Infinite series of compact hyperbolic manifolds, as possible crystal structures

Abstract

Previous discoveries of the first author on so-called hyperbolic football manifolds and our recent works (2016-17) on locally extremal ball packing and covering hyperbolic space H 3 with congruent balls had led us to the idea that our "experience space in small size" could be of hyperbolic structure. In this paper we construct an infinite series of oriented hyperbolic space forms so-called cobweb (or tube) manifolds Cw(2z, 2z, 2z) = Cw(2z), 3 ≤ z odd, which can describe nanotubes, very probably.