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The least-area tetrahedral tile of space

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Abstract

We determine the least-area unit-volume tetrahedral tile of Euclidean space, without the constraint of Gallagher et al. that the tiling uses only orientation-preserving images of the tile. The winner remains Sommerville’s type 4v.

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Acknowledgements

The results presented in this paper came from research conducted by the 2017 Geometry Group at the Williams College SMALL NSF REU. We would like to thank our adviser Frank Morgan for his guidance on this project, as well as Stan Wagon [3, Chapt. 4] for sending us his code on reliable computation methods used in this paper. We would also like to thank the National Science Foundation; Williams College; Michigan State University; University of Maryland, College Park; and Massachusetts Institute of Technology.

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Authors and Affiliations

  1. Michigan State University, East Lansing, USA

    Eliot Bongiovanni

  2. University of Maryland, College Park, USA

    Alejandro Diaz

  3. Williams College, Williamstown, USA

    Arjun Kakkar

  4. Massachusetts Institute of Technology, Cambridge, USA

    Nat Sothanaphan

Authors
  1. Eliot Bongiovanni
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  2. Alejandro Diaz
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  3. Arjun Kakkar
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  4. Nat Sothanaphan
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Correspondence to Alejandro Diaz.

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Bongiovanni, E., Diaz, A., Kakkar, A. et al. The least-area tetrahedral tile of space. Geom Dedicata 205, 51–93 (2020). https://doi.org/10.1007/s10711-019-00465-x

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  • DOI: https://doi.org/10.1007/s10711-019-00465-x

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