Linear astral configurations with dihedral symmetry

A linear astral ( n k ) configuration is a collection of points and straight lines, so that each point lies on k lines and each line passes through k points, with ⌊ k + 1 2 ⌋ symmetry (transitivity) classes of points and lines under rotations and reflections mapping the configuration to itself. We discuss the possible structures of astral ( n 5 ) configurations with dihedral symmetry group D m in the Euclidean plane, and we provide methods to investigate the existence of such configurations. In doing so, we introduce a new class of astral ( n 3 ) configurations.