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Having all internal angles below 180 degrees

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That only applies to polygons or polyhedra. You can have convex solids that are curved and have no angles.

A convex shape is one in which, if you take any two points on the surface of the shape or inside it, then the whole of the straight line joining those two points is on the surface of the shape of inside it.

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Q: What does convex mean in geometric terms?
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