The polyhedral groups are based on the symmetry of platonic solids : the tetrahedron, octahedron, cube, icosahedron, and dodecahedron, with Schläfli symbols {3,3}, {3,4}, {4,3}, {3,5}, and {5,3} respectively. The Coxeter groups for these are: [3,3] (), [3,4] (), [3,5] () called full tetrahedral symmetry, octahedral symmetry, and icosahedral symmetry, with orders of 24, 48, and 120.