For the future, for the Drawing Machine, for the Solver Engine, I defined a sexehex by a string of 6 characters, in relation to the edge sex, clockwise top-left starting. I used the character "M" for Male, the character "F" for Female and the character "-" (minus) for the Neuter edge. The string "F-MFMM" defines the sexehex in the picture. To rotate the sexehex you must shift the string: "MF-MFM" is the same sexehex 60° clockwise rotated. To flip the sexehex you must invert the characters order: "MFM-FM" is the same sexehex fliped on west-est axis.
A sexehex is also defined by the coordinates of the center. Every sexehex center can be placed on the grid below.

For example: the string "6,2,--M-MF" defines exactly the last sexehex. Every (x,y)sexehex borders on 6 other sexehexes: (x-1,y-1) (x+1,y-1) (x+2,y) (x+1,y+1) (x-1,y+1) (x-2,y).
A simple Basic program prints all the sexehex strings without mistakes. You can see the results in ascii text and in a picture (25KB). I propose this numeration as a standard.

I prepared here a program for Win95/.. .It is able to draw the puzzle solutions from a text (draw only, not solve). If you have Microsoft Visual Basic (5.0 or later), or its .dll, you can download a little zipped file (23KB). Else you must download the big install file (1.4MB sorry).