[nkrisc]

How do you define sex? Because what you just described sure sounds like a third sex to me.

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.

[chiefalchemist]

Actually. No.

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.