Classification of symmetric toroidal orbifolds

@article{Fischer2013ClassificationOS,
  title={Classification of symmetric toroidal orbifolds},
  author={Maximilian Fischer and Michael Ratz and Jes'us Torrado and Patrick K. S. Vaudrevange},
  journal={Journal of High Energy Physics},
  year={2013},
  volume={2013},
  pages={1-53}
}
A bstractWe provide a complete classification of six-dimensional symmetric toroidal orbifolds which yield $ \mathcal{N}\geq 1 $ supersymmetry in 4D for the heterotic string. Our strategy is based on a classification of crystallographic space groups in six dimensions. We find in total 520 inequivalent toroidal orbifolds, 162 of them with Abelian point groups such as $ {{\mathbb{Z}}_3},{{\mathbb{Z}}_4},{{\mathbb{Z}}_6}\hbox{-}\mathrm{I} $ etc. and 358 with non-Abelian point groups such as S3, D4… 

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