The Huckel band structure is analytically investigated for a family of
arbitrary-width pi-network polymers which may be viewed as being cut
from the graphite lattice. For wider strips a portion of two nearly no
nbonding bands on either side of the Fermi energy are found to be loca
lized to opposite edges of the strip. Novel consequences of these edge
-localized band orbitals are considered and correlated to a simple res
onating valence bond picture.