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arXiv · 1708.06054

On Edge's correspondence associated with \cdot 222

Ichiro Shimada
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Abstract

We describe explicitly the correspondence of Edge between the set of planes contained in the Fermat cubic 4-fold 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 the Leech lattice, and A and B are fixed points of the Leech lattice such that OAB is a regular triangle of edge length 2. Using this description, we present Conway's isomorphism from PSU(6,4) to \cdot 222 in terms of matrices.

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Ichiro Shimada. 2017-08-21. On Edge's correspondence associated with \cdot 222. https://arxiv.org/abs/1708.06054

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