Johnson solids are not vertex-transitive
E620679
Johnson solids are a finite set of strictly convex polyhedra with regular polygonal faces that are neither uniform nor vertex-transitive, distinguished from Platonic and Archimedean solids by their irregular vertex configurations.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Johnson solids are not vertex-transitive canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6801821 — 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: Johnson solids are not vertex-transitive Context triple: [Archimedean solids, contrastWith, Johnson solids are not vertex-transitive]
-
A.
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.
-
B.
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.
-
C.
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.
-
D.
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.
-
E.
Regular Complex Polytopes
"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.
- 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: Johnson solids are not vertex-transitive Target entity description: Johnson solids are a finite set of strictly convex polyhedra with regular polygonal faces that are neither uniform nor vertex-transitive, distinguished from Platonic and Archimedean solids by their irregular vertex configurations.
-
A.
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.
-
B.
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.
-
C.
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.
-
D.
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.
-
E.
Regular Complex Polytopes
"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.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
class of polyhedra
ⓘ
finite set ⓘ |
| areCataloguedBy | J1 to J92 ⓘ |
| areConvex | true ⓘ |
| areConvexPolyhedra | true ⓘ |
| areEdgeTransitive | false ⓘ |
| areFaceTransitive | false ⓘ |
| areFiniteInNumber | true ⓘ |
| areNonUniformConvexPolyhedra | true ⓘ |
| areNotInfiniteFamilies | true ⓘ |
| areNotKeplerPoinsotSolids | true ⓘ |
| areNotStarPolyhedra | true ⓘ |
| areThreeDimensional | true ⓘ |
| areUniform | false ⓘ |
| areVertexTransitive | false ⓘ |
| definedBy | Norman Johnson ⓘ |
| definitionYear | 1966 ⓘ |
| differFrom |
Archimedean solids by lack of uniformity
ⓘ
Platonic solids by lack of vertex-transitivity ⓘ antiprisms by more complex combinatorial structure ⓘ prisms by more complex combinatorial structure ⓘ |
| distinguishedFrom |
Archimedean solids
ⓘ
Platonic solids ⓘ antiprisms ⓘ prisms ⓘ |
| edgeTransitivity | not edge-transitive in general ⓘ |
| enumeratedBy | Norman Johnson ⓘ |
| faceTransitivity | not face-transitive in general ⓘ |
| hasCardinality | 92 ⓘ |
| hasFaceType | regular polygons ⓘ |
| hasProperty |
non-antiprismatic
ⓘ
non-prismatic ⓘ non-uniform polyhedra ⓘ not vertex-transitive ⓘ strictly convex ⓘ |
| hasSymmetryProperty |
generally low symmetry
ⓘ
not vertex-transitive ⓘ |
| hasVertexConfiguration | irregular ⓘ |
| haveEqualAngles | not necessarily ⓘ |
| haveEqualEdgeLengths | not necessarily ⓘ |
| haveMixedFaceTypes | often ⓘ |
| haveRegularButNonIdenticalFaces | true ⓘ |
| haveRegularFaces | true ⓘ |
| sharedProperty | all faces are regular polygons ⓘ |
| sharePropertyWith | Platonic solids ⓘ |
| verificationYear | 1969 ⓘ |
| verifiedBy | Viktor Zalgaller ⓘ |
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: Johnson solids are not vertex-transitive Description of subject: Johnson solids are a finite set of strictly convex polyhedra with regular polygonal faces that are neither uniform nor vertex-transitive, distinguished from Platonic and Archimedean solids by their irregular vertex configurations.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.