The trihexaflexagon, essentialy, is a flattened moebius strip. It is a strip of paper which has been folded in a very specific way to obtain an interesting result. It looks like this on both sides (. = fold, other characters indicate edge):
  /\   .\
 /  \ .  \
\    /.   /
 \  /  . /
A very interesting thing happens when you push all the fold lines back. You get a Y shape, looking from the front, but when you open up the Y on the front, a new face is revealed. That's right: if you take a trihexaflexagon, colour both sides, and then "flex" it, a new face will be exposed which you have not coloured yet. That's about all there is to the trihexaflexagon, so you might want to look at the complexity of the hexahexaflexagon. Hint: the trihexaflexagon is 3 faced (tri). What can you guess about the hexahexaflexagon?

If you wish to construct any type of hexaflexagon, go to this url, as the images really help: