PreprintCC BY 4.0Zenodo
E8‑Induced Phi‑Scaled Acoustic Bandgap Hierarchy in 3‑D Printed Quasicrystals — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
The 240 root vectors of E8 naturally partition into eight phi‑scaled families, each resonating at 132 Hz × φⁿ (n = 0…7). By arranging the vertices of the rhombic triacontahedron (the E8 3‑D projection fundamental domain) as the unit cell of a 3‑D printed acoustic metamaterial, these families manifest as a cascade of complete bandgaps that follow a Fibonacci scaling law. Excitation at the base 132 Hz frequency triggers lossless energy transfer through the hierarchical bandgap network, revealing a universal mechanism for phi‑tuned phononic control rooted in E8 geometry.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Related
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BibTeX
@misc{caldin2026e8induced,
title = {{E8‑Induced Phi‑Scaled Acoustic Bandgap Hierarchy in 3‑D Printed Quasicrystals — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23431562},
url = {https://zenodo.org/records/23431562},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - E8‑Induced Phi‑Scaled Acoustic Bandgap Hierarchy in 3‑D Printed Quasicrystals — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/17
PB - Zenodo
DO - 10.5281/zenodo.23431562
UR - https://zenodo.org/records/23431562
AB - The 240 root vectors of E8 naturally partition into eight phi‑scaled families, each resonating at 132 Hz × φⁿ (n = 0…7). By arranging the vertices of the rhombic triacontahedron (the E8 3‑D projection fundamental domain) as the unit cell of a 3‑D printed acoustic metamaterial, these families manifest as a cascade of complete bandgaps that follow a Fibonacci scaling law. Excitation at the base 132 Hz frequency triggers lossless energy transfer through the hierarchical bandgap network, revealing a universal mechanism for phi‑tuned phononic control rooted in E8 geometry. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -