This repository contains the code, functions, and additional material associated with the paper:
"Constructing triangulations and corresponding polyhedra with dihedral symmetry"
Authors: Meike Weiß, Vanishree Krishna Kirekod, Reymond Akpanya, Alice C. Niemeyer, Daniel Robertz
Abstract
A planar triangulation is a planar drawing of a maximal planar graph such that (1) any two drawn edges intersect at most in their endpoints and (2) every face of the drawing is bounded by a 3-cycle of the planar graph. In this paper, we investigate the construction of polyhedra arising from maximal planar graphs. In particular, we construct a family of maximal planar graphs with dihedral automorphism groups. Moreover, we demonstrate that these graphs can be realized as polyhedra in the Euclidean 3-space with dihedral symmetry groups. We achieve this result by exploiting Grünbaum-colourings.
The repository includes implementations of the algorithms and methods described in the paper:
- Graph Construction: Scripts to generate maximal planar graphs with dihedral symmetry groups.
- Polyhedral Realizations: Functions for embedding maximal planar graphs in 3D Euclidean space as polyhedra with dihedral symmetry.
Examples of generated triangulations and their corresponding polyhedral realizations.
Precomputed graphs and polyhedra for specific cases discussed in the paper. STL files for 3D printing.