19. As shown in Figure 1, a regular dodecahedron (a polyhedron composed of 12 congruent regular pentagons) is floating in space, with two faces horizontal: the top face is surrounded by five sloping faces forming the upper ring, and the bottom face is surrounded by five sloping faces forming the lower ring. Then there are ( ) different ways to move from the top face to the bottom face through a series of adjacent faces, such that each face is visited at most once, and it is not allowed to move from the lower ring to the upper ring.
(A) 125
(B) 250
(C) 405
(D) 640
(E) 810
19. E.

Since the movement starts from the top face and ends on the bottom face, without moving from the lower ring to the upper ring or retracing the sloping faces, the movement must proceed in the order of the top face, a series of upper ring faces, a series of lower ring faces, and finally the bottom face.

Because the top face is adjacent to five upper ring faces, there are five choices. Starting from the top face, there are nine choices for the next move before moving down: walking clockwise 1, 2, 3, or 4 faces, walking counterclockwise 1, 2, 3, or 4 faces, or moving directly down to the lower ring face without passing through any other upper ring faces.

Then, there are two choices, where the lower ring face is first encountered (since each upper ring face is adjacent to two lower ring faces), and again there are nine choices for the next move. Finally, continue to the bottom face to complete the journey.
Thus, multiplying all the choices together gives
$$
5 \times 9 \times 2 \times 9 = 810 \text{. }
$$