preprintZenodo (CERN European Organization for Nuclear Research)Apr 7, 2026GREEN OA

The Uniqueness of the Foam Cell: Exhaustive Face Laplacian Check of All Fedorov Parallelohedra

LMLuke Martinelli
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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.

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Topics & keywords

Topics
Keywords
  • Eigenvalues and eigenvectors
  • Uniqueness
  • Laplace operator
  • Face (sociological concept)
  • Adjacency list
  • Integer (computer science)
  • Square (algebra)
UN Sustainable Development Goals
  • Reduced inequalities
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