Geodesic
Lattice Platonic Solids and their Ehrhart polynomial
Acta mathematica Universitatis Comenianae, Tome 82 (2013) no. 1, pp. 147-158 
E. J. Ionascu; E. J. Ionascu. Lattice Platonic Solids and their Ehrhart polynomial. Acta mathematica Universitatis Comenianae, Tome 82 (2013) no. 1, pp. 147-158. http://geodesic.mathdoc.fr/item/AMUC_2013_82_1_a10/
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     author = {E. J. Ionascu and E. J. Ionascu},
     title = { Lattice {Platonic} {Solids} and their {Ehrhart} polynomial},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {147--158},
     year = {2013},
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     url = {http://geodesic.mathdoc.fr/item/AMUC_2013_82_1_a10/}
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Voir la notice de l'article provenant de la source Comenius University

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.