Stitch the coils or braided strips to each other using a heavy-duty needle and quilting thread. Make your stitches loose enough so that you don't pull the strips too tight, which would give the rug a tendency to curl.
Lace the coils or strips together with a large darning needle and lacing cord. Choose a lacing cord in a color that goes well with all the colors in your rug. Push the needle alternately through adjoining coils and knot the lacing at intervals. If you make the laces almost invisible, your rug will be reversible.
Make your rug by crocheting the strips instead of braiding them. Use the largest crochet hook and coil the strips as you crochet them by adding or dropping stitches. Add an extra stitch when you want to curve the rug outward and drop a stitch when you want to tighten the curve. Lay the rug on a work table as you crochet and stick straight pins through the coils into the table. This helps to keep the rug flat and prevent the edges from curling and also helps you keep track of dropped or extra stitches so that you add or subtract them evenly all the way around the rug.