ACTA MATHEMATICA
UNIVERSITATIS COMENIANAE





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
-->





Acta Mathematica Universitatis Comenianae
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