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July 27, 20260 citationsOpen Access

Penrose Tilings Show Forbidden Symmetry in Aperiodic Quasicrystals

Penrose Tilings: Forbidden Symmetry in Aperiodic Quasicrystals — E8 Intelligence Research

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Authors

ACAndrew Stewart Caldin

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Overview

Finding shows fivefold symmetry is possible in aperiodic quasicrystals, implying new structural insights.

Key Points

  • To explore the mathematical possibility of fivefold symmetry in aperiodic quasicrystals using Penrose tilings.
  • Mathematical analysis of Penrose tilings involving thin and thick rhombi with respective angles.
  • Examination of Bragg peaks in quasicrystal diffraction patterns indicating fivefold symmetry.
  • Connection of geometric concepts such as the golden ratio and pentagon geometry to the tiling structure.
  • Demonstrated that fivefold rotational symmetry is possible in aperiodic quasicrystals via Penrose tiling.
  • Identified sharp Bragg peaks in diffraction patterns consistent with fivefold symmetry.
  • Revealed relationships between angles in Penrose tiling and the golden ratio, enhancing understanding of geometric harmony.

Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a6700a340bca442e0d4a839https://doi.org/10.5281/zenodo.21545146
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