The aft hemisphere was bolted to the front hemisphere. They were spaced a distance apart to provide a spherical shape, as the two hemispheres were not quite full hemispheres. (These were inexpensive security mirror ceiling tiles made of PMMA). The spacing worked out well, because the original had a wide equatorial feature. This was represented by a band of plastic automotive molding, which helped to cover the mechanical support structure. The equatorial feature was aft of center in the original, and the hemispheres were cut slightly unequally in order to evoke this configuration.
The mating structures were screwed and clamped in place to ensure repeatable positioning.
Other decorative embellishments on the aft hemisphere were round features, one on the main axis and one offset. The main axis feature was a support lug, and the offset feature was an electrical connection. These were assembled from PVC parts, as well as aluminum rod, a sawed and sanded-down RF connector, screws, glue, and paint. The aft hemisphere was quite thin in the area where these features mounted, so I reinforced the attachment area with fiberglass.
Both hemispheres were primed, blacked, then chrome painted, before assembly.