There are two rows from Pascal's Triangle that are immediately of interest. The numbers 1, 6, 15, 20, 15, 6 and 1 could be used for the center of the flexagon and the numbers 1, 8, 28, 56, 70, 56, 28, 8, and 1 could be used for consecutive numbering along the edge as in the 1 through 9 flexagon which yielded a 'magic flexagon' of sorts.
I definitely think that there is enough potential to merit a little investigation. Of course there is always lots of
room to think of combining other ideas with the search. Time to get them
'Try'hexaflexagons flexing!
By Vernon Gutenkunst (B.S. in Chemistry, Army Musician, B.A. in Interdepartmental Sociology)
Flexagon Re'flex'ions Home Page URL: http://hometown.aol.com/verndrei/flex00.html