The most symmetric 3D crystal networks, explained

What is it about?

This article is a short commentary on recent work by Li, O’Keeffe and Treacy, who asked a simple question: among all the ways atoms can repeat in three-dimensional crystals, which patterns are the most symmetric of all? They show that only a tiny “royal family” of three-dimensional networks qualifies, in much the same way that the five Platonic solids are the most symmetric shapes in ordinary geometry. In the commentary I explain, in non-technical terms, what these special crystal networks look like, how they are classified, and how they connect to modern materials such as metal–organic frameworks and architected mechanical metamaterials.

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Why is it important?

Knowing which crystal networks are “maximally symmetric” gives scientists a clean map of the most fundamental building blocks for designing new materials. These highly symmetric patterns already underlie many porous crystals and can guide the creation of future materials for gas storage, catalysis and mechanical metamaterials. By translating the mathematics of these networks into plain language, the commentary helps make this powerful but under-appreciated framework more visible to chemists, materials scientists and engineers.

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