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A graphite model obtained by decorating a quasiperiodic icosahedral surface with heptagonal and hexagonal rings of sp² hybridized carbon is presented. We have generated closed compact fullerenes with icosahedral symmetry, genus 11, without dangling bonds and no pentagonal rings (no positive curvature). Additionally, cubic fullerenelike structures (Oₕ 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 generated. The geometry and stability of these nanostructures are discussed.
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Terrones et al. (1997) studied this question.
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