Light duly cast; twaddle below withdrawn: see Low Rollers thread. WFL On 1/11/13, Fred lunnon <fred.lunnon@gmail.com> wrote:
My argument concerns just the cross-section of the region around one particular tetrahedral edge of the surface, and cut off by the extended neighbouring faces of the tetrahedron.
The Minkowski average combines a Reuleaux "cusp" with a Meissner cyclide: its cross-section is the mean of a pair of adjacent arcs with a single arc, yielding some kind of non-circular curve with a rounded apex of greater curvature, and only its endpoints in common with either summand.
The Roberts comprises an lower portion shared with the Releaux arcs, capped higher up by a circular arc.
The two curves are evidently incongruent; therefore so are the completed surfaces.
Finally, while I'm prepared to believe that there may be some obvious or well-known reason why this global Minkowski surface should retain the constant curvature of its summands, the matter remains currently beyond my comprehension --- can anybody cast any light here?
Fred Lunnon