Fizz Political Compass
When inspecting the three fundamental axioms of fizz, one may notice that "We hate everything" and "We love everything" are logical opposites of one another. One may ask the question, why don't we have the logical opposite of the third axiom, "Everything matters"? By introducing its logical opposite, "Nothing matters", we may construct a two dimensional plane by placing axes for each statement. We present a horizontal axis for whether or not we love everything or hate everything, and a vertical axis for whether or not everything matters or nothing matters.
We may think of this plane as a political compass since it defines an entire spectrum of where someone may lie with respect to hating or loving everything and thinking that everything or nothing matters.
On this compass, we may locate fizz as the triangle whose corners are "Everything matters", "We hate everything", and "We love everything".
By rotating and flipping this triangle, we obtain the fizz variants of Anti-fizz, Rotational Fizz, and Rotational Anti-fizz (or Anti-Rotational Fizz).