20 gauge florist's wire, waxed paper, purple and red tissue paper, clear Elmer's glue, DMC E211 Pearlescent Effects Lilac embroidery floss, electric tea lights
needle-nose pliers/wire clippers, transparent plastic ruler, pencils, red purple and lilac Sharpies, clothespins, cups or bowls, scissors, a small piece of cardboard, tape
First I made the wire frames. The rectangular lantern is approximately 3x3x6 inches. The smaller circles for the round lantern were formed around the rim of the little pink cup and the large, pseudo-equatorial circle was formed around the rim of the small glass bowl. My measurements were only approximate and I was making it up as I went along, so they ended up rather lopsided.
I decided to cover the frames with a base layer of waxed paper before putting on the outer casing of pleated tissue paper. The rectangular lantern has already been done, and the object covered in clothespins in the lower left corner is the round lantern, in progress. I am also working on making tassels by wrapping the floss around a piece of card. Each tassel is wrapped eight times. I'm not very skilled yet about binding off tassels.
Rather than wrapping the lanterns with a continuous sheet, I decided to make four panels to go around. The panels for the rectangular lantern are in three layers -- a base of waxed paper, a layer of purple tissue paper with just the central oval of the design cut out, and a second layer of purple tissue paper with the whole design cut out. I used the full width of the waxed paper as the height of the panels.
The short sides of the panels for the round lantern are approximately 1/4th of the circumference of the smaller wire circles in the frame, and the width at the middle of the hexagon is approximately 1/4th of the circumference of the larger wire circle in the frame. The height of the panels is 4x the average measurement from one of the smaller wire circles of the frame to the pseudo-equatorial larger circle. I did something a little different with the design for this lantern; it still has a base of waxed paper, but I put on only one layer of red tissue paper with all the holes cut out and filled in the outer parts of the design with lilac Sharpie.
When all the tissue paper layers were dry (I worked on this project over two days), I cut apart the panels and folded them accordion-style. The rectangular panels are being glued to the frame. In the front, I've put wire clips in the tassels to attach them to the bottom of the lantern frame. As you can see in the third picture, the tassels were initially quite frizzy. I smoothed them out with a little bit of glue. I used similar clips to attach strings at the top of each lantern for hanging.