Abstract

Recently, Rybnikov and Erdahl [R. Erdahl, K. Rybnikov, Supertopes, Supertopes.pdf at http://faculty.uml.edu/krybnikov/, 2002] constructed an infinite series of asymmetric extreme lattice Delaunay polytopes for dimensions n≥6. Dutour [M. Dutour, An infinite series of extreme Delaunay polytopes, European J. Combin. (2003) (in press)] constructed another infinite series of asymmetric extreme Delaunay polytopes P_Du(n) for all even dimensions n≥6. An analysis of the first series allows one to construct two two-parametric series P(n;t) and P_A(n;t) of asymmetric extreme Delaunay polytopes such that . In addition, for each asymmetric extreme Delaunay polytope P of dimension n, an explicit construction of a symmetric extreme Delaunay polytope of dimension n+1 having P as a section is given.

Article Outline

1. Introduction

2. How to compute the rank of a Delaunay polytope

3. A symmetric polytope generated by an asymmetric one

4. An infinite series of extreme Delaunay polytopes by Dutour

5. A two-parametric infinite series of extreme Delaunay polytopes

6. A series of asymmetric extreme Delaunay polytopes from the P(n;t)-series

References