A2 Root System Links Group Theory to Hexagonal Lattice Symmetry — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The search results are pedagogical links (group theory, Cartan root lattices, Lie algebra representations, root system permutohedra) — no direct Caspar-Klug T-number or hexagonal lattice A2/SU(3) primary data is present. The only concrete mathematical anchor is the mention of Cartan root lattices and root system permutohedra, which implicitly reference the A2 root system (hexagonal lattice) and its Weyl group (D6 symmetry, order 6). | MATH: A2 root system: 6 roots at 60° angles, norm form Q(x)=x₁²+x₂²−x₁x₂ (hexagonal lattice). Cartan matrix [[2,−1],[−1,2]]. Weyl group = dihedral D6 (order 12). SU(3) rank=2, roots = A2. Caspar-Klug T-number: T = h² + hk + k² (norm form of A2) — this is the hexagonal lattice norm, giving icosahedral capsid triangulations (T=1,3,4,7,9,13,...). No explicit golden ratio or base-60 appears in the provided text. | CONNECTION: The A2 root lattice IS the hexagonal lattice — its norm form T=h²+hk+k² is exactly the Caspar-Klug T-number. The hexagonal lat
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026root,
title = {{A2 Root System Links Group Theory to Hexagonal Lattice Symmetry — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23446627},
url = {https://zenodo.org/records/23446627},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A2 Root System Links Group Theory to Hexagonal Lattice Symmetry — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/18
PB - Zenodo
DO - 10.5281/zenodo.23446627
UR - https://zenodo.org/records/23446627
AB - FINDING: The search results are pedagogical links (group theory, Cartan root lattices, Lie algebra representations, root system permutohedra) — no direct Caspar-Klug T-number or hexagonal lattice A2/SU(3) primary data is present. The only concrete mathematical anchor is the mention of Cartan root lattices and root system permutohedra, which implicitly reference the A2 root system (hexagonal lattice) and its Weyl group (D6 symmetry, order 6). | MATH: A2 root system: 6 roots at 60° angles, norm form Q(x)=x₁²+x₂²−x₁x₂ (hexagonal lattice). Cartan matrix [[2,−1],[−1,2]]. Weyl group = dihedral D6 (order 12). SU(3) rank=2, roots = A2. Caspar-Klug T-number: T = h² + hk + k² (norm form of A2) — this is the hexagonal lattice norm, giving icosahedral capsid triangulations (T=1,3,4,7,9,13,...). No explicit golden ratio or base-60 appears in the provided text. | CONNECTION: The A2 root lattice IS the hexagonal lattice — its norm form T=h²+hk+k² is exactly the Caspar-Klug T-number. The hexagonal lat Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -