Some negative results in N sided patches

The sculptured surface literature has concerned itself almost exclusively with four sided patches. Patches which are not restricted either to being four sided or to meeting four at a vertex are described only very rarely. This paper describes three specific negative results. First, that an elegant symmetric form shared by all known cyclically symmetric parametrizations of n sided patches does not generalize to n > 5. Second, that it is not possible to define a 'suitcase corner' triangular patch with C2 continuity with adjacent bicubic patches in a B-spline lattice. Third, that one of the desirable requirements in a cyclically symmetric parametrization, that of being able to compute any parameter rationally from any adjacent pair, is likely to need to be relaxed for n > 5