Editing Leech lattice (section)

==History==
Many of the cross-sections of the Leech lattice, including the [[Coxeter&ndash;Todd lattice]] and [[Barnes&ndash;Wall lattice]], in 12 and 16 dimensions, were found much earlier than the Leech lattice. {{harvtxt|O'Connor|Pall|1944}} discovered a related odd unimodular lattice in 24 dimensions, now called the ''odd Leech lattice'', one of whose two even neighbors is the Leech lattice. The  Leech lattice was discovered in 1965 by {{harvs|txt|authorlink=John Leech (mathematician)|first=John|last= Leech|year=1967|loc=2.31, p. 262}}, by improving some earlier sphere packings he found {{harv|Leech|1964}}.

{{harvs|txt|authorlink=John Horton Conway|last=Conway|year=1968}} calculated the order of the [[automorphism group]] of the Leech lattice, and, working with [[John G. Thompson]], discovered three new [[sporadic group]]s as a by-product: the [[Conway groups]], Co<sub>1</sub>, Co<sub>2</sub>, Co<sub>3</sub>. They also showed that four other (then) recently announced sporadic groups, namely, [[Higman-Sims group|Higman-Sims]], [[Suzuki sporadic group|Suzuki]], [[McLaughlin group (mathematics)|McLaughlin]], and the [[Janko group]] J<sub>2</sub> could be found inside the Conway groups using the geometry of the Leech lattice. (Ronan, p.&nbsp;155)

{{quote box
|align=right
|width=33%
|quote=Bei dem Versuch, eine Form aus einer solchen Klasse wirklich anzugeben, fand ich mehr als 10 verschiedene Klassen in Γ<sub>24</sub>
|source={{harvtxt|Witt|1941|loc=p. 324}}
}}
{{harvtxt|Witt|1941|loc=p. 324}},  has a single rather cryptic sentence mentioning that he found  more than 10 even unimodular lattices in 24 dimensions without giving further details. {{harvtxt|Witt|1998|loc=p. 328–329}} stated that he found 9 of these lattices earlier in 1938, and found two more, the [[Niemeier lattice]] with A{{su|p=24|b=1}} root system and the Leech lattice (and also the odd Leech lattice), in 1940.