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?
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3 comments:

  1. charlieMay 19, 2011 at 11:05 PM

    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).

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  2. Roice NelsonMay 19, 2011 at 11:15 PM

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

    ReplyDelete
  3. DartNovember 2, 2024 at 3:52 AM

    From my experience, to be able to have a checker board you need to have an even number of edges meet at each vertex

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