Note: I did not look at your link before posting this answer. The triple helix system looks quite complicated and somewhat unlikely to involve naturally from simple chemicals.
Consider the ABC sex determination system for diploid individuals, where A, B and C are chromosomes with a distinct form that can pair up. Each of A, B and C contains a distinctive gene that encodes for a protein necessary for viability, two of which combine to determine the sexual characteristics. Two of the same are too much, the resulting individual is not viable and culled in an embryonic stage. This naturally leads to the forms AB, AC and BC as only existing forms.
Now suppose that the chromosomes also encodes other proteins that, apart from the sexual characteristics, also have a great impact on the morphology of the creatures. 29
For instance, chromosome A holds genes that induce a (far) greater size and territorial protection, while form B induces more muscles and form C promotes intelligence. This leads to:
* AB: big, strong and dumb and quite territorial
* AC: big, weak, smart and quite territorial
* BC: small, strong, smart and not territorial at all
Individuals produce gametes of either kind without differentiation among the gametes of either chromosome type (A, B or C) or source of the individual (AB, AC or BC) and further suppose the actual reproduction is performed by pooling a bunch of gametes in an aquatic environment with sufficient nutrition, like terrestrial fish. The following options present themselves:
* asexual reproduction, just the gametes of a single individual. 50% chance of producing what is essentially a clone
* bisexual reproduction, the gametes of two individuals of same sex or different sex. Again 50% chance of producing offspring, half of which are essentially clones
* trisexual reproduction, the gametes of three individuals, two out of three individuals of the same sex again gives a 50% chance of producing offspring with less likelihood of clones, three individuals of different sex gives a 66% percent chance of producing offspring with less likelihood of clones.
As the latter option, three different sexed individuals pooling their gametes produces more offspring with a balanced mix of sexes this is the favored option, especially if the chances of survival of an embryo or larva are quite slim, but approximately equal for all three sexes, again not unlike terrestrial fish. 1008