  Any convex polytope whose combinatorial automorphism group has two orbits on
the flags is isomorphic to one whose group of Euclidean symmetries has two
orbits on the flags (equivalently, to one whose automorphism group and symmetry
group coincide.) Hence, a combinatorially two-orbit convex polytope is
isomorphic to one of a known finite list, all of which are 3-dimensional: the
cuboctahedron, icosidodecahedron, rhombic dodecahedron, or rhombic
triacontahedron. The same is true of combinatorially two-orbit normal
face-to-face tilings by convex polytopes.
