Constructions for regular polytopes

Constructions for chiral polytopes

An abstract polytope of rank n is said to be chiral if its automorphism group has two orbits on flags, with adjacent flags lying in different orbits. In this paper, we describe a method for constructing finite chiral n-polytopes, by seeking particular normal subgroups of the orientation-preserving subgroup of n-generator Coxeter group (having the property that the subgroup is not normalized by ...

Constructions of antimagic labelings for some families of regular graphs

In this paper we construct antimagic labelings of the regular complete multipartite graphs and we also extend the construction to some families of regular graphs.

Regular polytopes

Constructions and obstructions for extremal polytopes

In the fall of 2001, I was finishing my computer science undergrad studies and Martin Skutella suggested that I take the course " Linear optimization " , a course offered to beginning math grad students and taught by Prof. Günter Ziegler. Following his advice, my fellow student Roman Wagner and I took the course, and failed badly. We lacked the necessary linear algebra and so the teaching assis...

Extremal Constructions for Polytopes and Spheres

Acknowledgements It is only fitting to continue the tradition and cite Manuel Abellanas [1] in first place. Without him and his constant encouragement, none of this would have happened. all combis in Berlin, for all the support and the excellent working environment christoph eyrich, for my´sliwska and teaching me all the λ α τ ε χ i know (and then some) Volker Kaibel, for the strongly non-polyn...