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If you have access to a 3d printer, could you print corner joints to help make the dome stronger? It would mean your tape hinges wouldn't go quite end to end on the segments, and you'd slot the panels into the joints as you assembled it. I know I've seen several files for dome connectors for 3d printing.
Give them a coating of silicone. There are several mold and mask making compounds that are body safe when cured.
Caustic Soda is sodium hydroxide, also known as Lye. Yes, it can be nasty if you're not careful handling it, but it's also a primary component of soap.
The punch looks like a pretty standard leather punch, aside from the big thing on the end, available from Tandy or other leather supply stores. You can either get fixed size punches, or ones where you have a handle and tips that you screw on and off for various hole sizes.
How about doing glow in the dark dots all over clear marbles or those little glass stones, and filling a jar with those? It'd probably look even more like a jar full of some mysteriously glowing liquid. Just don't shake it.
I like this idea. It occurs to me that it could be combined with the heat sealer part of a vacuum sealer system maybe. Just pull the tubing most of the way out of the bag and apply the heat sealer below it. Should give a much better seal than using tape.