Regular Complex Polytopes
E415575
"Regular Complex Polytopes" is a seminal mathematical monograph by H. S. M. Coxeter that systematically develops the theory of regular polytopes in complex projective spaces.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Regular Complex Polytopes canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4105488 — 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: Regular Complex Polytopes Context triple: [H. S. M. Coxeter, notableWork, Regular Complex Polytopes]
-
A.
Regular Polytopes
"Regular Polytopes" is a classic mathematical monograph by H. S. M. Coxeter that systematically develops the theory and classification of highly symmetric polytopes in various dimensions.
-
B.
Polytopes
Polytopes are large-scale multimedia architectural and musical installations created by Iannis Xenakis that combine sound, light, and spatial design into immersive, mathematically structured environments.
-
C.
Kepler–Poinsot polyhedra
The Kepler–Poinsot polyhedra are the four regular star polyhedra that extend the concept of Platonic solids into non-convex, self-intersecting forms.
-
D.
The Fifty-Nine Icosahedra
The Fifty-Nine Icosahedra is a classic mathematical monograph by H. S. M. Coxeter that systematically classifies and analyzes the distinct stellations of the regular icosahedron.
-
E.
Euler’s polyhedron formula
Euler’s polyhedron formula is a fundamental result in topology and geometry that relates the numbers of vertices, edges, and faces of a convex polyhedron through the equation V − E + F = 2.
- 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: Regular Complex Polytopes Target entity description: "Regular Complex Polytopes" is a seminal mathematical monograph by H. S. M. Coxeter that systematically develops the theory of regular polytopes in complex projective spaces.
-
A.
Regular Polytopes
"Regular Polytopes" is a classic mathematical monograph by H. S. M. Coxeter that systematically develops the theory and classification of highly symmetric polytopes in various dimensions.
-
B.
Polytopes
Polytopes are large-scale multimedia architectural and musical installations created by Iannis Xenakis that combine sound, light, and spatial design into immersive, mathematically structured environments.
-
C.
Kepler–Poinsot polyhedra
The Kepler–Poinsot polyhedra are the four regular star polyhedra that extend the concept of Platonic solids into non-convex, self-intersecting forms.
-
D.
The Fifty-Nine Icosahedra
The Fifty-Nine Icosahedra is a classic mathematical monograph by H. S. M. Coxeter that systematically classifies and analyzes the distinct stellations of the regular icosahedron.
-
E.
Euler’s polyhedron formula
Euler’s polyhedron formula is a fundamental result in topology and geometry that relates the numbers of vertices, edges, and faces of a convex polyhedron through the equation V − E + F = 2.
- F. None of above. chosen
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical monograph ⓘ scholarly work ⓘ |
| associatedWith |
Coxeter groups theory
ⓘ
reflection group theory ⓘ |
| audience |
graduate students in mathematics
ⓘ
research mathematicians ⓘ |
| author |
H. S. M. Coxeter
ⓘ
Harold Scott MacDonald Coxeter ⓘ
linked to:
H. S. M. Coxeter
|
| contribution |
classification of regular complex polytopes associated with complex reflection groups
ⓘ
systematic development of the theory of regular complex polytopes ⓘ |
| describes | regular polytopes in complex projective space ⓘ |
| field |
complex geometry
ⓘ
geometry ⓘ mathematics ⓘ polytope theory ⓘ |
| genre |
advanced mathematics text
ⓘ
research monograph ⓘ |
| hasAuthorProfession |
geometer
ⓘ
mathematician ⓘ |
| hasPart |
chapters on complex reflection groups
ⓘ
chapters on examples of regular complex polytopes ⓘ chapters on symmetry and regularity conditions ⓘ |
| influencedBy | Regular Polytopes ⓘ |
| language | English ⓘ |
| mathematicalSubjectClassification |
20F55
ⓘ
51M20 ⓘ 52B11 ⓘ |
| notableFor |
detailed classification of regular complex polytopes
ⓘ
extending the theory of regular polytopes to complex projective spaces ⓘ rigorous group-theoretic approach to complex polytopes ⓘ |
| relatedWork | Regular Polytopes ⓘ |
| subjectOf | research in higher-dimensional geometry ⓘ |
| topic |
Coxeter groups
ⓘ
linked to:
Coxeter group
complex projective spaces ⓘ complex reflection groups ⓘ complex tessellations ⓘ regular polytopes ⓘ symmetry ⓘ unitary reflection groups ⓘ |
| usedIn |
the study of complex hyperplane arrangements
ⓘ
the study of complex reflection groups ⓘ the study of symmetry in complex projective spaces ⓘ |
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: Regular Complex Polytopes Description of subject: "Regular Complex Polytopes" is a seminal mathematical monograph by H. S. M. Coxeter that systematically develops the theory of regular polytopes in complex projective spaces.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.