Tigger has been sleeping like this ever since he was a kitten. When I first chanced upon this pose, it was in the middle of the night. My house then had white marble floors. The faint glow of city lights and the poor contrast between cat and floor made it difficult to distinguish which way he was actually facing. As you can see from the above illustration, the answer was: both.

This is a picture from the reverse angle to prove that he really is sleeping!

And now, a close up for all observers interested in paw-suspension bridges. Integrity of the structure can be maintained for up to 5 hours. :p