Coxeter group
E1246953
UNEXPLORED
A Coxeter group is an abstract group generated by reflections across hyperplanes, fundamental in the classification and study of regular polytopes, tessellations, and symmetries in geometry and algebra.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Coxeter group canonical | 1 |
| Coxeter groups | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T16991609 — 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: Coxeter group Context triple: [Regular Polytopes, relatedConcept, Coxeter group]
-
A.
Weyl group
A Weyl group is a finite reflection group associated with a root system that encodes the symmetries of Lie algebras and Lie groups in representation theory and geometry.
-
B.
Coxeter–Dynkin diagrams
Coxeter–Dynkin diagrams are graphical representations that encode the structure of reflection groups and root systems, widely used in the classification of regular polytopes, Lie algebras, and symmetries.
-
C.
Conway groups
Conway groups are a set of three closely related sporadic simple groups discovered by John H. Conway in the study of symmetries of the Leech lattice in group theory.
-
D.
Harada–Norton group
The Harada–Norton group is one of the 26 sporadic simple groups in finite group theory, notable for its large order and close relationship to the Monster group.
-
E.
Chevalley groups
Chevalley groups are a broad class of linear algebraic groups constructed over arbitrary fields that generalize classical Lie groups and play a central role in the classification of finite simple groups.
- 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: Coxeter group Target entity description: A Coxeter group is an abstract group generated by reflections across hyperplanes, fundamental in the classification and study of regular polytopes, tessellations, and symmetries in geometry and algebra.
-
A.
Weyl group
A Weyl group is a finite reflection group associated with a root system that encodes the symmetries of Lie algebras and Lie groups in representation theory and geometry.
-
B.
Coxeter–Dynkin diagrams
Coxeter–Dynkin diagrams are graphical representations that encode the structure of reflection groups and root systems, widely used in the classification of regular polytopes, Lie algebras, and symmetries.
-
C.
Conway groups
Conway groups are a set of three closely related sporadic simple groups discovered by John H. Conway in the study of symmetries of the Leech lattice in group theory.
-
D.
Harada–Norton group
The Harada–Norton group is one of the 26 sporadic simple groups in finite group theory, notable for its large order and close relationship to the Monster group.
-
E.
Chevalley groups
Chevalley groups are a broad class of linear algebraic groups constructed over arbitrary fields that generalize classical Lie groups and play a central role in the classification of finite simple groups.
- F. None of above. chosen
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Coxeter groups