Definition:Symmetry Group

Definition
Let $P$ be a geometric figure.

Let $S_P$ be the set of all symmetries of $P$.

Let $\left({S_P, \circ}\right)$ be the algebraic structure such that $\circ$ denotes the composition of mappings.

Then $\left({S_P, \circ}\right)$ is called the symmetry group of $P$.

Also see

 * Symmetry Group is a Group