Abstract
The configuration of bitangents of a smooth quartic curve in P 2 ( C ) has been a classical object of study. In particular for the Klein curve xy 3 + yz 3 + zx 3 = 0 it is highly symmetric (Baker 1935; Klein 1879). Key concepts are Steiner sets and Aronhold sets (Dickson, 1961). We give a complete description of these sets for the Klein curve and of their orbits under the group of the curve, using the relation between the geometric configuration, the Coxeter graph (Coxeter, 1983) in various appearances and the regular 2-graph on 28 points (Taylor, 1977). Also a model is provided for the self-dual configuration of 21 + 28 points and 21 + 28 lines associated with the Klein curve.
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