Soak the basket reeds in a large bucket with water. They need to the soaked for about 15 minutes before they will be flexible enough for this project.
Fold your square paper in half in one direction and then in half again the opposite direction. You want to find the center point.
Measure four inches from the left side of the paper's edge and mark the place along the folded center line. Measure four inches from the right edge and mark the paper along the folded center line.
Set a compass to four inches and place the point on the left mark along the center line. Draw a half circle in the top box. Then, create a half circle in the lower left box. Move the compass point to the right mark on the center line and draw half circles in the upper and lower right boxes. It should form a oval on the entire piece of paper.
Cut out the oval with scissors and use it as a template for the 12-by-18-inch styrofoam sheet. Trace the oval onto the styrofoam with a marker. Mark the center with the pencil and draw a line through oval lengthwise as a guide for the other reed pole marks.
Mark the doorways along the oval by marking 3/4-inch above and below the central line at the ends of the oval. Mark each place with a dot for where the reed poles will go into.
Mark one dots along the long side of the oval in the center on the top and mark a dot on the bottom, too. Be sure the pencil marks are deep enough to find later. Mark two dots between the center dots and the doorway dots. They should be equidistant and two inches apart. You will end up with a total of 12 marks around the oval, equal distance from each other.
Dip one end of a 17-inch reed with wood glue and insert it into one of the doorway marks. Place glue on the other end and then place into the opposite doorway mark. Repeat with the other 17-inch reed into the other doorway posts.
Add glue to the end of a 15-inch reed and place in the bottom center mark. Add glue to the other end and insert it into the opposite mark. Tie the poles where they cross with string. Insert the other 15-inch reed poles in the same fashion. Add glue to the ends and then insert into the opposite ends. Tie string at each intersection of the poles.
Wrap the 24-inch reed around the wigwam structure three inches from the bottom. Secure it with the string starting from the doorway posts so they remain open. Wrap a 15-inch reed two or three inches above the 24-inch reed. Secure with the string.
Cover the entire wigwam structure with the felt squares. Slightly overlap each piece starting from the bottom by a doorway. Glue the pieces in place and leave a small hole at the top for a smoke hole.