Politics doesn't really have dimensions to begin with, things like the Political Compass are just abstractions of ideas and positions that attempts (unsuccessfully, IMO) to provide shortcuts to understanding the broader image of a viewpoint.
As an example, Marxism-Leninism and AES states espouse and implement more democratic structures, but harshly oppressed opposition from liberals, monarchists, and fascists. This is certainly "authoritarian," but I don't think that's a bad use of authority. Rather, all systems and positions are "authoritarian" in different directions and towards different groups. You get where this is getting muddy and rather than clarifying, it's actually adding more confusion?
As a side-note, if you think Communists are "just as detestable" as Nazis, I think you need to look more critically at these movements historically. Blackshirts and Reds is a great comparison of fascism and communism historically, proving them to be completely uncomparable in terms of sheer brutality and who they served, the bourgeoisie or the proletariat, while taking a critical look at the USSR and why it dissolved.