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The reflection poles (there are 7 total, plus one broken one) are a part of the energy puzzle that Atrus designed in order to grant access to the Voltaic Tusk and the Linking Book contained within. These poles direct the beam of light emitted from the focusing lens and re-direct it to the next reflector until the beam arrives at its intended final destination; the prism.
When Saavedro followed Sirrus and Achenar to J'nanin to bring them to task for what they had done to Narayan, they tied him to one of the poles and burned their Linking Book back to Myst as they linked out in front of him. In order to get himself free, Saavedro was forced to break the pole he was tied to. While this puzzle would likely have had multiple solutions in the past, after Saavedro broke free, there was only one possible solution left.