The Tiling Atlas
A catalogue of tilings of the plane, the sphere, and the hyperbolic plane.
Start hereWhat is a tiling?The eleven uniform tilingsWhy exactly eleven?
The collections
Play
all three geometries33,089 tilings
Explore any tiling in the atlas from the interactive viewer.
Library
complete through k = 64,596 Euclidean tilings
Every tiling on a filterable shelf: geometry, tile class, symmetry.
Theory
exactly 11, provenUndersand the concepts
In the theory section, you can learn about the geometric concepts behind tilings.
Parquet deformations
infinite familyTilings that deform across a strip, in the tradition of Huff and Hofstadter.
Hyperbolic
infinite family28,453 tilings
Tilings of the hyperbolic plane, developed into the Poincaré disk.
Spherical
finite catalogue40 tilings
Platonic and Archimedean solids as tilings of the sphere.
Aperiodic
not available yetpage not built yet
The hat and its relatives. Tilings that never repeat.
Substitution
not available yetpage not built yet
Penrose and the subdivision families.