If there are 10 political questions and each admits of only 2 answers there are 1024 possible opinion collections. However, in practice there is quite a lot of clustering of opinions, so we can cover a lot of political ground reasonably systematically. I use economic opinion as the basis.
There are 3 main economic opinions: corporatism, liberalism (in the classic sense still upheld by the Liberal International) and socialism (as found in the Socialist International). The purest forms of these are the vertices of an equilateral triangle. In practice most opinions are somewhere within the triangle. But there are opinions outside the triangle though not above it.
A corporatist gone mad is a fascist. He cannot distinguish socialism and liberalism, and calls both atomism.
A liberal gone mad is a libertarian. He cannot distinguish corporatism and socialism, and calls both collectivism.
A socialist gone mad is a communist. He cannot distinguish liberalism and corporatism, and calls both capitalism.
Communists, libertarians and fascists are all strongly convinced of the reasonableness, obviousness and scientific nature of their positions. There is little point in arguing with them on their core positions. All tout themselves as champions of freedom, which they say their opponents do not understand.
Living in their dimly lit caves, occasionally fighting with someone from one of the other two caves (each cave’s denizens think there is only one other cave), they sometimes meet someone who has been out in the daylight. They generally think he comes from the other cave.