H. Terrones et M. Terrones, QUASI-PERIODIC ICOSAHEDRAL GRAPHITE SHEETS AND HIGH-GENUS FULLERENES WITH NONPOSITIVE GAUSSIAN CURVATURE, Physical review. B, Condensed matter, 55(15), 1997, pp. 9969-9974
A graphite model obtained by decorating a quasiperiodic icosahedral su
rface with heptagonal and hexagonal rings of sp(2) hybridized carbon i
s presented. We have generated closed compact fullerenes with icosahed
ral symmetry, genus 11, without dangling bonds and no pentagonal rings
(no positive curvature). Additionally, cubic fullerenelike structures
(O-h symmetry) with genus 5, without dangling bonds and no pentagonal
rings have also been obtained. Extending this idea, closed perforated
tubules with no pentagonal rings and genus higher than 5 are also gen
erated. The geometry and stability of these nanostructures are discuss
ed.