Juggle Wiki
Juggle Wiki

To find the dual of a siteswap, subtract each number in the sequence from twice the number of objects in the pattern, and read the resulting sequence backwards. This will always result in a valid pattern for the same number of objects. If the dual of pattern A is pattern B, the dual of pattern B is pattern A.

When you subtract each number in the 4 object siteswap 552 from 8 (twice the number of objects), you get 336, and reading that sequence backwards you get another 4 object pattern: 633. When you do the same thing with 633, you get the pattern you started with: 552.

A siteswap can be its own dual. For example, 666000, 62340, and all arithmetic progression siteswaps, such as 12345, 741, and 9753, are self-dual.

The dual of a ground state siteswap is always a ground state siteswap, and the dual of a prime siteswap is always a prime siteswap. If a siteswap contains a number greater than twice the number of objects in the pattern, its dual will contain a negative number, which means the dual isn't actually jugglable, but you can turn it into a non-negative pattern for a higher number of objects by adding a certain number to each number in the siteswap.