Abstract
Plane curves with non-trivial collineation groups are rare: those of low order are thus interesting, and often exhibit special geometric features. The largest primitive plane group is A6. It is known by standard algebraic means that this fixes a sextic curve Ω. The present paper constructs Ω geometrically, and speedily obtains its most significant geometric property: its 72 inflexions lie by pairs on 36 biflexional tangents. There is no standard technique for determining the multiplicities of bitangents of plane curves. For Ω we show that each biflexional tangent counts 4-fold as a bitangent, and identify the other 180 ordinary bitangents. A brief comparison of the geometric properties of Ω with those of Klein’s quartic curve is given.
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Dye, R.H. The Plane Sextic Curve Fixed by A6 . Abh.Math.Semin.Univ.Hambg. 68, 17–24 (1998). https://doi.org/10.1007/BF02942548
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DOI: https://doi.org/10.1007/BF02942548