Generation of Local Symmetry-Preserving Operations

TL;DR

This paper presents a new, general framework for local symmetry-preserving operations on polyhedra and plane graphs, enabling systematic generation of all such operations without duplicates.

Contribution

It introduces a practical, broad definition of local symmetry-preserving operations and a method to generate all isomorph-free operations using base structures and extensions.

Findings

Framework applicable to arbitrary plane graphs

Ability to generate all local symmetry-preserving operations

Ensures operations are isomorph-free

Abstract

We introduce a new practical and more general definition of local symmetry-preserving operations on polyhedra. These can be applied to arbitrary plane graphs and result in plane graphs with the same symmetry. With some additional properties we can restrict the connectivity, e.g. when we only want to consider polyhedra. Using some base structures and a list of 10 extensions, we can generate all possible local symmetry-preserving operations isomorph-free.