Here are some of the parts and tools I used at this stage to create the interior space. After I lined up the two segments I didn't like the open feeling of the piece, but wanted it to have thickness. I decided to undo this work but save the cut pieces. I ended up cutting out 3 circles and segmenting them to make the final circle form.
Here is one segment wrapped in Japanese paper the meld the three pieces of foam core together. I ended up painting the sides the match the colors of the top. See the next few pictures.
Then I rearranged the segments into my favorite shape and turned the pieces over.
I decided to use a piece of Japanese paper (the same kind I used for the sides of each segment) with writing on it for the back. I laid a sheet of paper beneath this shape and traced each segment in pencil. Then I used a divider with pencil lead to trace a 1/8th inch indent. I cut out the paper and glued it down.