Construction of Negatively Curved Cubic Carbon Crystals via Standard Realizations

TL;DR

This paper presents a mathematical method for constructing physically stable, negatively curved cubic carbon crystals with Schwarz P-like surfaces using standard realizations of crystal lattices.

Contribution

It introduces a novel mathematical approach to design stable negatively curved cubic carbon structures based on standard realizations.

Findings

Constructed stable negatively curved cubic carbon crystals.

Developed a mathematical framework for crystal structure design.

Demonstrated the feasibility of Schwarz P-like surface reticulation.

Abstract

We constructed physically stable sp2 negatively curved cubic carbon structures which reticulate a Schwarz P-like surface. The method for constructing such crystal structures is based on the notion of the standard realization of abstract crystal lattices. In this paper, we expound on the mathematical method to construct such crystal structures.