•   Wikis

# Isometry group: Wikis

Note: Many of our articles have direct quotes from sources you can cite, within the Wikipedia article! This article doesn't yet, but we're working on it! See more info or our list of citable articles.

# Encyclopedia

Updated live from Wikipedia, last check: May 24, 2013 03:48 UTC (35 seconds ago)

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.

## Examples

• Consider a triangle in the plane with unequal sides. Then, the isometry group of the set of three vertices of this triangle is the trivial group. If the triangle has two equal sides which are not equal to the third, the isometry group is the cyclic group Z/2Z. If the triangle is equilateral, its isometry group is the permutation group S3.