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
Version to read:
PDF --> ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2012, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |