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The 36 Vertex Type

Raymond Aschheim

Ray presents the “D6” family of icosahedral quasicrystals. Emphasis is put on one member of the family, which fills space using only tetrahedrons–6 ‘golden’ tetrahedrons whose edges are of only two lengths related by the golden ratio. Ray briefly discusses their history, their relationships, how some have simple inflation rules, some can be transformed into others, and some have more complicated inflation rules. We can also compare their vertex types. They are a little more complicated than the Amman tiling and related to it, and also related to the quasicrystalline spin network (QSN), and the Elser-Sloane Quasicrystal. Ray explains the Inflation matrix and its eigenvalues.

THE BASICS

  • Emergence Theory Overview
  • Glossary
  • Emergence Theory Extras

Publications

Object Library

VIDEOS

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

THE GROUP

  • Our Staff
  • Associate Scientists
  • Our Mission
  • Our Story
  • Support Us
  • Media Coverage
  • Job Openings
  • Store
  • Grants
  • Contact

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