Triple
T1796817
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Mathematical Games |
E39621
|
entity |
| Predicate | notableTopic |
P494
|
FINISHED |
| Object |
Penrose tilings
Penrose tilings are non-periodic tilings of the plane that use a small set of shapes to create patterns with fivefold symmetry and no translational repetition, widely studied in mathematics and physics.
|
E201323
|
NE FINISHED |
How this triple was built (4 steps)
Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.
NER
Named-entity recognition
gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Penrose tilings | Statement: [Mathematical Games, notableTopic, Penrose tilings]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Penrose tilings Context triple: [Mathematical Games, notableTopic, Penrose tilings]
-
A.
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.
-
B.
Ulam spiral
The Ulam spiral is a graphical arrangement of the positive integers in a spiral pattern that reveals striking diagonal alignments of prime numbers, suggesting unexpected structure in their distribution.
-
C.
Farey tessellation
The Farey tessellation is a geometric partition of the hyperbolic plane into ideal triangles whose vertices correspond to rational numbers, closely linked to number theory and modular group actions.
-
D.
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.
-
E.
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.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Penrose tilings Triple: [Mathematical Games, notableTopic, Penrose tilings]
Generated description
Penrose tilings are non-periodic tilings of the plane that use a small set of shapes to create patterns with fivefold symmetry and no translational repetition, widely studied in mathematics and physics.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Penrose tilings Target entity description: Penrose tilings are non-periodic tilings of the plane that use a small set of shapes to create patterns with fivefold symmetry and no translational repetition, widely studied in mathematics and physics.
-
A.
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.
-
B.
Ulam spiral
The Ulam spiral is a graphical arrangement of the positive integers in a spiral pattern that reveals striking diagonal alignments of prime numbers, suggesting unexpected structure in their distribution.
-
C.
Farey tessellation
The Farey tessellation is a geometric partition of the hyperbolic plane into ideal triangles whose vertices correspond to rational numbers, closely linked to number theory and modular group actions.
-
D.
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.
-
E.
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.
- F. None of above. chosen
Provenance (5 batches)
The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.
| Step | Stage | Batch ID | Status | When |
|---|---|---|---|---|
| creating | Elicitation | batch_69a88632aa588190ba3978fde0db5bbd |
completed | March 4, 2026, 7:21 p.m. |
| NER | Named-entity recognition | batch_69aa6566cd808190a67f33ad47d8ca8e |
completed | March 6, 2026, 5:25 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69adb5d6cee88190b26814134037aba6 |
completed | March 8, 2026, 5:45 p.m. |
| NEDg | Description generation | batch_69adb8b626688190b4953d4549339dea |
completed | March 8, 2026, 5:58 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69adb9253fa08190bfb7d245208150c0 |
completed | March 8, 2026, 6 p.m. |
Created at: March 4, 2026, 7:32 p.m.