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High Quality Content by WIKIPEDIA articles! Toroidal coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional bipolar coordinate system about the axis that separates its two foci. Thus, the two foci F1 and F2 in bipolar coordinates become a ring of radius a in the xy plane of the toroidal coordinate system; the z-axis is the axis of rotation. The focal ring is also known as the reference circle.