It's so simple to see: Just put two well sharpened pencils on a flat surface. Their tips can still touch as well as you can resolve with the pencils in any number of non aligned positions.
Great analogy. But the pencil tip is the center of the pencil, and comes to a tip. It is parallel with the outside of the pencil, which is what you are using to align the flats. It two tips are not meeting a their tips, then one is hitting the others side, or cone.
Great analogy, but you failed to finish it. Same with finger tips. Any tip that is on center axis.
Would a pyramid be easier to see?
There is no way the center axises can aligned and the axises along the circumference, not aligned. All go together. Which is why you are able to do it different that the standard way, and have it work out. Just comes down to which is easier to see.
