Fullerenes with non-positive Gaussian curvature: Holey-balls and holey-tubes

Classical fullerenes such as C₆₀ and C₇₀ need 12 pentagonal rings of carbon for the closure of the cage. These pentagons produce the positive Gaussian curvature which gives the characteristic spherical shape. In this paper we propose a new family of fullerene-like structures which do not have pentagonal rings (no positive Gaussian curvature), no dangling bonds, possesing hexagons and heptagons only. The topology of this new family of perforated fullerenes (holey-balls) and nanotubes (holey-tubes) is higher than classical fullerenes presenting genus 5,11 up to 21. Holey balls can be icosahedral (I_h) and cubic (O_h). The geometry, elastic stabilities and possible applications of holey-balls and holey-tubes are studied.