Get the pink or blue styrofoam. Spray glue (3m 77) the sheets
together. Get a hot knife (ebay or hobby store) basically a wire that gets hot like a toaster coil. It will slice thru the styrofoam cleanly like butter. Then just glass them. Add a cool top out wood or corian or starboard or whatever you like.
Glass with epoxy
not poly or vinyl. When you make the cut save the other piece as the female piece to the male so you have a perfect fitting matched pair. Cut at a 45 degree angle so when you glass it the glass is smooth and bonds well and also it will seal better