So those aren't a third sex, it's individuals with both male and female reproductive cells.
"Three sex phenotypes in a haploid algal species give insights into the evolutionary transition to a self‐compatible mating system." -- i.e. how might self-pollinating plants have developed?
- producer of small gamete (human male)
- producer of large gamete (half of human female)
- incubator of embryo (half of human female)
In any case, I think what's being proposed is there are still on 2 unique sexes.
- some of the species have one - some of the species have the other - some have the ability of both.
Technically, yes, that's still only two.
Your description is premised on the assumption that there are only two sexes to begin with, and define the third sex in terms of the two sexes you assume to be the only ones that exist. Instead you could describe them as sexes A, B, and C where any of following pairings are valid for reproducing: A and B, A and C, B and C, or C and C.
You need two differnt "widgets" to tango, not three.
Unless you say Sex A and Sex B together is a third sex Sex A+B. But that would only make sense if A+Bs were unique in the sense that they can only mate with other A+Bs. Then A+B would be a third sex. That's not the case, is it?
Put another way, sex is a property, not a class.
> they can produce normal male or female colonies when they reproduce sexually with other P. starrii colonies