A coordinate system similar to toroidal coordinates but with fourth-degree instead of second-degree surfaces for constant μ so that the toroids of circular cross section are replaced by flattened rings, and the spherical bowls are replaced by cyclides of rotation for constant ν. The transformation equations are x | = | a/Λ sn μ dn ν cos ψ y | = | a/Λ sn μ dn ν sin ψ z | = | a/Λ cn μ dn μ sn ν cn ν, where Λ congruent 1 - dn^2 μ sn^2 ν

cyclidic coordinates | toroidal coordinates