I wanted to make a beret that was reversible, and none of the pages I saw online were quite what I needed. I had a flame-print piece of a fat quarter (not even a whole fat quarter, but I didn't need it all) and decided to pair it with a copper-colored liquid lamé.
I cut the largest circle I could from the cotton, about 18 inches in diameter, and cut another piece of the metallic knit. I did a little math to find the circumference* of that circle (56.4 inches). I needed to pleat or gather the edges to get something that I could wear. I subtracted 22 inches (head size) from the circumference, and got 34 (rounded down). I could make 34 1-inch pleats, or 17 2-inch pleats to get the band circumference I needed. I rounded the 17 to 16 for an even number, and marked 8 points on my circle, then marked the middle of each of those points to get 16. I made my pleats and ended up with an inner circumference of 24 inches -- too big for my head, but figured I could adjust it when I put the band on. I basted them together to keep the pleats as flat as possible.
I used the band pattern piece from my trusty McCall's beret pattern, and pinned it onto my beret, trying to be careful and cover the basted seam of the crown piece. (I didn't 100% succeed. I had to fix a couple of places where I missed when I flipped it inside out.) The band is a little off-kilter, but it's black velvet, so it doesn't show too badly.
I'm calling this experiment a success. I managed to do what I wanted to do: create a reversible beret. I will have to play with the math a little more on any hats I make like this going forward, and it would be worth it to make a pattern piece with the pleat points marked. (Also, liquid lamé is a bit of a pain to work with.) The hat is a little smaller than the others I've made, but that was the constraint of the cotton scrap. It's also pretty floppy; that could be fixed by adding a lightweight interfacing between the layers to give it a little more body. A larger circumference hat would require more, or larger, pleats.
* To figure the circumference of a circle, multiply the diameter by π (3.1415).
Because of some of the trouble I ran into with getting the pleats even, the pleats basted, and getting the band to completely cover the basting stitches, this wasn't as "quickie" as it might have been. But it worked. Going forward, I know I can do this again, and get the results I want. My concept worked. (Yay, me.) And since this was just messing around to see if I could do it, I don't have pics of the progress, only the finished piece. When I make another, I'll do a full tutorial of my process.