Platonic solids
E36442
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.
All labels observed (7)
| Label | Occurrences |
|---|---|
| Platonic solids canonical | 19 |
| De quinque corporibus regularibus | 1 |
| Lectures on the Icosahedron | 1 |
| Tetrahedron | 1 |
| cube–octahedron | 1 |
| dodecahedron–icosahedron | 1 |
| icosahedron | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T281296 — 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: Platonic solids Context triple: [Plato, hasPhilosophicalConcept, Platonic solids]
-
A.
construction of the regular 17-gon with straightedge and compass
The construction of the regular 17-gon with straightedge and compass is a classical geometric achievement, first shown possible by Carl Friedrich Gauss, that exemplifies the link between constructible polygons and number theory.
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B.
Mathematical Bridge
The Mathematical Bridge is a famous wooden footbridge at Queens' College, Cambridge, known for its elegant arch that is constructed entirely from straight timbers.
-
C.
Minkowski sum
The Minkowski sum is a fundamental operation in geometry and convex analysis that combines two sets by adding every vector in one set to every vector in the other, widely used in areas such as optimization, robotics, and computational geometry.
-
D.
Q-balls
Q-balls are hypothetical, stable, non-topological solitons predicted in certain quantum field theories, often considered as exotic candidates for dark matter or new physics beyond the Standard Model.
-
E.
Pyramid
Pyramid is a lightweight, flexible Python web framework designed to scale from small applications to large, complex systems while offering great configurability and extensibility.
- 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: Platonic solids Target entity description: 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.
-
A.
construction of the regular 17-gon with straightedge and compass
The construction of the regular 17-gon with straightedge and compass is a classical geometric achievement, first shown possible by Carl Friedrich Gauss, that exemplifies the link between constructible polygons and number theory.
-
B.
Mathematical Bridge
The Mathematical Bridge is a famous wooden footbridge at Queens' College, Cambridge, known for its elegant arch that is constructed entirely from straight timbers.
-
C.
Minkowski sum
The Minkowski sum is a fundamental operation in geometry and convex analysis that combines two sets by adding every vector in one set to every vector in the other, widely used in areas such as optimization, robotics, and computational geometry.
-
D.
Q-balls
Q-balls are hypothetical, stable, non-topological solitons predicted in certain quantum field theories, often considered as exotic candidates for dark matter or new physics beyond the Standard Model.
-
E.
Pyramid
Pyramid is a lightweight, flexible Python web framework designed to scale from small applications to large, complex systems while offering great configurability and extensibility.
- F. None of above. chosen
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
class of polyhedra
ⓘ
geometric solids ⓘ mathematical concept ⓘ |
| areAll |
convex regular polyhedra
ⓘ
edge-transitive polyhedra ⓘ examples of regular maps on the sphere ⓘ face-transitive polyhedra ⓘ finite polyhedra ⓘ isogonal polyhedra ⓘ isohedral polyhedra ⓘ isotoxal polyhedra ⓘ vertex-transitive polyhedra ⓘ |
| areContrastedWith |
Archimedean solids
ⓘ
Kepler–Poinsot polyhedra ⓘ |
| areSubsetOf |
convex polyhedra
ⓘ
regular polyhedra ⓘ |
| associatedWith | Plato ⓘ |
| classificationCriterion | regularity of faces and vertices ⓘ |
| describedIn |
Book XIII of Euclid's Elements
ⓘ
Euclid's Elements ⓘ |
| dualPair |
cube–octahedron
ⓘ
linked to:
Platonic solids
dodecahedron–icosahedron ⓘ
linked to:
Platonic solids
tetrahedron–tetrahedron ⓘ |
| edgeProperty | same number of faces meet at each edge ⓘ |
| existIn | three-dimensional Euclidean space ⓘ |
| faceType | congruent regular polygons ⓘ |
| hasMember |
cube
ⓘ
dodecahedron ⓘ icosahedron ⓘ
linked to:
Platonic solids
octahedron ⓘ tetrahedron ⓘ |
| hasProperty |
convex
ⓘ
highly symmetrical ⓘ regular polyhedra ⓘ |
| haveDualityProperty | each has a dual Platonic solid ⓘ |
| haveHistoricalOrigin | ancient Greek mathematics ⓘ |
| numberOfElements | 5 ⓘ |
| philosophicalRole | linked to classical elements in Platonism ⓘ |
| studiedBy | Euclid ⓘ |
| symmetryGroupType | finite rotation groups ⓘ |
| topology | homeomorphic to the sphere ⓘ |
| uniquenessProperty | only five convex regular polyhedra exist in 3D Euclidean space ⓘ |
| usedIn |
architecture
ⓘ
art ⓘ chemistry ⓘ classical philosophy ⓘ crystallography ⓘ geometry ⓘ group theory ⓘ |
| vertexProperty | same number of faces meet at each vertex ⓘ |
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: Platonic solids Description of subject: 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.
Referenced by (25)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Platonic solids
linked to: Platonic solids
linked to: Platonic solids
linked to: Platonic solids
linked to: Platonic solids
linked to: Platonic solids
subject linked to:
Johnson solids are not vertex-transitive
subject linked to:
Johnson solids are not vertex-transitive