 For any regular polytope the symmetry group (here a complex reflection group, called a Shephard group) acts transitively on the flags, that is, on the nested sequences of a point contained in a line contained in a plane and so on.More fully, say that a collection "P" of affine subspaces (or "flats") of a complex unitary space "V" of dimension "n" is a regular complex polytope if it meets the following conditions