I used to make things like this as a job years ago.
You have to build a round air tight base (like a rubbish bin) then on top of this you make 2 x circular 15mm ply rings that are able to be bolted together quickly.
The bottom ring is mounted to the "bin" in an air tight manner.
You heat a circular sheet of 3mm acrylic in some type of pizza oven to about 110C. This is the temp that turns the acrylic sheet into a rubbery state.
You put the heated acrylic sheet on top of the "bin" and clamp it with the top ring (so it is now all air tight). You apply a vacuum to the sealed bin causing the soft acrylic to sag into the bin in a perfectly spherical shape. The measurement of the radius is adjusted by the amount of vacuum.
Once the acrylic cools it will maintain the shape permanently(or when it is re heated) .Then off to a vacuum sputtering plant to aluminiumize the first surface. This is how airplane cockpit windows were made in WW2.
http://www.bayplastics.co.uk/images/...lic_sphere.jpg
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