# Dimer models and group actions

## TL;DR

This paper constructs specific dimer models with symmetries matching their characteristic polygons, leading to new examples of non-commutative resolutions for certain complex singularities in three dimensions.

## Contribution

It introduces a method to create symmetric dimer models that yield non-commutative crepant resolutions for non-toric Gorenstein singularities.

## Key findings

- Constructed symmetric dimer models with desired properties
- Provided examples of non-commutative crepant resolutions
- Extended understanding of singularities in algebraic geometry

## Abstract

We construct a consistent dimer model having the same symmetry as its characteristic polygon. This produces examples of non-commutative crepant resolutions of non-toric non-quotient Gorenstein singularities in dimension 3.