I tried encoding it in base 6, 7, and 8, laid out on rectangles in various configurations, and kept wanting to tear out my hair.
Galaxite might be a beautiful mineral, but it was not cooperating with my usual lace design methods. Finally, I remembered that I’d been meaning to experiment with making a stitch pattern that’s suited to a kind of crescent shawl that seems to be popular at the moment – cast on a few stitches, and increase three stitches at each edge every two rows. It turns out that it worked nicely to plug the base 8 version of Galaxite into the flat diamond that tiles to make a good crescent shawl (because of the malleability of knitting).
Fear not: I am also including a more standard rectangular version.