On the Six Cross-Ratios of Four Points

If one of the cross-ratios of a range (ABCD) is λ, the others are 1/λ, 1-λ, 1/1-λ, λ-1/λ, λ/λ-1.

The homographic operations which derive the six cross-ratios from any one of them must clearly form a group of order six; since all these cross-ratios can be obtained as cross-ratios of the range AB'C'D', where B'C'D' is any permutation of BCD, this group is identical in structure with the permutation group of three symbols.