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 using JavaScript and then displayed somewhat interactively using Scalar Vector Graphics (SVG). A recent standards compliant browser is required for this to work - I've been using Firefox and Chrome.
Note that 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.
This is all very much under construction. There are many things left to implement, lots of bugs to fix, and much for me still to understand.
Last update: 2011-01-20.
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.
If the tilings fail to work then you might like to check out these screenshots:
Sam Gratrix, Gratrix.net.