Why is this method used, when the basic rule in math is different?
The center point of a polygon, in math, is defined as: "The point inside a regular polygon that is equidistant from each vertex."
Meaning it should be the same center point as the circle.
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Photoshop considers a path to be an arbitrary path and has no concept of a path being a regular polygon.
Gotcha. This helps after a lot of hairpulling due to a wobbling wheel animation.