Find vertices of a polygon given 1 vertex and the center point in 3D space

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Is there a method to calculate the vertices of a polygon given just 1 vertex of the polygon and its center point? I found this post maths - find vertices when 1 vertex and center point is given in polygon on the topic, but it's only for 2 dimensions. Can this be extrapolated to 3 dimensions? Thanks!

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Given the center of a (regular) polygon and one of the vertices, you can find infinitely many polygons in three-dimensional space.

To get a unique polygon, you'll need (say) another vertex to define the plane the polygon rests in.