Answer: Permutations that preserve distances are also known as isometries or distance-preserving transformations.
Explanation:
Permutations that preserve distances refer to a type of mathematical transformation that preserves the distances between pairs of points in a geometric space. In other words, if you have a set of points arranged in a particular way and you apply a permutation that preserves distances, the resulting arrangement of points will have the same distances between each pair of points as the original arrangement. This type of permutation is important in geometry and can be used to study properties of geometric objects such as polyhedra, graphs, and other structures. Permutations that preserve distances are also known as isometries or distance-preserving transformations.