[[!redirects symmetry group]] # Symmetry A **symmetry** of an object is a [[transformation]] that can be applied to the object with the result that the object looks the same after the transformation as it did before. The identity transformation is considered to be a symmetry of every object. # Rotational Symmetry The **rotational symmetries** of an object are those symmetries which are [[rotations]]. # Reflectional Symmetry The **reflectional symmetries** of an object are those symmetries which are [[reflections]]. # Symmetry Group The **symmetry group** of an object consists of all of its symmetries. This includes the identity transformation. Symmetries can be _composed_ in that applying one symmetry and following it by another produces a transformation that is also a symmetry, namely that also has the effect of making the object look the same as it did originally. This makes the symmetries into a mathematical structure called a _group_. category: definition [[!redirects rotational symmetry]] [[!redirects rotational symmetries]] [[!redirects symmetries]] [[!redirects reflectional symmetry]] [[!redirects reflectional symmetries]] [[!redirects reflective symmetry]] [[!redirects reflective symmetries]]