Here's a great way to make use of even-count tubular peyote stitch. Swarovski rivolis and fancy stones have become very popular, mostly due to the fantastic work of Laura McCabe. The photo below is my Ice Queen Pendant, which features a Swarovski rivoli in the center.
Before you begin your bezel, coat the back of your rivoli (if it's foiled) with clear fingernail polish. Do this because skin oils, lotions, and perfumes and interact with the foil and cause it to come off the crystal. Without the foil on the back of the rivoli, you'll lose the color and sparkly effect. And do it first so the polish is dry by the time you're ready to hold onto the rivoli.
Use about a yard of conditioned thread and cylinder beads (Aikos, Delicas, or Treasures). In the photos shown below, I'm using a 16mm rivoli. String on the number of cylinder beads necessary to go around the rivoli. You can find a chart that tells you how many you are likely to need here. The number can vary due to your tension and the specific beads you're using.
For my 16mm rivoli, I'm using 42 Aikos. String your cylinders and double/triple count to be sure you have the correct number. Now we have to form a circle. I like to circle back through about half of the beads, leaving a 6–8” tail. The other way to do it is to tie your thread into a circle, being sure you leave a bit (about a bead's width) of room, i.e., don't make your circle too tight.
I prefer to circle back through beads for two reasons: First, as long as I don't split my thread with my needle (which should never happen anyway), I can adjust the tension in the first row of peyote. Second, if I make a mistake and have to pull stitches out, I don't have a knot with which to argue.
So, once you have a circle of beads, stitch one row of tubular peyote, continuing to use the same cylinder beads. Be sure to step up at the end of the row. You now have three rows of peyote (see how to count rows of peyote here, scroll down to step 8).
Now stitch two rows of peyote with size 15 rounds. The photo below shows three rows of peyote complete and the first row of 15s started. Notice the beads are forming a tube, not a doily, i.e., the beads are lying flat on my finger.
Set the rivoli inside the bezel to see how it fits. The circle of beads should be slightly larger than the rivoli, i.e., the cylinders should appear all around the edge of the rivoli.
This is the back of the work. You might have to add a row or two of 15 charlottes to snug the bezel around the rivoli (I added one row of charlottes to this side of the bezel). The charlottes can tighten up your bezel a bit, but sometimes they are there just to add detail. If you stitch into the back of the bezel with the rivoli in place, be very careful not to scratch the foil with your needle.
Move working thread to front side of bezel and stitch one row of peyote with size 15 rounds. Now hold the rivoli inside the bezel, being careful not to scratch the crystal with your needle.
Stitch one more row of peyote with 15 rounds (a total of two rows). Check the fit and add a row or two of 15 charlottes, as needed. End threads. Et voila, you have caputred your rivoli!