Is there a way to identify whether a face is of circular shape and it's center?. All I have is the face and it's vertices.
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Three non-aligned points are enough to unambiguously define a circle. You find the center as the intersection of two mediatrices. http://www.manufacturinget.org/2011/07/construct-circle-through-three-points/
When you have the center, you can check that all points are at the same distance from it.