Yaacov, did you find a way to fit the tuck flex into your current framework of the flexagon formulas and edge weights?  Will it extend to other flexes?  As I've played around with building a flexagon simulator, I've simply gone for a low level description of how a flex works.

It's interesting to note that the tuck flex requires an extra hinge opposite where you perform the flex (as Yaacov has modeled), not because that hinge gets flexed, but because you need to be able to open the flexagon up enough to be able to perfrom the flex.  This is what makes the tuck flex and its inverse not always completely symmetric.  On flexagons with more triangles per side, this restriction is relaxed somewhat in that only one of any number of hinges needs to open up so you can do the tuck flex.

Scott Sherman