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August 2, 20260 citationsOpen Access

Penrose Tiling Shows Fivefold Symmetry in Aperiodic Quasicrystals

Penrose Tiling: Fivefold Symmetry in Aperiodic Quasicrystals — E8 Intelligence Research

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Authors

ACAndrew Stewart Caldin

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Overview

Finding demonstrates mathematical possibility of fivefold symmetry in quasicrystals, indicating new material class.

Key Points

  • This research aims to demonstrate the mathematical feasibility of fivefold symmetry in aperiodic quasicrystals using Penrose tiling.
  • Analyzed Penrose tiling patterns for fivefold symmetry using angles of 36° and 72°.
  • Investigated diffraction patterns revealing sharp Bragg peaks characteristic of aperiodicity.
  • Explored geometric relationships governed by the golden ratio and their implications in higher-dimensional projections.
  • Penrose tiling proved that fivefold symmetry is possible in aperiodic quasicrystals, challenging classical crystallography.
  • Diffraction patterns exhibited sharp Bragg peaks consistent with fivefold symmetry.
  • Geometric harmony was established through tile area ratios and vertex configurations defined by the golden ratio.

Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a6eeaaf1b0468a7eeab30bfhttps://doi.org/10.5281/zenodo.21714307
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