The Fifty-Nine Icosahedra
E412210
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| The Fifty-Nine Icosahedra canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4105490 — 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: The Fifty-Nine Icosahedra Context triple: [H. S. M. Coxeter, notableWork, The Fifty-Nine Icosahedra]
-
A.
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.
-
B.
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.
-
C.
Archimedean solids
Archimedean solids are a set of thirteen highly symmetric, semi-regular convex polyhedra characterized by identical vertices and faces composed of more than one type of regular polygon.
-
D.
Platonic solids
Platonic solids are the five highly symmetrical, convex polyhedra (tetrahedron, cube, octahedron, dodecahedron, and icosahedron) that have identical regular polygonal faces and are fundamental in geometry and classical philosophy.
-
E.
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.
- 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: The Fifty-Nine Icosahedra Target entity description: 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.
-
A.
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.
-
B.
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.
-
C.
Archimedean solids
Archimedean solids are a set of thirteen highly symmetric, semi-regular convex polyhedra characterized by identical vertices and faces composed of more than one type of regular polygon.
-
D.
Platonic solids
Platonic solids are the five highly symmetrical, convex polyhedra (tetrahedron, cube, octahedron, dodecahedron, and icosahedron) that have identical regular polygonal faces and are fundamental in geometry and classical philosophy.
-
E.
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.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical monograph ⓘ |
| aimsTo | enumerate all distinct stellations of the regular icosahedron ⓘ |
| analyzes | distinct stellations of the regular icosahedron ⓘ |
| author |
H. S. M. Coxeter
ⓘ
H. S. M. Coxeter ⓘ
surface form:
Harold Scott MacDonald Coxeter
|
| classificationCriterion | face-extension rules for stellation ⓘ |
| coAuthor |
H. T. Flather
ⓘ
J. F. Petrie ⓘ P. Du Val ⓘ |
| countryOfPublication | Canada ⓘ |
| field |
discrete geometry
ⓘ
mathematics ⓘ polyhedral geometry ⓘ |
| focusesOn | stellations of the regular icosahedron ⓘ |
| hasFormat | print ⓘ |
| hasIllustrationsBy | J. F. Petrie ⓘ |
| hasMainObjectOfStudy | regular icosahedron ⓘ |
| hasMainPolyhedron | icosahedron ⓘ |
| hasNotation | geometric notation for stellation regions ⓘ |
| hasPageCountApprox | 50–60 pages ⓘ |
| hasReprints | yes ⓘ |
| influenced |
later work on uniform polyhedra
ⓘ
research on stellated polyhedra ⓘ |
| isConsidered |
classic work in polyhedral geometry
ⓘ
standard reference on stellations of the icosahedron ⓘ |
| isUsedBy |
mathematical model builders
ⓘ
polyhedron researchers ⓘ |
| isUsedIn | advanced geometry courses ⓘ |
| language | English ⓘ |
| numberOfStellationsClassified | 59 ⓘ |
| provides |
combinatorial analysis of stellations
ⓘ
diagrams of stellated icosahedra ⓘ geometric analysis of stellations ⓘ systematic classification of icosahedron stellations ⓘ |
| publicationYear | 1938 ⓘ |
| publisher | University of Toronto Press ⓘ |
| relatedTo |
Kepler–Poinsot polyhedra
ⓘ
regular polyhedra ⓘ stellations of the dodecahedron ⓘ |
| subject |
geometry
ⓘ
polyhedra ⓘ regular icosahedron ⓘ stellation ⓘ |
| uses | symmetry of the icosahedral group ⓘ |
| usesConcept |
stellation diagram
ⓘ
symmetry planes of the icosahedron ⓘ |
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: The Fifty-Nine Icosahedra Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.