Once again: dodecahedrons are a naturally-occurring shape.
Side question about probability: if I had a die and I wanted to test just how crappy it was, I would want to roll it multiple times and track how often different faces came up. How many rolls would give me a reasonable measure of about how often each face would come up? (Sigma to some level).
Fun fact: pyrite is naturally cubical in it’s crystal lattice. The occurrence of dodecahedral pyrite crystals is a phenomenon known as pyritohedral symmetry, where basically what would be each square face of a cube is replaced with two pentagonal faces, producing a pseudo-pentagonal crystal.
Assuming you meant to say ‘pseudo-dodecahedral’, pyrite crystals are real dodecahedra. Just not regular dodecahedra.
I meant that they do not have true internal icosahedral symmetry like a quasi-crystal.
Well, if you count dice as “practical objects”. Though those don’t actually demand Platonic solids, either: Catalan solids, dipyramids, and deltoidohedra also work, as well as various distortions of those. Or, heck, little plastic pigs, if you’re not concerned about your dice being “fair”.
Depends on how much crappiness you’re willing to tolerate. Is it OK if one side comes up 10% more than others? 1%? 0.001%? The more precision you want, the more rolls it will take to be confident you have that precision.
There’s a whole two-parameter family of shapes made up of twelve identical faces. The Platonic dodecahedron and the rhombic dodecahedron are both members of this family, and the cube and tetrahedron are degenerate members, too (where multiple faces end up flat to each other and so merge into a single face). I made a 3D model of representative members of the family.
I have no trouble imagining them to be game pieces or fortune telling devices but I’m having trouble reconciling the holes on the various sides being marginally different sizes with ease of play or divination.
When tossing dice, it’s very easy to see what number comes up. With these, it would be quite difficult at a glance to determine which size hole was up. I believe the holes being slightly differing sizes has a more important function than just telling you which side is up.
It’s speculated, by me, that the faces might have been covered with richly decorated parchment (or bark, etc) with those materials having long disintegrated from the artifacts.
I’ll bet there’s an intact one in a bog or under something somewhere. Well, not bet. Hope hard, I guess.
IMHO, the augur did cover the sides with a removable piece, made of leather or other material that can be cut into a continuous piece.
https://www.twinkl.ch/resource/dodecahedron-3d-shape-net-us-m-1652381495
That then was likely hold in place over the dodecahedron with loops or holes over the studs.
That would BTW make it a bit more easy to roll, my theory is than the augur knew about where the bigger holes were located (less weight), and made sure that (depending on the customer) the side that the augur preferred was the one that likely ended on top.
A cover with painted images or writing could also hide weights added inside the dodecahedron, virtually ensuring that what the augur wanted came on top, specially for a very important customer.
Well, I also proposed that earlier too. I do agree with that part were you hope that we get lucky and find a specimen or pieces preserved on or next to the dodecahedrons.
Of course, now that I was wondering, what if one’s theory is correct? Well, if there is little evidence coming from the digs, one should check at least how ancient Romans did hold pieces of clothing, leather, etc.
Just now, the candle lighted over my head. (Yes it should be an LED light bulb now, but we are in Ancient Rome 
)
So, one of the most popular ways to hold pieces of leather or wool in ancient Rome, was with a fibula.
And yes, a good number of those are metal pieces with rounded studs, similar to the studs in the dodecahedrons. Incidentally, the fibula was in part a pin, but then the studs likely had another reason to be, as I propose, as a part that allowed the wearer to make adjustments.
And while looking at the uses of the round studs in a fibula I ran into this:
That 2nd piece from the right is reported to be from the 8th century, while the dodecahedrons came from the 2nd to the 4th centuries, notice the round studs and the concentric circle symbols!
A deliberately-biased die would explain differently-sized holes, but it wouldn’t explain all of the holes being different-sized. If that was the purpose, then you’d want one side with no hole at all, to maximize the weight that was down, and all the other sides with holes as big as you could get away with without the thing falling apart.
Wedgwood (2023) describes one ancient interpretation of concentric circles, as posited by the 2nd century CE Stoic philosopher Hierocles:
Hierocles, a Stoic of the second century ce, famously deployed an image of the ‘concentric circles’ that surround each of us. … Instead, it is designed to illustrate how it is ‘appropriate to act’ in certain cases. … According to his view, each of us has a duty of mutual aid towards every other human being—but a weightier duty towards those who are socially closer than those who are more distant. The fundamental principle is that each of us has the duty of being an ‘ally’ of every other human being in serving the natural purposes of all the circles to which we and that other human being both belong.
Wiki elaborates:
Hierocles describes individuals as consisting of a series of circles: the first circle is the human mind, next comes the immediate family, followed by the extended family, and then the local community. Next comes the community of neighbouring towns, followed by your country, and finally the entire human race. Our task, according to Hierocles was to draw the circles in towards the centre, transferring people to the inner circles, making all human beings part of our concern.
We’ve covered concentric circle symbology before, a couple of times:
8th centure BCE. Note that that is literally one thousand years of separation. And that fibula is Phrygian, which is a completely different culture from Gaulish or Roman. Not even the same continent.
The knobs are just decoration - they appear on plenty of other Phrygian artefacts, so clearly not serving a utilitarian function unique to fibulae. And there’s an evolution of them over time on Phrygian fibulae, from simple to more complex to disappearing completely by the Classical period - way before the Roman Empire.
It’s likely they derive from the earlier Near Eastern decorating technique of rivets and studs.
Bow fibulae are also called “digitated” fibulae, due to the radiating knobs that resemble fingers or digits; over time, their style changed. While the knobs of early (4th-century) fibulae were functional (holding the springs of the pin), they later became purely decorative.
Incidentally, I do agree that what I said is just one theory of many, and I do take other evidence into account, I do think that a design that had so many similarities to the dodecahedrons deserves to be looked at, it might still point to the dodecahedrons to be more like a decoration item rather that an auger tool.
Because there is a military connection, it could be that the dodecahedrons were just a fancy attachment or holder of leather and other armor that became a rage in those centuries for the high rank military guys or the elites then.
The one you were talking about was NOT an early fibula.
You can start by explaining the hundreds of years of time and the thousand miles of geography gaps between the one and the other.
If that’s true, where are the undecorated versions?
Here
and here
and just for comparison alongside knob-decorated ones, here:
Lots more where that came from.
I apologize if I’m misunderstanding your post. But I meant, if the knobs are just decorative, where are the stand alone dodecahedrons with no (decorative} knobs.
As an example, here’s another item in the plain and decorative versions.
You are. When I said ‘just decorative’ I was talking about knobs on Phrygian fibulae. Dodec knobs may well have had some function, even if only as legs.