Definition

A shape has rotational symmetry of order $n$ if rotating it by $360/n$ degrees about the center maps it onto itself, and $n$ is the largest such integer, so the minimum angle of rotation is $360/n$ degrees; all regular n-gons have rotational symmetry of order $n$, and every shape has "trivial" rotational symmetry of order $1$ at $360$ degrees. A figure with rotational symmetry of order $2$ also has point symmetry. Formally, the rotation $R_{360/n}$ is an element of the symmetry group $\text{Sym}(F)$, and the cyclic subgroup it generates is isomorphic to $\mathbb{Z}_n$; combined with reflections, the full symmetry group becomes the dihedral group $D_n$. For 3-D objects, rotational symmetry about different axes generates groups such as cyclic ($C_n$), dihedral ($D_n$), tetrahedral ($T$), octahedral ($O$), and icosahedral ($I$) groups; the five Platonic solids have rotational symmetry groups $T$ ($12$ elements) for the tetrahedron, $O$ ($24$ elements) for the cube and octahedron, and $I$ ($60$ elements) for the dodecahedron and icosahedron, and these are the only finite subgroups of $SO(3)$.