Santa's Puzzle

One of the gifts I received at Christmastime was this fiendish puzzle. You may have seen them about. Known as Galileo's Globe, the simple idea is to pull it apart and then put it all back together again. There are probably about 20 pieces in all.
So far, I have managed to take out 3 pieces. Can't figure how to get the next one out. I reckon my chances of putting it all back together again are roughly zero. Always assuming I ever manage to dismantle the thing at all.
Thinks..... what if I were to photograph each step in the dismantling and then refer to the shots when re-assembling? Do you think that would be cheating?