Tuesday, May 17, 2011

Three Different Views of the Same Tiling

Here are three images of the same {4,6} tiling. The "{4,6}" notation is called the Schläfli symbol. The 4 means it is a tiling of squares. The 6 means that 6 squares meet at every vertex. Check it in the pictures!

A view centered on a square:

A view centered on an edge:

A view centered on a vertex:

I bet you noticed that the tiling is checkerboarded (hyperbolic chess anyone?). Can you figure out what property is required to allow a tiling to be checkerboarded? If so, let me know in the comments!

Q: What made these pictures?


  1. That's really cool! These pictures and your comment about the checkerboarding help me get a better feel for hyperbolic surfaces (although I still don't fully grok them).

  2. re: your comment "I still don't fully grok them", all I can say is... that's ok, neither do I! :D