Atrinary, Aternary, or Atertiary (abbreviated AT) is an umbrella term referring to any genders that are completely unrelated to maleness, masculinity, femaleness, femininity, neutrois-ness, or neutrality, and is nowhere in between those things, while also not necessarily being genderless (although agender people may also identify as atrinary). An atrinary person may feel a strong sense of gender, however that gender is completely unrelated from the gender trinary.
The Gender Trinary
The gender binary refers to men and women, while the term non-binary encompasses all genders that are not strictly man or woman. However, non-binary includes genders that are in between male and female (such as androgyne), as well as genders that are in some way related to masculinity or femininity, (such as proxvir and juxera). The term abinary was created to refer to any genders which are completely unrelated to masculinity or femininity and is nowhere in between. Examples of abinary genders include neutrois, aporagender, agender. Abinary genders are often called "unaligned" and are often related to neutrality.
The "gender trinary" refers to this trifecta of masculine genders, feminine genders, and neutral genders. Atrinary, therefore, refers to any genders which are completely removed from the concepts of masculinity, femininity, and neutrality, or anything in between them. Maverique, some aporagenders, and many xenogenders are examples of atrinary genders. By definition all atrinary genders are also abinary, but not all abinary genders are atrinary.
Atrinary appear to have been coined by arco-pluris on beyond-mogai-pride-flags on June 11, 2018. The original flag was created at the same time. The flag has no confirmed meaning.
The other flag was also created by arco-pluris on August 16, 2018. The flag also has no meaning but resembles the abinary flag and used the color teal, which is often considered an atrinary color.