Rules say reconstructions are allowed but doesn't specify if illustration counts.
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Those are objects from the Roman Empire. About 130 have been found in total.
They are typically made of brass and fit in the hand but can vary from 35 grams to a kilo. Each side has holes of different sizes with rings around them. On each corner you will find a sphere protruding.
But there are three things you won't find.
- you won't find them in or near the capital. They are found all over the European part of the empire including Britain, but never once in the Near East or African portions of the empire and also never in what we call Italy today.
- you won't find why they exist. There is no known use for them that survives scrutiny. But you will find lots of speculation.
- you won't find any markings. No labeles, no symbols, no gauges, or numbers. Just holes with rings.
Are they part of a mystery colt, some rather expensive game piece, blacksmith training? No one knows.
Find a 3D print file and make one yourself and ponder it for a while. Or draw one. I haven't found any woodworking plans. Maybe I could fix that.
Micron, A5.
I think the biggest appeal of the dodecahedron was that it allowed a person to keep track of a dozen ciphers at the same time. That would be only useful in a region where there was constant conflict with outsiders (unlike Africa or Italy), and where there was a good chance of the enemy knowing some basic Latin (unlike in the East).
If the hypothesis from the video is accurate, you'd only need compatibility between dodecahedra of two people if they were in communication with each other; for example, between a legatus and his immediate subordinates. And even then, you don't need both dodecahedra to be identical, only a single side being identical is enough.