From Wikipedia, the free encyclopedia
Jump to: navigation, search
For other uses, see Toroid (disambiguation).
A toroid using a square.
A torus is a type of toroid.

In mathematics, a toroid is a doughnut-shaped object, such as an O-ring. It is a ring form of a solenoid. Its annular shape is generated by revolving a plane geometrical figure about an axis external to that figure which is parallel to the plane of the figure and does not intersect the figure.[1] When a rectangle is rotated around an axis parallel to one of its edges, then a hollow cylinder (resembling a piece of straight pipe) is produced.

If the revolved figure is a circle, then the surface of such an object is known as a torus.

More generally, a toroid may have any number of holes, may or may not be orientable, and its surface may be decomposed into polygonal faces.[2]

One of the best-known applications of the toroid shape is in a Tokamak device, which uses a magnetic field to confine a plasma in the shape of a torus.

See also[edit]


  1. ^
  2. ^ Stewart, B.; "Adventures Among the Toroids:A Study of Orientable Polyhedra with Regular Faces", 2nd Edition, Stewart (1964).

External links[edit]

  • The dictionary definition of toroid at Wiktionary