In abstract algebra, the **symmetry group** of an object (image, signal, etc.) is the group of all isometries under which the object is invariant with composition as the operation. It is a subgroup of the isometry group of the space concerned. If not stated otherwise, this article considers symmetry groups in Euclidean geometry, but the concept may also be studied in wider contexts; see below.

Read more about Symmetry Group: Introduction, One Dimension, Two Dimensions, Three Dimensions, Symmetry Groups in General

### Other articles related to "symmetry group, group, symmetry, groups, symmetry groups":

**Symmetry Group**s in General

... See also Automorphism In wider contexts, a

**symmetry group**may be any kind of transformation

**group**, or automorphism

**group**... Conversely, specifying the

**symmetry**can define the structure, or at least clarify what we mean by an invariant, geometric language in which to discuss it this is ... For example, automorphism

**groups**of certain models of finite geometries are not "

**symmetry groups**" in the usual sense, although they preserve

**symmetry**...

### Famous quotes containing the words group and/or symmetry:

“Even in harmonious families there is this double life: the *group* life, which is the one we can observe in our neighbour’s household, and, underneath, another—secret and passionate and intense—which is the real life that stamps the faces and gives character to the voices of our friends. Always in his mind each member of these social units is escaping, running away, trying to break the net which circumstances and his own affections have woven about him.”

—Willa Cather (1873–1947)

“What makes a regiment of soldiers a more noble object of view than the same mass of mob? Their arms, their dresses, their banners, and the art and artificial *symmetry* of their position and movements.”

—George Gordon Noel Byron (1788–1824)