Abstract
An \((n+1)\)-toroid is a quotient of a tessellation of the n-dimensional Euclidean space with a lattice group. Toroids are generalisations of maps on the torus to higher dimensions and also provide examples of abstract polytopes. Equivelar toroids are those that are induced by regular tessellations. In this paper we present a classification of equivelar \((n+1)\)-toroids with at most n flag-orbits; in particular, we discuss a classification of 2-orbit toroids of arbitrary dimension.
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Acknowledgements
Both authors where supported by PAPIIT-México under Project Grant IN101615 as well as by the National Council of Science and Technology of Mexico (CONACyT México). The authors also want to thank the anonymous referee as well as Isabel Hubard and Daniel Pellicer for their valuable comments on this work. The research on this paper was developed while the first author was a visiting student in Centro de Ciencias Matemáticas, National Autonomous University of Mexico (UNAM), Unidad Morelia, Mexico, and the second author was a student in the same institution.
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Collins, J., Montero, A. Equivelar Toroids with Few Flag-Orbits. Discrete Comput Geom 65, 305–330 (2021). https://doi.org/10.1007/s00454-020-00230-y
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DOI: https://doi.org/10.1007/s00454-020-00230-y