In 3-dimensional space, an offset of a polyhedron is computed by
shifting all facets inwards while keeping them parallel to their
initial orientation. By following the moving vertices,
the straight skeleton is revealed.
The moving edges divide the polyhedron into cells
with useful geometric properties, such as monotonicity.
Compared to straight skeletons of polygons in the plane,
computing initial offsets is different: In the very first moment,
vertices of degree greater than three have to be split.
You can find further information about the straight skeleton
in some of my publications.
Furthermore, I would appreciate your getting in
Feel free to upload a polyhedron of your choice.