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A simple proof is given that the Hückel aromaticity rules generalise to cycles with an arbitrary number of half-twists, T; addition/removal of half-twists two at a time preserves all eigenvalues and degeneracies, so that closed-shell aromatic systems occur at π-electron counts 4N + 2, and antiaromatic at 4N for even T, and vice versa for odd T.

Graphical abstract: Aromaticity rules for cycles with arbitrary numbers of half-twists

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