Mate, I made mine out of MDF and on the underside I used a protractor that I found on the web and printed it very large then marked out the 36 points.
I used a "spade" drill bit (Speedbore) and drilled holes to about a depth of 7mm this allows for a kitchen door knob to drop into the hole that I attached to the end of a 2" x 1/2" stick that is attached to my bottom base plate (also MDF but only 600mm square) The stick is only attached at one end and the other carries the kitchen cupboard door knob (a fancy chrome knob!) the stick pushes/flexes down when I push on it to allow manual rotation to the next stop. The two pieces of MDF are joined with a "Lazy Susan" bearing wheel that was designed for rotating a large television or cabinet.
Over the top of this set up I had the missus stitch up vinyl covers that have elastic around the edge. ( I have both White and Black versions that easily swap) also the same material for floor and background covering. I light the objects through a white home made tent (sort of thing) made of cotton. (This stops shadows) and light from the outside with many flood lights. (from all sides)
Ended up costing a bit by the time I was done but the results have been good and it all packs up for easy transporting etc. Though most shooting is done in my studio.