Three-spin correlations <S1S2S3> and <SiS1S2> are derived in terms of <Si> for the Ising model on lattices having coordination number q = 3, where S1, S2 and S3 are nearest-neighbor spins of Si. It is found that all homogeneous lattices have the same ratio <S1S2S3>/<Si>, and all regular lattices have the same ratio <SiS1S2>/<Si>.