So if you join squares and hexagons alternately, you get something squareish, and the centre is roundish, and you'd think you could put a rivoli in the hole but no. I really really wanted to, but it just didn't work: the beadwork would distort and act bitchy and sneer at me.
I had to settle for a square with a round hole. Using four millimetre beads to weave the base makes a substantial earring or modest pendant; you could also join them end-to-end for a necklace or bracelet - and I might! The version with bigger beads has the potential to be pretty fancy: if not a rivoli, there should be a way to use chatons, and if there is, then I WILL use them.
I'm a bit focused on rivolis since I'm somewhat flush with them after Bead and Button.
I also did a little experiment with end-to-end dodecahedra. Yes, it looks a bit crooked in the picture, doesn't it?