[3] A concrete model consists of two unit circles in perpendicular planes, each passing through the center of the other.

The Hopf fibration is a continuous function from the 3-sphere (a three-dimensional surface in four-dimensional Euclidean space) into the more familiar 2-sphere, with the property that the inverse image of each point on the 2-sphere is a circle.

[12][13] It consists of two covalent loops, formed by pieces of protein backbone, closed with disulfide bonds.

The Hopf link topology is highly conserved in proteins and adds to their stability.

[3] It has also long been used outside mathematics, for instance as the crest of Buzan-ha, a Japanese Buddhist sect founded in the 16th century.