Lattice Platonic Solids and their Ehrhart polynomial

Details Lattice Platonic Solids and their Ehrhart polynomial Lattice Platonic Solids and their Ehrhart polynomial

2011-11-04

arxiv.org/abs/1111.1150v1

Mathematics

Combinatorics

12 pages, 4 figures

Scientific paper

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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