From Polyhedra to Crystals: A Graph-Theoretic Framework for Crystal Structure Generation

TL;DR

This paper introduces a graph-theoretic method for crystal structure generation based on polyhedral tiling, improving efficiency and interpretability over traditional random methods, and demonstrating its effectiveness on common crystal types.

Contribution

A novel geometric and topological framework encoding polyhedra as dual graphs for systematic crystal structure prediction.

Findings

Successfully reconstructed FCC, HCP, and BCC structures from dual graphs.

Provides a new pathway for generating crystal structures based on polyhedral targets.

Potential to accelerate discovery of new materials in electronics and energy storage.

Abstract

Crystal structures can be viewed as assemblies of space-filling polyhedra, which play a critical role in determining material properties such as ionic conductivity and dielectric constant. However, most conventional crystal structure prediction methods rely on random structure generation and do not explicitly incorporate polyhedral tiling, limiting their efficiency and interpretability. In this highlight, we introduced a novel crystal structure generation method based on discrete geometric analysis of polyhedral information. The geometry and topology of space-filling polyhedra are encoded as a dual periodic graph, and the corresponding crystal structure is obtained via the standard realization of this graph. We demonstrate the effectiveness of our approach by reconstructing face-centered cubic (FCC), hexagonal close-packed (HCP), and body-centered cubic (BCC) structures from their dual periodic graphs. This method offers a new pathway for systematically generating crystal structures based on target polyhedra, potentially accelerating the discovery of novel materials for applications in electronics, energy storage, and beyond.