Lattice Platonic Solids and their Ehrhart polynomial
Combinatorics
2011-11-07 v1 Number Theory
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.
Cite
@article{arxiv.1111.1150,
title = {Lattice Platonic Solids and their Ehrhart polynomial},
author = {Eugen J. Ionascu},
journal= {arXiv preprint arXiv:1111.1150},
year = {2011}
}
Comments
12 pages, 4 figures