Honeycomb cutting in 3D always generates smooth limiting surfaces, but      never generates smooth limiting surfaces in 4D. Honeycomb cutting refers to an edge cutting scheme for convex polyhedra. For three-dimensional polyhedra, it is "parallel" to the honeycomb refinement scheme by Dyn, Levin and Liu. This means that the limiting surfaces are C¹ because the smoothness arguments for the refinement scheme also apply to the cutting scheme.

 However, I will show that a straightforward generalization of the cutting scheme to higher dimensional polyhedra cannot generate smooth limiting polyhedra. This, in return, also holds for the honeycomb refinement scheme for higher dimensional polyhedra. In my talk, I will embed these results in a discussion of general edge cutting schemes. In particular, I will mention the 4-6-8 scheme, as is it may be a more promising candidate for a successful generalization to higher dimensions than simple honeycomb cutting.