Tilings Encyclopedia | Roger Penrose

One manifestation of the famous Penrose tilings. In fact, this is the first manifestation found by Penrose, the Penrose rhomb, the Penrose kite-dart and the Robinson triangle tilings are refinements of this one. (You may also click ‘Penrose’ below ‘MLD-class’ above to see the others.) Their properties are discussed on the page Penrose rhomb. For a more detailed discussion see [GS87] .

Finite Rotations Polytopal Tiles Mld Class Penrose

Penrose Rhomb

Certainly the most popular substitution tilings. Discovered in 1973 and 1974 by R. Penrose in - at least - three versions (Rhomb, Penrose kite-dart and Penrose Pentagon boat star), all of them forcing nonperiodic tilings by matching rules. It turns out that the three versions are strongly related: All three generate the same mld-class. These tiles, their matching rules and the corresponding substitution was studied thoroughly in [GS87] . A lot of information can be found there.

Without Decoration Finite Rotations Polytopal Windowed Tiling Canonical Substitution Tiling Rhomb Tiles Mld Class Penrose Matching Rules

Penrose Kite Dart

A classic, using a kite (blue) and a dart (orange) as prototiles. See Penrose Rhomb for more details.

Without Decoration Finite Rotations Polytopal Windowed Tiling Polytopal Tiles Mld Class Penrose

Roger Penrose

Discovered Tilings