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 ${\displaystyle F_{1}}$ and ${\displaystyle F_{2}}$ in bipolar coordinates become a ring of radius ${\displaystyle a}$ in the ${\displaystyle xy}$ plane of the toroidal coordinate system; the ${\displaystyle z}$-axis is the axis of rotation. The focal ring is also known as the reference circle.