, and we discuss the existence of astral (n4) configurations with only chiral symmetry.
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Leah Wrenn Berman (2008) studied this question.
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