As I said in that old gh forum thread- for the general case where the vertices have valence greater than 3, even if the faces are planar, there won’t exist any vector along which you can offset the vertices that gives planar faces parallel to those of the original faces.

If you do offset all the faces by the same amount, usually they will not intersect in a single point, so each vertex in the original will turn into multiple vertices in the offset.

For valence 4, the specific condition the mesh needs to meet is indeed for the faces around each vertex to be *tangent to a common cone*.

For general freeform shapes you need to do some optimisation to meet this condition.

Here’s an example that lets you deform a mesh, then make it strictly conical and planar, and calculates the offset so that every solid panel has parallel planar faces of the same thickness

conical_offset.gh (27.1 KB)

(see also these old threads 1, 2)