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.)
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.