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This note wants to explain how to obtain meaningful pictures of (possibly high-dimensional) convex polytopes, triangulated manifolds, and other objects from the realm of geometric combinatorics such as tight spans of finite metric spaces and tropical polytopes. In all our cases we arrive at specific, geometrically motivated, graph drawing problems. The methods displayed are implemented in the software system polymake.
Let $ngeq 3$ and $r_n$ be a $3$-polytopal graph such that for every $3leq ileq n$, $r_n$ has at least one vertex of degree $i$. We find the minimal vertex count for $r_n$. We then describe an algorithm to construct the graphs $r_n$. A dual statement
We study the problem of embedding graphs in the plane as good geometric spanners. That is, for a graph $G$, the goal is to construct a straight-line drawing $Gamma$ of $G$ in the plane such that, for any two vertices $u$ and $v$ of $G$, the ratio bet
We report on a recent implementation of patchworking and real tropical hypersurfaces in $texttt{polymake}$. As a new mathematical contribution we provide a census of Betti numbers of real tropical surfaces.
Timeslices are often used to draw and visualize dynamic graphs. While timeslices are a natural way to think about dynamic graphs, they are routinely imposed on continuous data. Often, it is unclear how many timeslices to select: too few timeslices ca
In this paper we introduce and study the class of d-ball packings arising from edge-scribable polytopes. We are able to generalize Apollonian disk packings and the well-known Descartes theorem in different settings and in higher dimensions. After int