The hole size seems to vary a lot, but the little knobby feet seem more consistent. Is that to allow something to flow flow in or out as opposed to sitting flat on the surface?
The feet have to be the same size so that it would sit on a table (I assume) on each of whichever 5 points apply.
The feet might be for air circulation if it was filled with a little cloth bag as a potpourri. Or, air circulation if there was something burning inside like a candle or if it was supporting a little dish of burning charcoal. Also the feet probably represent planets or stars orbiting the little cosmos model. As I mentioned (or alluded to) earlier the feet allow one to put it on a scroll you are writing on in ink, keeping the scroll open, the feet being small they minimize the chance of smearing the work, and allow air to circulate so the ink would dry.
Tent pole connectors: I was guessing at one time that they might also attach to holes and slots in leather straps in some kind of tent pole connector. But, the metal is too thin and weak to be used for anything beyond its own weight and falling from a table onto a tile floor once in a while. IMHO. Doesn’t seem practical as any kind of a connector for intersecting tent poles or standards as there are no real sockets or place for two or three members to go through at the same time.
In some cases, the feet are mushroom-shaped - and it’s been suggested that this was for the purpose of inserting them (like buttons) through leather, or to aid in the attachment of cords.
There’s this one:
http://www.georgehart.com/virtual-polyhedra/figs/roman-icosahedron.jpg - which looks like it might have been an incense burner or something.
-and I’ve seen another one similar to that which was (from memory) a triangular pyramid - again, with very small holes.
First thing I thought of was incense burner on seeing the object, I think it is difficult to appreciate how vital a part of a dwelling these are unless you live in a non-airtight house. Just to keep mosquitoes away at least.
[QUOTE=Wikipedia]
The function or use of the dodecahedra remains a mystery
[/QUOTE]
Nonsense. They’re quite evidently d12s. Some folks in the Legion must have played Ogre PCs wielding Longswords or Katanas, that’s all.
Joke aside, I learned about something new today. Those are neat, thanks !
The icosahedron appears to have either no holes, or very small ones, which would seem to suggest a different purpose than the dodecahedra.
And the strangest thing of all is that if these things had some purpose, why did people stop making and using them?
And yet the design, construction and decoration is tantalisingly similar.
And why aren’t they mentioned in surviving writings, depicted in murals or mosaics?
From the photos the finish seems somewhat crude and utilitarian, which would suggest it is a tool of some sort. If it were more ornament, and/or had a finer finish, I would suspect it is a decorative device or religious artifact.
:dubious: It’s been in the dirt a while.
I was just reading about these the other day. This writerthinks they’re Celtic, and connected to Pythagorean mathematic mysticism.
That is why I think they are for some utterly mundane purpose, something so commonly everyday, it renders its existence unremarkable. That would preclude religious or scientific applications.
Too small and hard to draw or make a mural of would be my guess. About the size of an apple. And, they were more associated with the Celts than the Romans, the Romans being the ones having the money for fresco paintings and such.
Interesting that that there are twenty feet (vertexes) and that the Celts used a number base of 20.
On the feet being mushroom shaped: not really. They are more like teardrop shaped, joining the surface at a roughly 90 degree corner. Like the lower 3/4 of a teardrop anyway. I had looked at that closely. They could still work as a strap tie, but they would not work great.
Maybe they were like a fad that lasted a hundred years or so. A popular christmas (winter solstice) present for a while. Like a Rubic’s cube, Newton’s cradle, reproduction of a religious relic or icon, little metal Empire State building or Eiffel Tower minature, metal softball championship trophy, '68 New York worlds fair miniature (hollow grid globe with continents), desktop toy, conversation piece. Little transitory curiosities of special interest to those who had them, but with little practical value. Reminders of a pilgrimage, rite of passage, sign of accomplishment, social club, cult following, award, or graduation.
Maybe they encode coordinates for time travelers. 
No, on some examples, they are in fact quite mushroom-shaped - like pegs or buttons. There’s a fairly clear example about halfway down this page:
http://s8int.com/phile/page49.html
Very slightly concave at the bottom, but not really mushroom shaped. More very-short dick-headed. 
Could work as a leather buckle though, more than most of them. That is an extra finely detailed one BTW!.
Or a string was wound around the pegs. For some reason.
It seems almost too good condition to be genuine, I sometimes think.
A ball-toss game?
With progressively more difficult targets?