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How do I coordinate a polyrythm between players via music notation?

The question is mostly music notation-based.

I can have multiple players doing their own rhythms no problem. But if I want to end the piece when all of the timings sync back up, how do I do that via music notation?

I looked through all the symbols I could find, but I could not find anything that includes any sort of "if" statement.

Alternatively, I could just list out every beat, but when having a 3:5:7:29 rhythm or something else ridiculous - the amount of space required to write that out in full is prohibitive.