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Classification of Quasicrystals by intersecting lattices and spheres

Raymond Aschheim

We discover how successive shells of onion-like spheres intersecting square grids in high dimensional spaces will classify points of integral coordinates as solutions of Diophantine equations.

From this very simple construction emerges a deep link between the geometry of quasicrystals and the algebraic numbers, and also a link to number theory, from the sigma function counting the divisors, to more advanced Jacobi elliptic function and Dirichlet L-Series. Many applications to quasicrystals of icosahedral symmetry are presented, including the QSN.

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THE BASICS

  • Emergence Theory Overview
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  • Emergence Theory Extras

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  • Movies
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  • Guest Lectures & Presentations
  • Visualizations and Animations
  • For Fun

THE GROUP

  • Our Staff
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  • The Theory
    • The Basics
      • Emergence Theory Overview
      • Glossary
      • Emergence Theory Extras
    • Publications
      • All Papers
      • Golden Ratio/Packing of Tetrahedra
      • Geometry
      • Geometric Topology
      • Quasicrystals
      • E8 Quasicrystals and the QSN
      • Spin Network
      • Number Theory
      • Unification
      • Cosmology
      • Quantum Computing
      • Conference Materials
    • Videos
      • Movies
      • QGR Lectures and Presentations
      • Guest Lectures and Presentations
      • Visualizations and Animations
      • For Fun
      • Meet Our Scientists
    • Object Library
  • The Group
    • Our Staff
    • Associate Scientists
    • Our Mission
    • Our Story
    • Media Coverage
    • Job Openings
    • Blog
    • Teespring Store
    • Grants
    • Contact
  • Support Us