Statements (80)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
Penrose tiling |
| gptkbp:alternativeName |
aperiodic_tiling
pentagon_tiling tessellation tiling |
| gptkbp:canBe |
periodic
aperiodic |
| gptkbp:discoveredBy |
gptkb:Roger_Penrose
|
| gptkbp:discoveredIn |
1918
2015 |
| gptkbp:firstPublished |
1974
|
| gptkbp:hasApplication |
gptkb:architecture
physics quasicrystals mathematical art |
| gptkbp:hasEdgeMatchingRule |
arrow matching
color matching decorated tiles |
| gptkbp:hasFeature |
aperiodicity
finite local complexity hierarchical structure inflation rule local isomorphism matching rules non-repeating pattern self-similarity |
| gptkbp:hasMathematicalConstant |
gptkb:Golden_ratio
|
| gptkbp:hasMathematicalField |
mathematical quasicrystals
tiling theory |
| gptkbp:hasNumberOfKnownTypes |
15
|
| gptkbp:hasProperty |
non-periodic
quasiperiodic can tile the plane with congruent pentagons convex pentagons can sometimes tile the plane discovered by Karl Reinhardt not all pentagons can tile the plane last type discovered by Casey Mann, Jennifer McLoud-Mann, and David Von Derau |
| gptkbp:hasTilingOrder |
long-range order
global aperiodicity local fivefold symmetry no translational symmetry non-periodic order quasiperiodic order rotational symmetry |
| gptkbp:hasType |
gptkb:P2_tiling
gptkb:P3_tiling gptkb:kite_and_dart_tiling gptkb:rhombus_tiling Penrose tiling |
| gptkbp:namedAfter |
gptkb:Roger_Penrose
|
| gptkbp:notableExample |
gptkb:Cairo_tiling
gptkb:Prismatic_pentagon_tiling gptkb:Type_15_pentagon_tiling gptkb:Type_1_pentagon_tiling |
| gptkbp:relatedTo |
gptkb:Penrose_triangle
gptkb:Penrose_stairs gptkb:Ammann_tiling gptkb:Escher_tiling gptkb:Golden_ratio Penrose tiling mathematical tiling non-periodic tiling quasicrystal diffraction convex pentagon non-convex pentagon regular tiling |
| gptkbp:shape |
gptkb:palace
|
| gptkbp:studiedIn |
gptkb:geometry
gptkb:mathematics |
| gptkbp:symmetry |
fivefold rotational symmetry
|
| gptkbp:type |
plane tiling
polygonal tiling |
| gptkbp:usesShape |
dart
kite rhombus |
| gptkbp:bfsParent |
gptkb:Roger_Penrose
gptkb:Sir_Roger_Penrose gptkb:frescoes |
| gptkbp:bfsLayer |
4
|