Rotating Möbius Band
 
Maple 8 code:
 
with(plots):
pic := n ->
[plot3d([8+2*x*cos(1/2*y), y, x*sin(1/2*y)],
   x=-1..1,y=0..2*Pi,coords=cylindrical,grid=[2,30],
   orientation=[270-9*n,45],scaling=constrained)];
display(seq(pic(n),n=0..39),insequence=true);
   

Comments: 
  1. It is actually the viewpoint that is being rotated by this Maple code, rather than the surface.  However, the effect is that of the surface rotating in 3-space.
  2. The animation consists of 40 frames, each with viewpoint rotated 9 degrees from the previous frame.
  3. An animation editor was used to slow down the animation, to add transparency, and to optimize the GIF image to an acceptable 66K.