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Brunnian link

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This four-component link is a Brunnian link.

In knot theory, a branch of mathematics, a Brunnian link is a nontrivial link that becomes trivial if any component is removed. In other words, cutting any loop frees all the other loops (so that no two loops can be directly linked).

The name Brunnian is after Hermann Brunn. Brunn's 1892 article Über Verkettung included examples of such links.

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:

  • 12-crossing link.
    12-crossing link.
  • 18-crossing link.
    18-crossing link.

Real world Examples

Many disentanglement puzzles and some mechanical puzzles are variants of Brunian Links, with the goal being to free a single piece only partially linked to the rest, thus dismantling the structure.

References

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