Carbon nanotube research was greatly stimulated by
the initial report of observation
of carbon tubules of
nanometer
dimensions[ l] and the subsequent report
on the observation
of conditions for the synthesis of
large quantities of nanotubes[2,3].
Since these early re-
ports, much work has been done, and the results show
basically that carbon nanotubes behave like rolled-up
cylinders of graphene sheets of sp2 bonded carbon
atoms, except that the tubule diameters in some cases
are small enough to exhibit the effects of one-dimen-
sional (1D) periodicity. In this article, we review sim-
ple aspects of the symmetry of carbon nanotubules
(both monolayer and multilayer) and comment on the
significance
of symmetry for the unique properties
predicted for carbon nanotubes because of their 1D
periodicity.