# Algorithm to Choose Consistent Normals for All Faces on a Polyhedron

I have a polyhedron $P$, in 3D, which consists of $f$ faces, each face consists of $V$ vertexes.

My question is, how to choose a consistent normal orientation for all the faces? Consistent here means that if I unfold all the faces of that polyhedron onto a common plane all the normals will agree.

For the sake of argument, the polyhedron can be either convex or concave. However, it can be unfolded onto a plane without overlap.

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Is it convex? If no: Can it be unfolded onto a plane without overlap? If no: Is it non-self-intersecting? Oh, and do you have a point in the interior? That would help. – TonyK Feb 9 '11 at 8:57
@Tony, for the sake of argument, the polyhedron can be either convex or concave. However, it can be unfolded onto a plane without overlap. – Graviton Feb 9 '11 at 9:03