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On Edge’s correspondence associated with \(\cdot 222\)

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Abstract

We describe explicitly the correspondence of Edge between the set of planes contained in the Fermat cubic fourfold in characteristic 2, and the set of lattice points T of the Leech lattice such that OABT is a regular tetrahedron, where O is the origin of , and A and B are fixed points of such that OAB is a regular triangle of edge length 2. Using this description, we present Conway’s isomorphism from to in terms of matrices.

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Acknowledgements

Thanks are due to the referee for comments on the first version of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, 739-8526, Japan

    Ichiro Shimada

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  1. Ichiro Shimada
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Correspondence to Ichiro Shimada.

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This work was supported by JSPS KAKENHI Grant Numbers JP16K13749, JP16H03926.

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Shimada, I. On Edge’s correspondence associated with \(\cdot 222\) . European Journal of Mathematics 4, 399–412 (2018). https://doi.org/10.1007/s40879-017-0183-z

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  • DOI: https://doi.org/10.1007/s40879-017-0183-z

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