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Szöllősi–Östergård: Constructions of maximum few-distance sets
Ferenc Szöllősi and Patric R. J. Östergård, Constructions of maximum few-distance sets in Euclidean spaces, Electronic Journal of Combinatorics 27(1) (2020), P1.23. DOI: 10.37236/8565.
Primary full paper. Checked passage and scope.
Theorem 16 classifies maximum planar six-distance sets: their size is 13, and the three types, up to similarity, are a regular 13-gon, a regular 12-gon with its center, and a regular hexagram with its center. The theorem and its following discussion were checked in the full paper, pp. 15–16. It is a computer-assisted classification using graph generation and Gröbner bases; its exhaustive computation was not rerun here.