Group theory In terms of group theory, if G is the symmetry group of a polyhedral compound, and the group acts transitively on the polyhedra (so that each polyhedron can be sent to any of the others, as in uniform compounds), then if H is the stabilizer of a single chosen polyhedron, the polyhedra can be identified with the orbit space G/H – the coset gH corresponds to which polyhedron g sends the chosen polyhedron to.
Group theory In terms of group theory, if G is the symmetry group of a polyhedral compound and the group acts transitively on the polyhedra (so that each polyhedron can be sent to any of the others, as in uniform compounds) then if H is the stabilizer of a single chosen polyhedron the polyhedra can be identified with the orbit space G/H – the coset gH corresponds to which polyhedron g sends the chosen polyhedron to.