Steinmetz solid
E61291
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Steinmetz solid canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T490381 — 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: Steinmetz solid Context triple: [Charles Proteus Steinmetz, knownFor, Steinmetz solid]
-
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.
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.
-
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.
Levitated Mass
Levitated Mass is a large-scale outdoor sculpture by artist Michael Heizer featuring a massive suspended boulder installed at the Los Angeles County Museum of Art.
-
E.
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.
- 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: Steinmetz solid Target entity description: 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.
-
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.
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.
-
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.
Levitated Mass
Levitated Mass is a large-scale outdoor sculpture by artist Michael Heizer featuring a massive suspended boulder installed at the Los Angeles County Museum of Art.
-
E.
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.
- F. None of above. chosen
Statements (37)
| Predicate | Object |
|---|---|
| instanceOf |
geometric solid
ⓘ
mathematical object ⓘ solid of intersection ⓘ |
| appearsIn |
problems on triple integrals
ⓘ
undergraduate calculus textbooks ⓘ |
| boundary | formed by cylindrical surfaces ⓘ |
| category | solid of revolution applications ⓘ |
| context | Euclidean 3-dimensional space ⓘ |
| coordinateSystem |
often described in Cartesian coordinates
ⓘ
often described in cylindrical coordinates ⓘ |
| definedAs | intersection of two or more cylinders at right angles ⓘ |
| dimension | 3 ⓘ |
| field |
calculus
ⓘ
geometry ⓘ solid geometry ⓘ |
| generalizationOf | intersection of more than two mutually perpendicular cylinders ⓘ |
| hasAxisConfiguration | cylinder axes intersect at right angles ⓘ |
| hasExample | intersection of two perpendicular unit cylinders ⓘ |
| hasProperty |
high degree of symmetry
ⓘ
non-convex surface ⓘ smooth surface ⓘ |
| namedAfter | Charles Proteus Steinmetz ⓘ |
| relatedTo |
cylinder
ⓘ
multiple integrals ⓘ volume of intersection ⓘ |
| specialCase | intersection of two equal cylinders of radius r with perpendicular axes ⓘ |
| studiedFor |
applications in analytic geometry
ⓘ
integration over complex regions ⓘ symmetry properties ⓘ |
| symmetry |
invariant under 90-degree rotations exchanging cylinder axes
ⓘ
symmetric with respect to coordinate planes containing cylinder axes ⓘ |
| topology | simply connected ⓘ |
| usedIn |
examples of change of variables in integration
ⓘ
multiple integral exercises ⓘ visualization of solid intersections ⓘ volume computation problems ⓘ |
| visualization | often illustrated as a shape with four rounded lobes ⓘ |
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: Steinmetz solid Description of subject: 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.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.