The design of the ceiling has been an interesting problem. It's almost never seen in the series - presumably because it isn't actually there. Actually in a few scenes with the earliest doctor you can see the studio lighting and gantry above the top of the roundels!
So I've had a pretty open hand to design whatever I liked. I decided to go with the "Three Doctors" design, but updated in the centre to fit with the fourth Doctor's decor.
I built lowered edge panels, each with one or two roundel diffusers in them. In spite of the ten foot ceiling, my room actually isn't really tall enough, so the drop ceiling is only about 6". There's a further inch at the top of the roundel panels to give them clearance to open. I surrounded the drop ceiling with 1 1/2" strips each a foot long, matching the design of the columns. These were glued onto 1/4" plywood and screwed into the real ceiling. The centre part of the ceiling is more bathroom board, which sits above an overhang of the 1 1/2" strips.
The central feature in the ceiling is my Power Octagon, which also appears in the first Doctor's first story. Oddly although it's referred to as the Power Octagon in at least one story, it's actually hexagonal. Well I built an octagonal one from MDO. It has lighting diffusers on the underside, and is lit with red rope lights so it glows "powerfully". When the main lights are down it looks quite effective.
Building the ceiling was incredibly hard work. Each drop-ceiling roundel panel was custom fitted and usually had to be test fitted three or four times before it was correct. Sitting atop a step ladder with a 30-40 lb enclosure while I drew a pencil line along the ceiling in 85-90 degree heat (because of the lighting) was no joke! I had to throw one panel out because I hadn't guessed correctly about the dimensions. As you can see I angled the inner edge, which looks a lot better than a vertical edge would have, I think, but was much harder to fit. Having them "upside down" also made things hard to visualize, so I had to be careful not to make mistakes with the fitting. Getting the Power Octagon in place was extremely hard, as it weighed even more than the drop ceiling panels. I built a mounting plate above it, with bolts dropping down so I could both mount it quickly (before my strength gave out) and also so I could "easily" bring it down for maintenance. Fortunately that hasn't been necessary.
I mounted everything on the ceiling very securely, partly because there's a room above, partly because the parts are heavy and partly because I live in an active earthquake zone. We've had three or four serious quakes in the last ten years here and some very minor building damage as a result. This is partly why they build houses out of wood here: brick is bad news in a quake.