Symmetry in Nature

A geometric shape Ŀ is said to be “symmetric” if there is a transformation that moves individual pieces of the object but doesn t change the overall shape. Such a transformation is called a symmetry element of Ŀ and the set of all symmetry elements is denoted by Aut(Ŀ). The set Aut(Ŀ) is a group under composition of functions. We name this group, the symmetry group of Ŀ. In this talk, the main properties of this group are considered into account.