An isohedron is a polyhedron with symmetries acting transitively on its faces. A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. For a connected manifold "M", the diffeomorphism group acts transitively on "M". More generally, the diffeomorphism group acts transitively on the configuration space "CM". This group acts "transitively" on all vertices, edges and triangles in the building. First, recall that the general linear group acts transitively on the -dimensional subspaces of . Every orbit is an invariant subset of "X" on which "G" acts transitively. That is, the symmetries of formula 1 act transitively on formula 1. Then the Galois group formula 4 acts transitively on the "P". It is simple linear algebra to show that GL acts transitively on those. "Eat" and "read" and many other verbs can be used either transitively or intransitively. For any vector space, the addition acts freely and transitively on the vector space itself. The spin group acts transitively on by rotations. Let act transitively on and pick some point in . It is not necessarily transitively normal, however.