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July 26, 20260 citationsOpen Access

Exploring Penrose Tilings and 5-Fold Symmetry in Aperiodic Quasicrystals

Penrose Tilings: 5-Fold Symmetry in Aperiodic Quasicrystals — E8 Intelligence Research

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Authors

ACAndrew Stewart Caldin

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Overview

This research reveals five-fold symmetry in aperiodic quasicrystals, indicating new geometric possibilities.

Key Points

  • The aim is to demonstrate the existence of five-fold rotational symmetry in aperiodic quasicrystals using Penrose tilings.
  • Analyzed non-repeating geometric rules in Penrose tilings.
  • Calculated properties using the golden ratio and hyperbolic geometry.
  • Applied C*-algebra and K-theory for classification.
  • Found that Penrose tilings exhibit five-fold symmetry, previously believed impossible in periodic structures.
  • Established connections between tile angles and the golden ratio.
  • Demonstrated that the inflation factor for Penrose tilings is equal to the golden ratio.
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Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a65a91fd3aea3239cd791f2https://doi.org/10.5281/zenodo.21524483
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