rhombicosidodecahedron
E620946
A rhombicosidodecahedron is a highly symmetric Archimedean solid with 62 faces (20 triangular, 30 square, and 12 pentagonal), 120 edges, and 60 vertices.
All labels observed (1)
| Label | Occurrences |
|---|---|
| rhombicosidodecahedron canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6801811 — 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: rhombicosidodecahedron Context triple: [Archimedean solids, hasElement, rhombicosidodecahedron]
-
A.
rhombicuboctahedron
A rhombicuboctahedron is a highly symmetrical Archimedean solid composed of 26 faces (8 triangular and 18 square), 24 identical vertices, and 48 edges.
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B.
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.
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C.
Johnson solids
Johnson solids are a set of 92 strictly convex polyhedra with regular polygonal faces that are not uniform, distinguishing them from Platonic, Archimedean, and other well-known regular and semi-regular solids.
-
D.
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.
-
E.
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.
- 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: rhombicosidodecahedron Target entity description: A rhombicosidodecahedron is a highly symmetric Archimedean solid with 62 faces (20 triangular, 30 square, and 12 pentagonal), 120 edges, and 60 vertices.
-
A.
rhombicuboctahedron
A rhombicuboctahedron is a highly symmetrical Archimedean solid composed of 26 faces (8 triangular and 18 square), 24 identical vertices, and 48 edges.
-
B.
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.
-
C.
Johnson solids
Johnson solids are a set of 92 strictly convex polyhedra with regular polygonal faces that are not uniform, distinguishing them from Platonic, Archimedean, and other well-known regular and semi-regular solids.
-
D.
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.
-
E.
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.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf | uniform polyhedron ⓘ |
| belongsToFamily | Archimedean solids ⓘ |
| hasAlternateName |
rhombicosidodecahedral polyhedron
ⓘ
small rhombicosidodecahedron ⓘ |
| hasCategory |
polyhedral geometry
ⓘ
three-dimensional geometry ⓘ |
| hasCircumradiusFormula | (a/2) * sqrt(8 + 2*sqrt(5)) ⓘ |
| hasConstructionMethod |
cantellation of the dodecahedron
ⓘ
cantellation of the icosahedron ⓘ rectification of the dodecahedron and icosahedron ⓘ |
| hasCoxeterDiagram | 4 3 5 ⓘ |
| hasDihedralAngleBetweenSquaresAndPentagons | 144 degrees ⓘ |
| hasDihedralAngleBetweenSquaresAndTriangles | 135 degrees ⓘ |
| hasDihedralAngleBetweenTrianglesAndPentagons | 150 degrees ⓘ |
| hasDiscoveryAttribution |
Archimedes of Syracuse
ⓘ
linked to:
Archimedes
|
| hasDualPolyhedron | deltoidal hexecontahedron ⓘ |
| hasEdgeCountRelation | each edge shared by 2 faces ⓘ |
| hasEdgeGraph | 4-regular graph with 60 vertices ⓘ |
| hasEdgeLengthSymbol | a ⓘ |
| hasEulerCharacteristic | 2 ⓘ |
| hasFaceCountRelation | 20 triangles + 30 squares + 12 pentagons = 62 faces ⓘ |
| hasFaceTransitivityCount | 3 ⓘ |
| hasFaceType |
regular pentagon
ⓘ
square ⓘ triangle ⓘ |
| hasInradiusToFacesFormula | (a/2) * sqrt(5 + 2*sqrt(5)) ⓘ |
| hasNet | multiple distinct nets ⓘ |
| hasNumberOfArchimedeanSolidIndex | 11 ⓘ |
| hasNumberOfEdges | 120 ⓘ |
| hasNumberOfFaces | 62 ⓘ |
| hasNumberOfPentagonalFaces | 12 ⓘ |
| hasNumberOfSquareFaces | 30 ⓘ |
| hasNumberOfTriangularFaces | 20 ⓘ |
| hasNumberOfVertices | 60 ⓘ |
| hasSchlafliSymbol | rr{5,3} ⓘ |
| hasSurfaceAreaFormula | A = (30 + 10*sqrt(3) + 12*sqrt(25 + 10*sqrt(5))) * a^2 ⓘ |
| hasSymmetryGroup |
Ih
ⓘ
icosahedral symmetry ⓘ |
| hasVertexConfiguration | 3.4.5.4 ⓘ |
| hasVertexFigureDescription | one triangle, two squares, one pentagon at each vertex ⓘ |
| hasVolumeFormula | V = (60 + 29*sqrt(5)) * a^3 / 3 ⓘ |
| hasWythoffSymbol | 3 | 5 2 ⓘ |
| isConvex | true ⓘ |
| isEdgeTransitive | true ⓘ |
| isFaceTransitive | false ⓘ |
| isSpaceFilling | false ⓘ |
| isUniform | true ⓘ |
| isVertexTransitive | true ⓘ |
| isZonohedron | true ⓘ |
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: rhombicosidodecahedron Description of subject: A rhombicosidodecahedron is a highly symmetric Archimedean solid with 62 faces (20 triangular, 30 square, and 12 pentagonal), 120 edges, and 60 vertices.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.