The Uniqueness of the Foam Cell: Exhaustive Face Laplacian Check of All Fedorov Parallelohedra
Abstract
The face adjacency Laplacian is computed for all five Fedorov parallelohedra. The truncated octahedron is proved unique in having prime discriminant (Δ=17), integer eigenvalue products (r₁r₂=16=Δ−1), and perfect square eigenvalue sum (r₁+r₂=9=3²). Pure mathematics — no physics assumptions required.
Fields of Study & Subjects
Graph theory and applications
Quasicrystal Structures and Properties
Finite Group Theory Research
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 7 April 2026
- Language
- EN
- Document type
- Preprint