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For other uses, see Toroid (disambiguation).
A toroid using a square.
A torus is a type of toroid.

In mathematics, a toroid is a surface of revolution with a hole in the middle, like a doughnut. The axis of revolution passes through the hole and so does not intersect the surface.[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. If the revolved figure is a circle, then the object is called a torus.

The term "toroid" is also used to describe a toroidal polyhedron. In this context a toroid need not be circular and may have any number of holes. A g-holed toroid can be seen as approximating the surface of a torus having a topological genus, g, of 1 or greater. The Euler characteristic χ of a g holed toroid is 2(1-g).[2]

See also[edit]


  1. ^ Weisstein, Eric W. "Toroid". MathWorld. 
  2. ^ Stewart, B.; "Adventures Among the Toroids:A Study of Orientable Polyhedra with Regular Faces", 2nd Edition, Stewart (1980).

External links[edit]

  • The dictionary definition of toroid at Wiktionary