Dihedral Extension of the C₁₂ Atlas Reflection Symmetry and the Structure of D₁₂
Abstract
ABSTRACTThis paper extends the cyclic symmetry framework of C₁₂ to the dihedral group D₁₂ by incorporating reflection symmetry. We prove that adding a single reflection operator satisfying r s r⁻¹ = s⁻¹ enlarges C₁₂ into D₁₂, the full symmetry group of the regular 12-gon. We characterize its structure, invariant subspaces, and spectral consequences for equivariant systems.
Fields of Study & Subjects
Finite Group Theory Research
Mathematics and Applications
Advanced Algebra and Geometry
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 23 February 2026
- Language
- EN