(This is the author of the article.) I agree! One of my favorite things about this topic is that you can prove the polyhedron version using very simple tools, s

(This is the author of the article.) I agree! One of my favorite things about this topic is that you can prove the polyhedron version using very simple tools, so it's possible to get a feel for the concept of curvature (at least for surfaces) with a lot less machinery than you'd need to study the corresponding concept for smooth surfaces.