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The coin-verifying hypothesis seems compelling
I collect ancient coins and this explanation doesn't fly for me. There's a certain amount of "artisanal-ness" in the production of ancient coins - which were all handmade. Like, I'm looking at a tray of coins right now and there's no way a simple go/no-go tool would be helpful. Also, for this purpose a simple handheld counterweight balance would be more accurate and portable. The existence of these simple balances, along with reference weights for various denominations, is well documented.
Moreover - if you're an ancient merchant, what is more important? The weight of the silver or the ability for it to pass for a denarius issued by Rome? Particularly for international trade, it seems to have been the former. Bankers' cuts and countermarks are commonly seen on coins, and seem to have been an early form of foreign exchange. (eg - I'm travelling from Athens to Ephesus with a stock of my local currency. If I pass it to a local banker in Ephesus, they can evaluate it, determine the local exchange in terms of silver, and give it a locally recognized countermark to assure their own merchants that they're getting the equivalent local value).
That being now off my chest, I've got no great answers for the dodecahedrons. I strongly suspect that it was a nifty thing that metal workers made as a master's thesis.
Why not just make that out of a flat piece of metal, or even a plank of wood though? Why bother with the very complicated 3D shape that took a lot more work to make?
Are all the sides equal on this dodecahedron? Maybe its for multiple coin types?
The holes through the holes are usually different sizes but I don't think any two examples are exactly alike. And you could have a board with several holes drilled in it to test multiple coin types.
Also, did the Roman empire issue 12 different sizes of coin?