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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  Open image in new window  such that OABT is a regular tetrahedron, where O is the origin of  Open image in new window , and A and B are fixed points of  Open image in new window  such that OAB is a regular triangle of edge length 2. Using this description, we present Conway’s isomorphism from  Open image in new window  to  Open image in new window  in terms of matrices.

On Edge’s correspondence associated with $$\cdot 222$$ · 222