Toroid

[1] For example, when a rectangle is rotated around an axis parallel to one of its edges, then a hollow rectangle-section ring is produced.

A g-holed toroid can be seen as approximating the surface of a torus having a topological genus, g, of 1 or greater.

Doughnuts are an example of a solid torus created by rotating a disk, and are not toroids.

[3] A toroid is specified by the radius of revolution R measured from the center of the section rotated.

Pappus's centroid theorem generalizes the formulas here to arbitrary surfaces of revolution.