Bend four wires of about 1 foot in length in the middle into an angle of 30 degrees to make the skeleton of an octahedron out of wire. Solder each pair of wires in the center so that they will stand up, looking like two teepees. Solder the four feet of the teepees together to make the skeleton of a shape with 8 equal-sized faces.
Cover the octahedron with paper glued to the wire skeleton if you want an example of an ordinary un-stellated octahedron. Otherwise, this is just the starting point to making a stellated octahedron. Now make the same skeleton as before, but this time use much longer wires, at least 4 feet long.
Cut the long wires where they meet with wire cutters and solder them together. Cover the entire frame with paper, and glue the paper to the frame. Do not do this all at one time -- do part of the figure and let it dry, and then do another part.
Display the stellated octahedron and similar figures in a glass case. An alternate method is to hang a figure from the ceiling. The best way to do this is with nylon fishing line.