Abstract
Closed fullerenes and nanotubes exhibiting high topologies from genus 5 to genus 21 are proposed. These structures (holey-balls and holey-tubes) possess only hexagonal and heptagonal (negative Gaussian curvature) rings of carbon with no dangling bonds and no pentagonal rings (no positive Gaussian curvature). Holey-balls and holey-tubes can be seen as finite zeolites since they present interconnected channels suitable for locating guest molecules or atoms such as alkali metals. The geometry, stability and possible applications are studied.
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