You'll need two plastic circles for the table top and the reflective mirror underneath. You have a few options, so depending on your budget and your access to tools, you can spend some money and get pre-cut pieces, or take a little more time and cut them yourself.

I used a pre-cut circle from Tap Plastics for the top of my table, since I want a really good seal on that piece. I used a band saw to cut the bottom circle out of some scrap plastic I had lying around, since the bottom circle doesn't show and doesn't need to have a perfect waterproof seal.

You'll also need a long strip of plastic to serve as the table edge. I used 1/8" polycarbonate from Tap Plastics and got them to cut it to size for me. It needs to be long enough to wrap all the way around your circle with a little extra for overlap.

I used a table saw to cut a shallow groove in my plastic, to better hold the table top in place and make for a better seal. (You may be able to get the plastic store folks to do this for you as well).

This is a bit of a delicate operation. Set the saw blade so it's barely peeking up out of the table, and clamp an extra fence onto your table's fence or your plastic might slide underneath.

Do a test on a piece of scrap to be sure you've got the depth right. It took 2 passes to get a wide enough shallow groove to set the table top in.

When you're done, you should have a nice even groove that runs the length of your table edge plastic. Mine is about 1/4" down from the top of the edge, creating a 1/4" lip around the top of the table to hold the bubble juice in. If I were to do this again I'd make the lip a little bit taller, maybe 1/2" instead of 1/4", to minimize spills.

Set your circle on a towel to raise it up about 1/4" from your workbench. Wrap your table edge piece around so the circle fits neatly into the groove. Use some E6000 glue to secure the overlapped section of the table edge. Clamp it securely and let it dry overnight.

Add clear waterproof silicone sealant around the top edge of your table. Press it into the joint and smooth it out nicely. Be sure to cover the whole edge - we're looking for a 100% waterproof seal here.

Once the sealant dries, fill the table top with water and check carefully for any leaks.

Apply your standard mirror film to the lower circle. Some films come with adhesive on one side, and some don't. Follow the manufacturer's directions to get the mirror smoothly applied onto your plastic.

If your film doesn't come with adhesive, you can use spray glue to attach it to the plastic. Don't worry too much if your film isn't perfect. This stuff is pretty hard to work with, but with our diffused surfaces it won't matter much if you have a few bubbles.

For my top circle I coated the underside with 3-4 very thin coats of mirror effect spray paint. Each coat adds a little more reflection. Keep adding coats until you have a one-way mirror that's got a nice amount of diffusion.

I finished it off with a coat of clear glaze spray paint to keep it from getting scratched.

You could instead use one-way mirror film here for a true infinity mirror look.

Once the silicone caulk on the top surface is dry, flip the table over and add another round of caulk on the underside of the table top. Grab your NeoPixel strip and press it into the caulk while it's wet. This silicone sealant will hold the pixels in place like glue.

Nestle the lower circle into place, resting it on the NeoPixel strip. Thread the Feather and wires around so the Feather isn't caught between the layers. Use a bit of hot glue to secure it to the bottom circle. It's a good idea to move it away from the edge a little bit, just to keep it extra-safe from any leaks.

Add a third round of silicone caulking to the underside of the second layer to secure everything in place.