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Theoretical modeling demonstrates the construction of three-periodic tangled helical nets from crystal scaffolds, revealing recurring geometric motifs across crystalline and biological systems.
In this paper, a selection of elegant, highly symmetric examples of three-periodic tangled nets and filaments is presented. They are constructed via familiar crystal nets using edges as geometric scaffolds for n-fold helical windings. Rather than providing a complete classification, this gallery of examples highlights recurring geometric motifs, offering insights into how periodic tangles are organized in crystalline, molecular and biological systems. This article is part of the theme issue ‘Geometry, materials and the imagination’.
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Myfanwy E. Evans (2026) studied this question.
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