There is no cube that is decomposable into smaller, different, cubes. All polygons are decomposable into triangles by adding only interior edges. Not all polyhedra are decomposable into tetrahedra by adding only interior faces. For polygons, all such decompositions have the same number of triangles. Some polyhedra can be decomposed different ways into different numbers of tetrahedra.
Every polygon has every interior point visible from some vertex.
Some polyhedra have interior points not visible from any vertex. Voronoi diagram's complexity is linear. A 3-D Voronoi diagram's complexity can be quadratic. Given two convex polygons, there exists an edge of one that separates them. Given two polyhedra, it is possible that none of their faces separate them.