Lattice Platonic Solids and their Ehrhart polynomial
E. J. Ionascu
Received: July 11, 2012; Revised: September 18, 2012; Accepted: September 20, 2012
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.
Keywords: Ehrhart polynomial; linear Diophantine equations; lattice points; cubes; tetrahedra; octahedra.
AMS Subject classification: Primary: 52C07, 05A15, 68R05
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