Many physical systems can be studied as collections of particles embedded in space, often evolving in time. Natural questions arise concerning how to characterize these arrangements—are they ordered or disordered? If they are ordered, how are they ordered and what kinds of defects do they possess? Voronoi tessellations, originally introduced to study problems in pure mathematics, have become a powerful and versatile tool for analyzing countless problems in pure and applied physics. We explain the basics of Voronoi tessellations and the shapes that they produce and describe how they can be used to characterize many physical systems.

Topics
Ideal gas, Granular materials, Crystallographic defects, Disordered solids, Computational methods, Convex geometry, Euclidean geometries, Partial differential equations, Geometric topology, Voronoi diagrams
© 2022 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
2022
Author(s)
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