Torus
In geometry, a
torus 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
ring torus or simply
torus if the ring shape is implicit. When the axis is tangent to the circle, the resulting surface is called a
horn torus; when the axis is a chord of the circle, it is called a
spindle torus. A degenerate case is when the axis is a diameter of the circle, which simply generates a 2-sphere. The ring torus bounds a solid known as a
toroid. The adjective
toroidal can be applied to tori, toroids or, more generally, any ring shape as in toroidal inductors and transformers. Real-world examples of toroidal objects include doughnuts, vadais, inner tubes, bagels, many lifebuoys, O-rings and vortex 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.