To upholster the chair I used a stretchy material I had lying around for a long time. I lucked out that I had a lot of it, I like the color and it is stretchy.
Instead of upholstery the chair could be painted and filled with cushions or pillows. This would be easier and cheaper. I've left the base unfinished on purpose. The new owner likes the look of it. A $20 papasan chair cushion from CraigsList is a perfect cushion for the inside.
The outer cover was made with 2 large half-circles sewn on the long curved edge. That piece was turned inside out, stretched onto the ball of the chair and held down with homemade tack strip. Tack strip is simply cardboard with nails embedded into it. I had both and wanted longer nails for a better hold so I made my own.
To make the entire inside surface cushy I used 1/2 inch foam covered with the same material. This thin foam layer makes a big difference. It's more comfortable for me to sit with my head above the edge of the cushion. This layer is much nicer to rest my head on than the cardboard surface.
I made my own 1/2 inch piping to give a nice appearance to the edge where the chair body and foam pieces meet. Piping is easily made by sewing long strips of material around piping cord. Use a zipper foot to keep the material tight against the cord. Tack the piping down the same as the outer covering.
Each wedge-shaped piece of foam has its material glued to it using a spray upholstery adhesive. It comes out of the can in a fan shaped stringy spray like silly string. It was perfect for securing the material to the foam. Because the rounded edge of my chair is not a straight line each foam insert was different. I cut each piece to fit its position and numbered the location and foam pieces. Make sure you don't number the side that gets covered by fabric!
I'm currently using T-pins to hold the foam pieces in the ball. These don't hold great and I may switch to sticky-backed velcro at a later time. They're holding for now though.
It was hard work, but I had a lot of fun on this project. If anyone else makes a version of it I'd love to see it.