Symmetry Group
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The symmetry group of an object (image, signal, etc.) is the group of all isometries under which it 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. The "objects" may be geometric figures, images and patterns, such as a wallpaper pattern. The definition can…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The symmetry group of an object (image, signal, etc.) is the group of all isometries under which it 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. The "objects" may be geometric figures, images and patterns, such as a wallpaper pattern. The definition can be made more precise by specifying what is meant by image or pattern, e.g., a function of position with values in a set of colors. For symmetry of physical objects, one may also want to take physical composition into account. The group of isometries of space induces a group action on objects in it.