Ideal spatial graph configurations

Abstract

Graphs are typically represented in published research literature as two-dimensional images, for obvious reasons. With the increased accessibility of 3D rendering software and 3D printing hardware, we can now represent graphs in three dimensions more easily. Years of published work in the field have led to certain ‘standard’ two-dimensional configurations of well-known graphs such as the Petersen graph or , but there is no such standard for illustrations of graphs in three-dimensional space. Ideally, a spatial graph configuration should highlight the primary properties and features of the graph, as well as be aesthetically pleasing to view. In this paper, we will suggest and realize standard ideal spatial configurations for a variety of well-known graphs and families of graphs. These configurations can help provide fresh three-dimensional intuition about certain families of graphs, in particular the relationships between graphs in the Petersen family.