Lattice Platonic Solids and their Ehrhart polynomial

2011/11/04 by Eugen J. Ionaşcu, Ionascu, Eugen J.
Mathematics · #05A15 #52C07 #68R05 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Number Theory (math.NT) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1111.1150

openalex publication_date 2011/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

First, we calculate the Ehrhart polynomial associated to an arbitrary cube with integer coordinates for its vertices. Then, we use this result to derive relationships between the Ehrhart polynomials for regular lattice tetrahedrons and those for regular lattice octahedrons. These relations allow one to reduce the calculation of these polynomials to only one coefficient.

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