Wythoffian Uniform Tilings

Welcome to my visualization of uniform tilings by Wythoffian construction, so named after mathematician Willem Abraham Wythoff. A uniform tiling is a tessellation of a two-dimensional surface by regular polygon faces with the restriction of being vertex-transitive. Such tilings are demonstrated in spherical, Euclidean and hyperbolic geometries.

The tiling is constructed by your web browser and allows some interactiveity. A recent web browser is required for this to work correctly. Please note the hyperbolic tilings can take some time to compute. If a box appears asking if you want to stop the script then just let it continue and all should be fine. Click the link below to get going!

Click For Wythoffian Uniform Tilings

This is very much an on going project. Over time I'll be adding new features so check back often. The last update was 2014-12-13.

Examples

The spherical tilings of the top row are based on the (3 5 2) fundamental. The Euclidean tilings of the middle row are based on the (3 6 2) fundamental. The hyperbolic tilings of the bottom row are based on the (3 7 2) fundamental.

Each row presents the following sequence of Wythoffian operations: Primal, Truncation, Rectification, Bitruncation, Birectification, Cantellation, Omnitruncation, Snub.

Screenshots

If the tilings fail to work then you might like to check out these screenshots:

Known Bugs

The Future

Links

Tiling information from Wikipedia:

The following sites have been a great source and inspiration:


Sam Gratrix, Gratrix.net.