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.
Read more about this topic: Polyhedral Compound
Famous quotes containing the words group and/or theory:
“The poet who speaks out of the deepest instincts of man will be heard. The poet who creates a myth beyond the power of man to realize is gagged at the peril of the group that binds him. He is the true revolutionary: he builds a new world.”
—Babette Deutsch (1895–1982)
“Lucretius
Sings his great theory of natural origins and of wise conduct; Plato
smiling carves dreams, bright cells
Of incorruptible wax to hive the Greek honey.”
—Robinson Jeffers (1887–1962)