Editing Leech lattice (section)

===As a complex lattice===

The Leech lattice is also a 12-dimensional lattice over the [[Eisenstein integers]]. This is known as the '''complex Leech lattice''', and is isomorphic to the 24-dimensional real Leech lattice. In the complex construction of the Leech lattice, the [[binary Golay code]] is replaced with the [[ternary Golay code]], and the [[Mathieu group M24|Mathieu group ''M''<sub>24</sub>]] is replaced with the [[Mathieu group M12|Mathieu group ''M''<sub>12</sub>]]. The ''E''<sub>6</sub> lattice, ''E''<sub>8</sub> lattice and [[Coxeter&ndash;Todd lattice]] also have constructions as complex lattices, over either the Eisenstein or [[Gaussian integers]].