Stiff interfacing, such as peltex, provides the bin's stability. Look for this double-side, fusible, heavyweight interfacing at your fabrics store. For the exterior fabric, anything goes: neutral linen, colorful cotton, and even crinkled velvet.
Download this pattern; cut out. Fold each fabric square into quarters and cut the pattern from each (one piece for the bin's exterior and one for the lining).
Unfold exterior and lining pieces (they will look like plus shapes). Place pieces right sides together. Using a 1/4-inch seam allowance, sew pieces together at each corner as shown.
For double-side fusible heavyweight interfacing, cut one 4-3/4-inch square and four 3-1/4×4-3/4-inch rectangles. Be as precise as possible for a level and even bin.
Center the interfacing square on the exterior piece of the plus shape; press with an iron to fuse in place. Clip into each corner, cutting just up to but not through the stitching. Turn right side out.
Slip an interfacing rectangle into each opening of the plus shape. Adjust interfacing rectangles so there is about 1⁄8 inch of space around interfacing sides to allow for topstitching. There should also be about 5⁄8 inch of fabric without any interfacing at the top of each opening; this will allow you to sew the bias tape on in Step 8 without sewing through the bulky interfacing. Press plus shape on both sides to fuse the interfacing pieces in place.
Topstitch around center and side interfacing pieces. Try to keep the fabric as flat as possible and stitching as straight as you can to avoid wrinkles in the fabric.
Place exterior side down. Open folds of double-fold bias tape. Fold one side of box up. Fold the end of bias tape under by 1/2 inch and place end of tape in center of a box side, aligning tape and box side edges; pin.
Tip: Packaged bias tape comes in many colors at the fabrics store (look for it by the zippers). It's used to finish the raw edges of fabrics, such as in this fabric bin.
Working around bin and leaving a 1/2-inch gap of unpinned bias tape at each corner, pin bias tape to all sides. Overlap ends of tape by at least 1 inch. Sew 1/2 inch below top edge of each side panel and corner.
Flip bias tape up and over the top of the basket to conceal the raw edges. Fold inside edge of bias tape under by 1/2 inch and secure using clothespins. Working from outside of basket, topstitch the bound edge a scant 1/8 inch above bottom of bias tape, catching inside of tape in seam.