Brunnian Braid
In knot theory, a branch of topology, a Brunnian link is a nontrivial link (knot theory), link that becomes a set of trivial unlinked circles if any one component is removed. In other words, cutting any loop frees all the other loops (so that no two loops can be Hopf link, directly linked). The name ''Brunnian'' is after Hermann Brunn. Brunn's 1892 article ''Über Verkettung'' included examples of such links. Examples The best-known and simplest possible Brunnian link is the Borromean rings, a link of three unknots. However for every number three or above, there are an infinite number of links with the Brunnian property containing that number of loops. Here are some relatively simple three-component Brunnian links which are not the same as the Borromean rings: Image:Brunnian-3-not-Borromean.svg, 12-crossing link. Image:Three-triang-18crossings-Brunnian.svg, 18-crossing link. Image:Three-interlaced-squares-Brunnian-24crossings.svg, 24-crossing link. The simplest Brunnia ...
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