MERLIN SCIENCE — Bravais Lattices and Weyl Groups: Confirming 3D Structural Taxonomy — E8 Intelligence Research

This video reviews established crystallographic taxonomy. The core material is standard textbook science: the 14 Bravais lattices in three dimensions, organized into seven crystal systems with their centering variants, and the role of Weyl groups in describing lattice symmetries. That is the finding, and it is not new. It is a confirmation of a structural framework that has been solid for over a century. For field context, we are looking at how discrete symmetry groups classify repeating patterns in space. The 14 lattices emerge from the constraint that any periodic crystal must obey one of these translational symmetries. Weyl groups, generated by reflections, act on root systems—families of vectors like A₂, B₂, and G₂—that encode the angular relationships between lattice directions. These groups are finite, and their action defines what symmetries a lattice can possess. The mechanism is straightforward and you can evaluate it directly. Quadratic forms define the metric of a lattice, Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com