# Coverings of Configurations, Prime Configurations, and Orbiconfigurations

## TL;DR

This paper explores the concept of coverings in configurations, introduces prime configurations and orbiconfigurations, and investigates conditions under which configurations are prime or bad, extending the theory of configurations with orbifold-like generalizations.

## Contribution

It introduces the notions of prime configurations and orbiconfigurations, and analyzes their properties and relationships, advancing the theoretical understanding of configuration coverings.

## Key findings

- Identifies conditions for configurations to be prime.
- Characterizes when orbiconfigurations are bad.
- Provides open questions for further research.

## Abstract

This exploratory paper considers the notion of a covering of a configuration and $G$-coverings which are coverings that are quotients under a semi-regular group action. We consider prime configurations, those which cannot $G$-cover other configurations, before considering orbiconfigurations. These are a generalized notion of a configuration in the spirit of an orbifold. We derive some specific results as to when configurations are prime as well as considering when an orbiconfiguration is bad - that is, when it cannot be $G$-covered by a configuration. A number of open questions are posited within.