A Question of the 3X4 Knight's Tour

I am working on a webpage which features the Knight's Tour on various sizes of boards—specifically, the 3×4 and square boards from 5×5 through 15×15. While on most boards, I only post one tour, I know from all sources I've seen that number the possible tours say that there are 16 undirected Knight's Tours of a 3X4 chessboard, and I would like to post them all on my webpage. However, I can only figure out twelve tours, which are near the top of that page: http://www.mrinitialman.com/Furcadia/furc_dreams.php?dream=nitetour&type=walk

What are the four that I'm missing, or (as I suspect) are there 16 only in theory, and actually 12 in practice?

I cannot POSSIBLY be the first to put this to the test!  I suck at chess, and this is a forum of awesome players!  SOMEONE must have the answer!

*Munches humble pie.*  It would seem that I have goofed.  Four of my 12 "solutions" were simply the tours traced in reverse, giving me 8 3X4 tours, which means that I have 8 more solutions--which means all I have to do is go from a 3X4 board to a 4X3 board for the other 8, which means 16 undirected tours.