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. The mapping of the sextuples of the symmetric substitution group GQ in a plane upon a quadric has been done by Emch. The 24 permutations of 4 elements X±j X2} X$, X4 considered as projective coordinates in ordinary space determine a configuration which may be mapped on a hypersurface in 54. I shall show that the hypersurface on which we will map is a hyperquadric cone. The map of every configuration on the hyperquadric will be a configuration in ordinary space, invariant under the G24. The mapping of the G24. We shall represent the elementary symmetric functions as follows:

On the mapping of the sets of 24 points of the symmetric substitution group 𝐺₂₄ in ordinary space upon a hyperquadric cone