I'm reading a book that provides an example of two hexagons that are not affinely isomorphic. One is a regular hexagon, and the other is not.
The book defines two polytopes (in this case hexagons) being affinely isomorphic if there exists an affine map from one of their spaces to the other, that is a bijection between the two polytopes.
I don't have much intuition for how a hexagon for example would be affected by an affine map.
I know that line-segments go to line-segments. I suppose this implies that vertices would also go to vertices? But i'm not sure. In any case none of this tells me why not any two hexagons are affinely isomorphic.