Archimedean solids
E156203
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.
All labels observed (5)
| Label | Occurrences |
|---|---|
| Archimedean solids canonical | 3 |
| Archimedean solid | 1 |
| Catalan solids | 1 |
| cuboctahedron | 1 |
| snub cube | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1358740 — 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: Archimedean solids Context triple: [Archimedes, knownFor, Archimedean solids]
-
A.
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.
-
B.
Steinmetz solid
The Steinmetz solid is a three-dimensional geometric shape formed by the intersection of two or more cylinders at right angles, often studied in calculus and solid geometry for its interesting volume and symmetry properties.
-
C.
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.
-
D.
Klein quartic
The Klein quartic is a highly symmetric algebraic curve of genus 3 that plays a central role in complex geometry, group theory, and the study of Riemann surfaces.
-
E.
Crystal Cubism
Crystal Cubism is a refined, later phase of Cubism characterized by clear, geometric structures and a more orderly, crystalline abstraction of forms.
- 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: Archimedean solids Target entity description: 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.
-
A.
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.
-
B.
Steinmetz solid
The Steinmetz solid is a three-dimensional geometric shape formed by the intersection of two or more cylinders at right angles, often studied in calculus and solid geometry for its interesting volume and symmetry properties.
-
C.
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.
-
D.
Klein quartic
The Klein quartic is a highly symmetric algebraic curve of genus 3 that plays a central role in complex geometry, group theory, and the study of Riemann surfaces.
-
E.
Crystal Cubism
Crystal Cubism is a refined, later phase of Cubism characterized by clear, geometric structures and a more orderly, crystalline abstraction of forms.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
class of polyhedra
ⓘ
mathematical object ⓘ |
| appliedIn |
architecture
ⓘ
art ⓘ chemistry ⓘ crystallography ⓘ |
| classificationCriterion | vertex configuration ⓘ |
| contrastWith |
Johnson solids are not vertex-transitive
ⓘ
Platonic solids have only one type of face ⓘ |
| hasElement |
Archimedean solids
self-linksurface differs
ⓘ
surface form:
cuboctahedron
icosidodecahedron ⓘ rhombicosidodecahedron ⓘ rhombicuboctahedron ⓘ Archimedean solids self-linksurface differs ⓘ
surface form:
snub cube
snub dodecahedron ⓘ rhombicuboctahedron ⓘ
surface form:
truncated cube
truncated cuboctahedron ⓘ truncated dodecahedron ⓘ truncated icosahedron ⓘ truncated icosidodecahedron ⓘ truncated octahedron ⓘ truncated tetrahedron ⓘ |
| hasHistoricalAttribution |
described by Archimedes (work now lost)
ⓘ
rediscovered and published by Johannes Kepler ⓘ |
| hasNumberOfElements | 13 ⓘ |
| hasProperty |
can be inscribed in a sphere
ⓘ
convex ⓘ each edge lies between two faces ⓘ each solid is edge-transitive only in some cases ⓘ each vertex has same arrangement of faces ⓘ faces are regular polygons ⓘ faces of more than one type of regular polygon ⓘ finite number of edges ⓘ finite number of faces ⓘ finite number of vertices ⓘ highly symmetric ⓘ not all faces are congruent in a given solid ⓘ vertex-transitive ⓘ |
| namedAfter |
Archimedes
ⓘ
surface form:
Archimedes of Syracuse
|
| relatedTo |
Archimedean solids
self-linksurface differs
ⓘ
surface form:
Catalan solids
Johnson solids ⓘ Kepler–Poinsot polyhedra ⓘ Platonic solids ⓘ |
| studiedIn |
geometry
ⓘ
polyhedral combinatorics ⓘ |
| subclassOf |
convex polyhedra
ⓘ
semiregular polyhedra ⓘ uniform polyhedra ⓘ |
| uses | regular polygons as faces ⓘ |
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: Archimedean solids Description of subject: 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.
Referenced by (7)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Archimedean solid
this entity surface form:
Catalan solids
this entity surface form:
cuboctahedron
this entity surface form:
snub cube