There're three kinds of it.
Any two of the same kind will give you that same kind.
Any two of the different kinds will give you the remaining kind.
What is it?
I don't know the answer. I'm trying to find a real-world embodiment for this concept.
Since there was a lot of misunderstanding I'll try to elaborate. Formally, we have three types (classes, families, kinds) of something, denote them $A,B$ and $C$. We can take instances of those types, like $a$ of $A$ ($a\in A$ as a notation), where $a$ is some specific object that is assosiated with the class $A$. We also have a mapping (combining, mixing, colliding) procedure $\times$ that for any $a_1,a_2\in A$, $b_1,b_2\in B$, $c_1,c_2\in C$:
$\qquad a_1\times a_2\in A,\quad b_1\times b_2\in B,\quad c_1\times c_2\in C$
$\qquad a_1\times b_1\in C,\quad b_1\times c_1\in A,\quad c_1\times a_1\in B$
The goal is to find a natural embodiment of these types, instances and mapping procedure that behaves by these rules without us having to explicitly explain them.
We can make up a bunch of forced examples, like the mechanics of some objects in a video game, or a part of some logic mechanism or schematics. But to construct such an example, we would actually need to lay out the rules once again. They don't emerge naturally and that's the problem.