In mathematics, the isometry group of a metric space is the set of all isometries from the metric space onto itself, with the function composition as group operation. Its identity element is the identity function.
A single isometry group of a metric space is a subgroup of isometries; it represents in most cases a possible set of symmetries of objects/figures in the space, or functions defined on the space. See symmetry group.
Read more about Isometry Group: Examples
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