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Lattice Platonic Solids and their Ehrhart polynomial

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Author(s): E. J. Ionascu

Journal: Acta Mathematica Universitatis Comenianae
ISSN 0862-9544

Volume: LXXXII;
Issue: 1;
Start page: 147;
Date: 2013;
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Keywords: Ehrhart polynomial | linear Diophantine equations | lattice points | cubes | tetrahedra | octahedra

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 tetrahedra and those for regular lattice octahedra. These relations allow one to reduce the calculation of these polynomials to only one coefficient.
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