X-Nico

6 unusual facts about Hopf link

Brunnian link

In other words, cutting any loop frees all the other loops (so that no two loops can be directly linked).

History of knot theory

For example, Thomson thought that sodium could be the Hopf link due to its two lines of spectra.

L10a140 link

In other words, no two loops are directly linked with each other, but all three are collectively interlinked, so removing any loop frees the other two.

The link group of the Hopf link, the simplest non-trivial link – two circles, linked once – is the free abelian group on two generators, $\mathbf{Z}^2.$ Note that the link group of two unlinked circles is the free nonabelian group on two generators, of which the free abelian group on two generators is a quotient.

Oloid

It is the convex hull of a skeletal frame made by placing two linked congruent circles in perpendicular planes, so that the center of each circle lies on the other circle.

Solomon's knot

In other words, if laid flat, the Solomon's knot is seen to have four crossings where the two loops interweave under and over each other (as opposed to only two crossings in the simpler Hopf link).