Emergent V₄ Symmetry in Cubic Lattice Cohomology: A Computational Study of Discrete Symmetry in FCC and Diamond Lattices
Abstract
We prove that the largest subgroup of A₄ acting on the cycle space of the FCC lattice is the Klein four-group V₄, with decomposition ker δ¹ ≅ 3·1 ⊕ χₐ ⊕ χᵦ ⊕ χ꜀. The 3-cycles of A₄ are geometrically obstructed by cubic periodicity. The same structure holds for the diamond lattice. We identify a structural parallel between this decomposition and the symmetry of the Apollonian gasket, developed in the companion paper.
Fields of Study & Subjects
Finite Group Theory Research
Geometric and Algebraic Topology
Mathematics and Applications
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 26 February 2026
- Language
- EN
- Document type
- Preprint