Yes, that˘s a tricky folding.  Typically you create a flexagon by folding adjacent faces together, hence the adjacent pairs of numbers that always appear in an unfolded strip.  But this numbering has no adjacent numbers.

Something that helps in folding is to know that I˘ve numbered the faces in the order they˘ll appear in the final stack.  So you˘ll have 1 on the outside, 2 on the back of the top pat, 2 facing it on the next pat, 3 on its backside, etc.  Fold the strip in the order the pats occur.  So start with the 1/2 pat then fold the 7/6 pat under it.  The next one is 3/4, so fold it between the first two pats.  1/8 goes at the bottom of the stack so the 1˘s will be on the outside when you˘re done.  Next tuck 5/6 between the 3/4 and 7/6.  Continue by tucking each pat into the appropriate spot in the stack.  It may be a bit tricky sticking the final pat into its proper place, but when you finish all the hinges should be properly nested and everything quite snug.

The state diagram for this one is simply a loop.  From each face you can only get to the faces immediately before and after it in the stack.  Analogous numberings exist for triangles, pentagons and higher order polygons.

I˘ve tried these numberings on edge flexagons and they seem to be almost impossible to fold and result in a very tightly bound stack rather than a working flexagon.

Scott Sherman