### Speaker

Dr
Gabor Gevay
(Bolyai Institute, University of Szeged)

### Description

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)

### Co-author

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