Barycentric Drawings of Periodic Graphs

Abstract

We study barycentric placement of vertices in periodic graphs of dimension 2 or higher. Barycentric placements exist for every connected periodic graph, are unique up to affine transformations, and provide a versatile tool not only in drawing, but also in computation. Example applications include symmetric convex drawing in dimension 2 as well as determining topological types of crystals and computing their ideal symmetry groups. © Springer-Verlag 2004.