Infinite series of compact hyperbolic manifolds, as possible crystal structures

TL;DR

This paper constructs an infinite series of hyperbolic 3-manifolds called cobweb manifolds, which could model nanotube structures, based on previous work on hyperbolic manifolds and packing problems.

Contribution

It introduces a new infinite series of hyperbolic space forms called cobweb manifolds, expanding the catalog of hyperbolic structures with potential applications in nanotechnology.

Findings

Constructed an infinite series of hyperbolic cobweb manifolds.

Proposed these manifolds as models for nanotube structures.

Extended previous work on hyperbolic manifolds and packing problems.

Abstract

Previous discoveries of the first author (1984-88) on so-called hyperbolic football manifolds and our recent works (2016-17) on locally extremal ball packing and covering hyperbolic space $\HYP$ 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 $Cw(2z, 2z, 2z)=Cw(2z)$, $3\le z$ odd, which can describe nanotubes, very probably.