The classification of Platonic solids is one of the first great classification theorems in mathematics. It's connected to the classification of finite subgroups of SO(3):

• The cyclic groups, **ℤ**/n

• The dihedral groups, D_{n}

• The symmetry group of the tetrahedron, A_{4}

• The symmetry group of the cube or octahedron, S_{4}

• The symmetry group of the dodecahedron or icosahedron, A_{5}

For the classification of finite subgroups of SO(3), see GroupProps: classification of finite subgroups of SO(3). The pictures of Platonic solids are from the Wikipedia article on Platonic solids. They were created by Cyp, who granted permission to use it under the GNU Free Documentation License.