In Chaikin's algorithm, we iteratively smooth a polygonal line by cutting corners

such that we arrive at a quadratic spline in the limit. For this and other edge preserving

corner cutting schemes, we have de Boor's most general result that the limiting curve is differentiable if

and only if the maximum angle flattens out eventually. In this talk, I will discuss face

preserving cutting for convex polyhedra, explain why de Boor's result can not easily be

generalized, go through counter examples and present results. Further, I introduce our 4-8

and 4-6-8 schemes, show outcomes of ongoing experiments, and may also briefly mention

our honeycomb and $\sqrt{3}$ cutting schemes.