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The six permutations of three elements #i, x 2 , x 3 considered as projective coordinates in a plane determine an involution of sextuples of points which may be mapped on a rational surface, f I shall show that in case of the involution thus defined the map is a quadric whose relation with the plane, established with sufficient details, will lead to some interesting geometric applications. The map of every configuration on the quadric will be a configuration in the plane, invariant under the G 6 , whose geometric properties have been investigated before.f

On the mapping of the sextuples of the symmetric substitution group 𝐺₆ in a plane upon a quadric