On the geometry of the ricochet locus

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This paper is a study of the so-called `ricochet configuration' (or R-configuration) which arises in the context of Pascal's theorem. We give a geometric proof of the fact that a specific pair of Pascal lines is coincident for a sextuple in R-configuration. We calculate the symmetry group of a generic R-configuration, as well as the degree of the subvariety R P⁶ of all such configurations. We also determine the SL(2)-equivariant defining equations for R, and show that it is an ideal-theoretic complete intersection of two invariant hypersurfaces.