Saturday, January 30, 2010

Beading another Kepler's Tiling

Today I ran across this article on "five-fold symmetry in crystalline quasicrystal lattices."   This figure of one of Kepler's famous tilings got me thinking about weaving beads.  I noticed that if I placed one bead on each pentagon, a little thread should hold them together nicely.  In search of a larger patch of this tiling of Kepler to guide me, I found this page on "aperiodic tilings" by Steve Dutch, and his fourth figure fit the bill perfectly.  (Thank you Professor Dutch for letting me post it here.)

The photo below shows the same patch of tiles rendered with size 11/0 seed beads and thread.

 My bead weave shows one bead for each pentagons in Dutch's illustration, plus I added exactly 10 extra shiny purple beads (red pentagons) around the perimeter to smooth out the edges and make the weave more circular and less scalloped.  Notice that this weave has holes in three different sizes.  The smallest holes (with 5 shiny purple beads) are the 5-pointed stars.  The medium holes have 10 beads around, and thus correspond to the decagons in the tiling, and the large holes are the double decagons.  This patch of beads measures about an 1.5 inches across, and when I smoosh it down, it lies flat.  I'm not sure if it would continue to lie flat if I enlarged the patch.

What I learned:  I learned that these matte brown and shiny purple beads look a bit funky together, but I was inspired to weave so I didn't think too much about what I pulled from my bead box.  Mathematically, I learned that this set of Kepler's tiles can be arragned in several different ways, including a nice periodic striped one that I had never seen before. (See the fifth figure.) This beading technique will also work with the fifth figure, but I haven't tried it yet.


  1. That would make a pretty awesome setting for a crystal or cabochon, or (layered in RAW) a pendant all by itself!

  2. I like your idea that is something I feel I need to try. what a clever use of beads.

  3. Fun! (and, no, I don't understand a bit of it, I just like the pretty pictures.)

  4. What a neat beaded tiling! There's something about five-fold symmetry that's just so visually pleasing.


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