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A round robin quilt is a medallion quilt that you work on with several other quilters. Each person in the group creates a center square or rectangle. Then it is passed on to the next person, who adds a "round". Then it is passed to the next person, then the next, until each person has added a round to it. It is then returned to the original person, who quilts and binds it. Usually, the group will lay out rules like (1) the maximum size of the center square, (2) the minimum / maximum width of each round, (3) whether you supply all the fabrics for the quilt or each person uses their own fabrirics for each round, (4) whether fabrics should be washed or unwashed if you are using your own fabrics, (4) colors you do and don't want used in the quilt, and (6) a time frame for passing the quilt to the next person.
A few years ago, one of the quilt guilds in the Houston area had a round robin show. There were at least 25 quilts with 5 rounds each.
I've never done a round robin, but I did do a row quilt with 7 other quilting friends. We each had a box in which we put all the fabrics we wanted used, but indicated in our instructions whether the others could use their own. We each picked a theme and we met once a month to pass the box onto the next person. We would have a showing of the row we had done that month, but the person who owned the quilt had to leave the room. That way, we got to enjoy everyone else's work that month. At the final meeting, the quilt was returned to the owner, who was completely surprised and had the fun of guessing which person had sewn which row.
Another thing we did was include a small notebook so that each person who worked on the quilt could do a little journaling when they sewed their row.
If you've never done a round robin, you might want to start out with a block exchange or a row quilt exchange first.