Penrose tilings
E201323
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.
All labels observed (7)
| Label | Occurrences |
|---|---|
| Penrose tilings canonical | 2 |
| P1 Penrose tiling | 1 |
| P2 Penrose tiling | 1 |
| P3 Penrose tiling | 1 |
| Penrose tiling | 1 |
| Penrose tiling (early conceptual contributions via family collaboration) | 1 |
| kite and dart Penrose tiling | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1796817 — 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: 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.
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
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
aperiodic tiling
ⓘ
mathematical object ⓘ non-periodic tiling ⓘ tiling of the plane ⓘ |
| developedBy | Roger Penrose ⓘ |
| fieldOfStudy |
crystallography
ⓘ
mathematical physics ⓘ mathematical tiling theory ⓘ mathematics ⓘ quasicrystal theory ⓘ |
| hasApplication |
architectural decoration
ⓘ
art and design ⓘ diffraction pattern analysis ⓘ modeling quasicrystalline solids ⓘ theoretical crystallography ⓘ |
| hasFeature |
admits inflation and deflation operations
ⓘ
finite local complexity ⓘ local matching rules determine global structure ⓘ self-similar under scaling by golden ratio ⓘ |
| hasProperty |
admits only non-periodic tilings with given prototiles and rules
ⓘ
any finite patch appears infinitely often ⓘ aperiodic ⓘ enforces aperiodicity via matching rules ⓘ exhibits fivefold rotational symmetry ⓘ hierarchical self-similarity ⓘ lacks translational symmetry ⓘ non-periodic ⓘ non-periodic but ordered structure ⓘ non-repeating pattern over the entire plane ⓘ quasi-periodic diffraction pattern ⓘ |
| hasVariant |
Penrose tilings
self-linksurface differs
ⓘ
surface form:
P1 Penrose tiling
Penrose tilings self-linksurface differs ⓘ
surface form:
P2 Penrose tiling
Penrose tilings self-linksurface differs ⓘ
surface form:
P3 Penrose tiling
Penrose tilings self-linksurface differs ⓘ
surface form:
kite and dart Penrose tiling
rhombus Penrose tiling ⓘ |
| inspired | discovery of quasicrystals ⓘ |
| namedAfter | Roger Penrose ⓘ |
| relatedTo |
Fibonacci sequence
ⓘ
aperiodic sets of prototiles ⓘ golden ratio ⓘ quasicrystals ⓘ |
| symmetryType |
decagonal symmetry
ⓘ
fivefold rotational symmetry ⓘ |
| timePeriod | introduced in the 1970s ⓘ |
| usesShape |
dart tile
ⓘ
kite tile ⓘ thick rhombus ⓘ thin rhombus ⓘ |
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: Penrose tilings Description of subject: 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.
Referenced by (8)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Penrose tiling
this entity surface form:
kite and dart Penrose tiling
this entity surface form:
P1 Penrose tiling
this entity surface form:
P2 Penrose tiling
this entity surface form:
P3 Penrose tiling
this entity surface form:
Penrose tiling (early conceptual contributions via family collaboration)