Am I infinitely stupid?

Yes, but a ploygon of infinite vertices is a circle.
More correctly, the limit of a regular convex polygon as the number of vertices goes to infinity, is a circle. This is also consistent with what Eagle said because the limit of the size of those vertices as number of vertices goes to infinity, is zero. When the angle of a vertex is zero, it ceases to be a vertex, hence a circle has no vertices.

As pointed out by cjp, infinity is useful for understanding limits but it does not make sense to talk about an object (in this case a regular polygon) as have an infinite number of anything.
 
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