Quasicrystals: Cut-and-Project Lattices, Modular Forms, and Non-Crystallographic Symmetries — E8 Intelligence Research

FINDING: Quasicrystals arise from cut-and-project of higher-dimensional lattices, linking modular forms, Macdonald identities, and lattice index Jacobi forms to non-crystallographic symmetries. | MATH: Cut-and-project method: Λ ⊂ ℝⁿ → ℝᵈ (d Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-07-27
DOI
https://doi.org/10.5281/zenodo.21617336
Primary Topic
Quasicrystal Structures and Properties
Type
preprint
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preprint

Quasicrystals: Cut-and-Project Lattices, Modular Forms, and Non-Crystallographic Symmetries — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Quasicrystal Structures and Properties
preprint

Quasicrystals: Cut-and-Project Lattices, Modular Forms, and Non-Crystallographic Symmetries — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Quasicrystals arise from cut-and-project of higher-dimensional lattices, linking modular forms, Macdonald identities, and lattice index Jacobi forms to non-crystallographic symmetries. | MATH: Cut-and-project method: Λ ⊂ ℝⁿ → ℝᵈ (d Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Quasicrystal Structures and Properties
DOIOpen Access PDFOpenAlex
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Quasicrystals: Cut-and-Project Lattices, Modular Forms, and Non-Crystallographic Symmetries — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS