One example is the assumption that “if two lines are parallel then they can never intersect.”
So… pretend they can intersect twice. That’ll mean things break, right? So you start doing geometry with that, and you get weird results, like “a triangle can have three 90° right angles.” Which is bonkers, but not inconsistent… And it keeps going, the geometry is weird, but it’s not broken, and then someone takes this strange set of rules and slaps them over a globe.
And then suddenly it intuitively makes sense. Longitude lines are parallel at the equator, but they do intersect at the north and south poles! If you take one eighth section of the sphere, each edge of it is “straight,” but each angle is also 90°.
So you start doing other rule changes, and they also make self consistent geometries. You get hyperbolic geometries where lines that are parallel get farther and farther from each other. You start to make weird lumpy geometries and they work!
And eventually you end up with a russian professor teaching a class where his sentence structure only makes sense if you mentally translate everything he says word-for-word into russian and your mind opens up and you can see the layers, you can see just how an Irish hero can walk from the mortal world to the fairy realms and never do more than just walk, you can see how paths to the shadow realms take you from layer to layer of reality.