Cut one hat side from lightweight cardboard or chipboard. Smoothly curve the side into a cylindrical shape, slipping the tab beneath the opposite straight edge; use double-sided tape to hold tab in place.
Trace one crown pattern on fusible interfacing. Loosely cut around the shape. Fuse crown interfacing to wrong side of velvet following the manufacturer's instructions. Cut out shape on traced line. Make 1/2-inch deep clips around the outside edge of the crown.
Place strips of double-sided tape around the top edge of the cardboard side. Center velvet crown on top, pressing clipped fabric to the tape.
Cut hate side covering from velvet. Referring to the pattern, turn under and secure hem using fabric glue; let dry. Turn under and glue a 3/8-inch seam allowance along the top edge; let dry.
Wrap and temporarily pin the velvet covering around the cardboard side, starting at the back seam and placing the glued seam allowance even with the top of the hat side. Glue velvet side in place using fabric glue; remove pins as you glue. Fold the bottom velvet seam allowance to the inside of the cardboard side; secure with crafts glue.
For the brim: Fuse two 8-inch squares of interfacing to wrong side of velvet following the manufacturer's instructions. Cut out squares. Center and trace brim pattern on interfaced side of one velvet square. Place velvet squares together with right sides facing. Sew on traced line, leaving opening to insert wire as indicated on pattern. Cut out brim 1/4-inch beyond sticking and clip into seam allowance.
Referring to pattern, cut a small x in the center of one brim piece. Note: Do not cut the x larger than the bottom of the side band.
Turn brim inside out through the x. Top-stitch around brim 3/8-inch from edge to form a casing. Cut a 30-inch piece of wire and insert into casing at opening. Twist wire ends together; clip excess wire. Slip-stitch opening closed.
Center side band atop center of brim, covering the x opening, and pin in place. Hand-sew base of side band to the brim, working from the brim top.