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Miracle Octad Generator
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Miracle Octad Generator : ウィキペディア英語版
Miracle Octad Generator
In mathematics, the Miracle Octad Generator, or MOG, is a mathematical tool introduced by for manipulating the Mathieu groups, binary Golay code and Leech lattice.
==Description==
The Miracle Octad Generator is an array of coordinates, arranged in four rows and six columns, capable of describing any point in 24-dimensional space. It is remarkable in the fact that it reflects all of the symmetries of the Mathieu group M24, despite its simplicity. More specifically, it preserves the maximal subgroups of M24, namely the monad group, duad group, triad group, octad group, octern group, sextet group, trio group and duum group. This makes it invaluable, as it can be used to study all of these symmetries without having to visualise 24-dimensional space.

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