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. For example when a rectangle is rotated around an axis parallel to one of its edges, then a hollow square-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.

See also

Notes

External links

The dictionary definition of toroid at Wiktionary

Toroidal

Toroidal describes something which resembles or relates to a torus or toroid:

See also

Torus

In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle. If the axis of revolution does not touch the circle, the surface has a ring shape and is called a torus of revolution.

Real-world examples of (approximately) toroidal objects include inner tubes, swim rings, and the surface of a doughnut or bagel.

A torus should not be confused with a solid torus, which is formed by rotating a disk, rather than a circle, around an axis. A solid torus is a torus plus the volume inside the torus. Real-world approximations include doughnuts, vadai or vada, many lifebuoys, and O-rings.

In topology, a ring torus is homeomorphic to the Cartesian product of two circles: S¹ × S¹, and the latter is taken to be the definition in that context. It is a compact 2-manifold of genus 1. The ring torus is one way to embed this space into three-dimensional Euclidean space, but another way to do this is the Cartesian product of the embedding of S¹ in the plane. This produces a geometric object called the Clifford torus, a surface in 4-space.