square looks the same, so this is also an element of our set, which is called it . The movement that does nothing is denoted by .

Generating the group

With composition as the operation, the set of all those movements forms a group. This group is the most concise description of the square's symmetry. Applying two symmetry transformations in succession yields a symmetry transformation. For instance a a, also written as a², is a 180° degree turn. a³ is a 270° clockwise rotation (or a 90° counter-clockwise

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