thumb|In the compound of five tetrahedra, the symmetry group is the (rotational) icosahedral group of order 60, while the stabilizer of a single chosen tetrahedron is the (rotational) tetrahedral group of order 12, and the orbit space (of order 60/12 = 5) is naturally identified with the 5 tetrahedra – the coset corresponds to the tetrahedron to which sends the chosen tetrahedron.
thumb|In the compound of five tetrahedra the symmetry group is the (rotational), icosahedral group of order 60, while the stabilizer of a single chosen tetrahedron is the (rotational) tetrahedral group of order 12, and the orbit space (of order 60/12 = 5) is naturally identified with the 5 tetrahedra – the coset corresponds to the tetrahedron to which sends the chosen tetrahedron.