A FULLERENE WITHOUT A SPIRAL

The spiral conjecture for fullerenes, namely that the surface of every fullerene may be unwound in at least one continuous spiral strip of edge-sharing five- and six-membered rings, is shown to be strictly false. The smallest tetrahedral fullerene that cannot be unwound in such a spiral has 380 atoms, and is the first in series of larger T symmetry fullerenes that disprove the conjecture. The practical utility of the spiral algorithn for counting fullerene cages with moderate numbers of carbon atoms remains unchallenged nevertheless, because fullerenes without spirals are very large and highly strained. © 1993