I’ve
had several different designs for the roundel panels in the console room. The
first attempt had ˝ inch MDF screwed to 1x8 pine
planks. The inner edges of the roundels were 4” strips of 1/8” bathroom board
cut very carefully to size and jammed into the hole. This really didn’t work
very well as I had to tack them in place and the bathroom board was too hard to
make the nails flush. Also I never did really figure out how to fit lighting
behind that version. I made one panel as a prototype and
ended up cutting it up and throwing it away. The white backing was the smooth
white lighting diffuser material (acrylic or styrene – both work, though the
acrylic is stronger and more flexible).

Strangely yellow...
The next
design was much more refined. I cut two ˝” MDO panels (plywood with a paper
veneer) with roundels and placed 1” spacers between them (to reduce weight –
2” thick solid material would have been great but terribly heavy). The
roundels are lined with smooth lighting diffuser sheeting cut on a table saw. I
cut them slightly long and then trim them by the millimetre until they snap into
place and hold tight without gluing. Some I did actually glue with caulking,
others I didn’t bother.

Earlier panels were cut with a jig-saw, but a router works much better...
I
stapled 2x4 foot sheets of lighting diffuser behind them. They split, but not
enough to show on the outside.
The
panels are nine feet tall – the roundels are on a 24” grid and are 20.5
inches in diameter. The panels with 3 roundels wide are thus fairly unwieldy,
though I’ve been able to move them without assistance. Plywood comes in 48x96
inch (4 foot by 8 foot) pieces, so I tiled the area
with several of them, the tiled them differently on the reverse side for extra
strength. Wherever there’s a seam on one side there’s unbroken wood on the
other side, so in spite of being joined, even the large panels are quite rigid.
I used spackling paste and wood filler to cover the joins and screws and glued
the spacers in place also. I've since discovered that my roundels are too large
- the ones in the show were 18" (presumably on 21" spacing).