I have always thought that this puzzle has many (not easy) solutions. Now I am practically sure. I omitted twelve 6-sexehexes and I obtained a pre-solution with a hole of 12 pieces (yellow in the picture below).

Then I worked on the edges A,B,C,...W (red). They are 22. Each edge is only male or female. 2^22 = 4,194,304 It is not a big number. A simple program could verify all combinations. It uses binary numbers (1=male, 0=female). Near the 12 pieces there are numbers. They represent rotated or flipped sexehexes. The solutions are twenty-two: