### A possible idea

Here is a raw idea.
In my work on “sliced cubes” I decomposed a brick into tents of various sizes.
That trick might work even better here.
The corners of a polyhedron can be more complex however.
Getting the signs right is easy for a brick; they alternate.
I cut my teeth on simple regular polyhedra.
Too the tents derived from a brick are similar, but not for polyhedra.

Choose a hyper plane outside the polyhedron.
Choose the vertex furtherest from the plane.
The first Htent is the set of points between the plane and the vertex that can see all the inner polyhedron surfaces.