A lot of great resource websites have disappeared through the years and one of the best was Anne Hawley's Hillsinger Fine Hand Beadwork. Some of you remember it and the techniques that came out of that site which are still actively used today like the very familiar spiral rope.
She also posted instructions for a nice geometric increase for working peyote in rounds to create medallions that were flat. Sort of like free standing rosettes, it's another technique that's used a lot and has been taught to other beaders who unfortunately missed her wonderful site.
If you know the technique and just want the graph paper, scroll down to the bottom. If you don't know, here's a quick overview so you can try it. It's not super detailed, so you should have some practice with tubular even count peyote before you try it.
This really does work better in seed beads, but my example is done in Delicas. They just take a little more patience for the first few rounds.
For this project, you'll need 2 colors of Delica beads, thread, and a needle.
Start by stringing your initial ring of beads, in this case, the base is 6 beads, tie a knot in the thread forming a ring, you don't want it too tight, because you'll need to put in a second row of beads between the beads of the first round. This is the tricky part but it does look better at least for me to do it this way than to string on 12 beads make a ring, then just do the 3 round. Try it both ways and see which one you like better. Hold it flat while you work the first few rounds between your thumb and index finger and be careful not to twist the beads you are working into the round. Have faith it will work, after you get the first few rounds done, it gets a lot easier.
The 3rd round is the increase round. Every 3 rounds you increase by the number of beads in the base round. So for this example, rounds 3, 6, 9, and 12 are the increase rows, and you do that by putting 2 beads instead of one at equal intervals around. This diagram shows the first round and the first rounds after increasing in gray, the second round and the second round after increasing in white, and the increase rounds in red with the increases themselves marked with dots.
After you finish each round, you make the step up the same way you do when you work tubular peyote.
Here's the pattern for my example which has 13 rounds.
This technique works with other counts for the base row, just remember to make the same number of increases in every 3rd round as the base number of beads you started with.
This technique works great to back round cabochons with, as a base to cylinder shaped amulet, or at the bottom of bottles and such that you are covering with peyote beadwork. If you make 2 rounds with one being 1 round bigger than the second, you can zip them up into a flat round bag leaving one or two sides open for the top.
Here's some graph paper for you to play with and create your own designs.