Leech lattice
E169185
The Leech lattice is a highly symmetric 24-dimensional lattice in Euclidean space, notable for its dense sphere packing and deep connections to sporadic simple groups and modular forms.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Leech lattice canonical | 10 |
| Niemeier lattices | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1483808 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Leech lattice Context triple: [Conway groups, relatedTo, Leech lattice]
-
A.
Klein quartic
The Klein quartic is a highly symmetric algebraic curve of genus 3 that plays a central role in complex geometry, group theory, and the study of Riemann surfaces.
-
B.
Conway’s topograph
Conway’s topograph is a geometric visualization tool introduced by mathematician John H. Conway to study binary quadratic forms and their arithmetic properties using a planar graph of curves and regions.
-
C.
Levine-Fricke Field
Levine-Fricke Field is the home softball stadium of the University of California, Berkeley Golden Bears, located on the university’s campus in Berkeley, California.
-
D.
Ulam spiral
The Ulam spiral is a graphical arrangement of the positive integers in a spiral pattern that reveals striking diagonal alignments of prime numbers, suggesting unexpected structure in their distribution.
-
E.
Gauss’s lemma in number theory
Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Leech lattice Target entity description: The Leech lattice is a highly symmetric 24-dimensional lattice in Euclidean space, notable for its dense sphere packing and deep connections to sporadic simple groups and modular forms.
-
A.
Klein quartic
The Klein quartic is a highly symmetric algebraic curve of genus 3 that plays a central role in complex geometry, group theory, and the study of Riemann surfaces.
-
B.
Conway’s topograph
Conway’s topograph is a geometric visualization tool introduced by mathematician John H. Conway to study binary quadratic forms and their arithmetic properties using a planar graph of curves and regions.
-
C.
Levine-Fricke Field
Levine-Fricke Field is the home softball stadium of the University of California, Berkeley Golden Bears, located on the university’s campus in Berkeley, California.
-
D.
Ulam spiral
The Ulam spiral is a graphical arrangement of the positive integers in a spiral pattern that reveals striking diagonal alignments of prime numbers, suggesting unexpected structure in their distribution.
-
E.
Gauss’s lemma in number theory
Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
24-dimensional lattice
ⓘ
even unimodular lattice ⓘ sphere packing ⓘ |
| automorphismGroup |
Conway groups
ⓘ
surface form:
Conway group Co0
Conway groups ⓘ
surface form:
Conway group Co1
Co3 ⓘ
surface form:
Conway group Co2
Conway groups ⓘ
surface form:
Conway group Co3
|
| basisVectorsCount | 24 ⓘ |
| belongsTo |
Leech lattice
self-linksurface differs
ⓘ
surface form:
Niemeier lattices
|
| constructedFrom |
binary Golay code
ⓘ
extended binary Golay code ⓘ |
| definedIn | Euclidean space ⓘ |
| dimension | 24 ⓘ |
| discoveredBy | John Leech ⓘ |
| discoveryYear | 1965 ⓘ |
| hasCoveringRadius | sqrt(2) ⓘ |
| hasDeterminant | 1 ⓘ |
| hasMinimalVectorLength | 2 ⓘ |
| hasPackingRadius | sqrt(2) ⓘ |
| hasProperty |
even inner products
ⓘ
no vectors of squared length 2 ⓘ self-dual ⓘ |
| hasRoots | false ⓘ |
| hasSymmetryProperty | highly symmetric ⓘ |
| hasThetaSeries | weight12ModularForm ⓘ |
| isDensestSpherePackingInDimension | 24 ⓘ |
| isEven | true ⓘ |
| isIntegral | true ⓘ |
| isNiemeierLatticeWithoutRoots | true ⓘ |
| isRootless | true ⓘ |
| isUnimodular | true ⓘ |
| kissingNumber | 196560 ⓘ |
| minimalNorm | 4 ⓘ |
| relatedTo |
Conway groups
ⓘ
E8 lattice ⓘ Golay code ⓘ Monster group ⓘ modular forms ⓘ moonshine theory ⓘ sporadic simple groups ⓘ vertex operator algebras ⓘ |
| spherePackingDensity | highestKnownIn24Dimensions ⓘ |
| usedIn |
coding theory
ⓘ
conformal field theory ⓘ finite group theory ⓘ sphere packing theory ⓘ string theory ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Leech lattice Description of subject: The Leech lattice is a highly symmetric 24-dimensional lattice in Euclidean space, notable for its dense sphere packing and deep connections to sporadic simple groups and modular forms.
Referenced by (11)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Niemeier lattices