Answer:
"permutations that preserve distances"
Explanation:
You want to know the meaning of "isometries" in the given discussion of dihedral groups.
The wording of the paragraph tells you the meaning:
"isometries ... are permutations that preserve distances."
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Additional comment
Often, writing that introduces an unfamiliar word will describe the meaning of that word. Here, the meaning is described, along with several examples (translations, rotations, reflections).
The word isometry has its origin in ancient Greek. The prefix "iso-" means "equal", and "-metry" comes from metron, meaning "measure." Effectively, an isometry is a transformation that preserves measures.