Is a polygon not considered convex if it has a hole? For example, say I drew 2 (different-sized) concentric squares. Is the inner square considered convex while the outer one is not? Are neither considered convex? I'm guessing the answer is the same for two (different-sized) concentric cubes. I forgot the technical test needed to determine convexity. If they are not convex, are they considered concave, or just "nonconvex"?
2026-03-27 14:45:27.1774622727
Precise definition of convex polygons/polyhedra
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I believe a polytope is convex when it is a convex set. So something with a hole is not convex, because I can pick two points on either side of the hole and the middle of the line is not inside the polytope.
I believe in the case of polytopes, non-convex is the same as concave (as in the case of polygons). However, in some other contexts such as concave functions, concave has a more narrow meaning than just "non-convex".