May 16 – 18, 2014
Rogla, Slovenia
UTC timezone

Zonographs and some of their applications

Not scheduled
Rogla, Slovenia

Rogla, Slovenia


Dr Gabor Gevay (Bolyai Institute, University of Szeged)


Zonohedra (or more generally, zonotopes) are a particular class of convex polytopes characterized by the property that all their 2-dimensional faces are centrally symmetric. We introduce a generalization of the graph of zonotopes, which we call a zonograph\/. We show through examples how zonographs can be used in the construction of $(n_k)$ configurations of points and circles. Zonographs also provide the possibility of a novel representation of regular maps, as follows. Let $\cal M$ be a suitable regular map of type $\{p, q\}$; furthermore, let the $f$-vector of $\mathcal M$ be $f(\mathcal M)=(v, e, f)$. Then there is a point-circle configuration of type $(v_q, f_p)$ such that the points of number $v$ correspond to the vertices of $\mathcal M$, the circles of number $f$ are circumcircles of the faces of $\mathcal M$. In addition, this configuration is isometric, which means that all of its circles are of the same size. The results presented here were obtained partly in joint work with Toma\v z Pisanski.

Primary author

Dr Gabor Gevay (Bolyai Institute, University of Szeged)


Prof. Tomaz Pisanski (University of Primorska, University of Ljubljana)

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