That’s brilliant - thanks
Another resource to check out:
has hole sizes also
Mangetout, you’re the Atomic Shrimp guy? Respect!
That I am. Thank you!
The dodecahedron is going to be my next published project - I’ve just got to finish off my Stirling engine first…
Well, that new academic paper I referenced here a couple days ago seems to have a ton of errors in the illustations.
Roman Dodecahedron as dioptron: analysis of freely available data
Amelia Carolina Sparavigna
Department of Applied Science and Technology
Politecnico di Torino, C.so Duca degli Abruzzi 24, Torino, Italy
1206.0946.pdf
Its an updated paper of only 11 pages, and I’m still wading through it. Mentions some German theories that were published in the 1950’s.
Errors:
-
Figure A1 has a diagram of the sides, lettered. “Face A” of the diagram, showing sides 1 through 5 is numbered okay. However “Face B” understanding the way the dodecahedron geometry works is then incorrect. It is shown as a mirror image of the way it would appear from the outside (or outside face). Otherwise the numbered holes would not correspond correctly. An alternate way of looking at “Face B” would be to assume it the view as shown is of “Face B” is from the the INSIDE of the dodecahedron, the sides 1’ through 5’ are then numbered correctly. They numbered holes would line up through the dodecahedron (side 1 to side 1’ et cetera). A similar illustration was used on her earlier paper on Roman Dodecahedrons this Spring (1204.6497.pdf), but Face B was shown with all dashed lines. Maybe reverse views are shown in dashed lines as a standard in Italy?
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Figures C1 and C2 are also incorrect. These are templates laid flat with holes shown. If we assume sides 1-5 are correct, the corresponding sides 2’, 3’, 5’ and 6’ are labeled incorrectly. For the holes to line up geometrically, 2’ should be labeled 6’, 3’ should be labeled 5’, 5’ should be labeled 3’, and 6’ should be labeled 2’.
How this affects the theory? Don’t know.
She just has a poor numbering system. You’d think she’d have 1’ opposite 1, 2’ opposite 2, 3’ opposite 3, etc. but she doesn’t.
Oops! My mistake. I hadn’t finished digesting the report and noticed from how the diagram how the near hole was greek letter prime and the far hole was corresponding greek letter.
Pretty bizarre that the system wasn’t carried through, and that the numbered holes don’t even use the same numbers! Never guessed someone would do something so counter-intuitive! Foggy thinking, poor presentation IMHO. Thanks.
Still finding mistakes. You’re right, its an effed up naming system that makes little sense. (If Face B had been mirrored it would have been rational)
Compounding this, to match her conclusions and numbering pairs, you have to rotate “Face B” 72 degrees CCW! It won’t match if you use the normal orientation with the top of the page being up! That’s the only way to get the hole pair 2’ and 6, the ones used in her example, to line up. After that, the effed up number system at last matches the rest of her pairs. As the Australians say crikey! What a bugger.
Found a third report by her, on ancient surveying instruments. Unfortunately, it has many of the same “mistakes”.
Explanation from the author of the paper:
“I have used in my papers the same notation of the paper
G. Guillier, R. Delage and P.A. Besombes, Une fouille en bordure des thermes de
Jublains
(Mayenne) : enfin un dodécaèdre en contexte archéologique!, Revue archéologique
de l’Ouest,
Vol.25, p. 269-289, 2008”
I finally got around to starting work on my replica - details of the project (in progress) are here:
http://www.atomicshrimp.com/st/content/dodecahedron
At the time of posting, I’ve completed the wax casting form (and it’s looking pretty good)…
Are you planning on including the concentric circles around the holes? If so, are you going to do that on the finished metal piece, or on the wax form?
Not sure - not all of them have that detail - some have blank faces - others are decorated with clusters of small circles.
A few interesting things came to light whilst I was making my wax form:
[ul]
[li]It turns out that the holes in opposing faces are almost the same - this should have been obvious from the descriptive tables I’d seen, but it just didn’t register. So it doesn’t seem likely that this is a taper gauge - or indeed a retort for conical or pointed bottles etc.[/li][li]I found that constructing the wax form is absurdly difficult - and it gets harder as you go along. Joining two faces together is hard - adding a third is harder still, and so on. Also, as more of the corner balls are added, it gets harder and harder to handle the form without damaging it. I think this lends weight to the notion that this is an apprentice’s masterpiece assignment.[/li][/ul]
Still not buying that explanation. This is the “god of gaps” argument, wherin any unexplained, complex object must have had no purpose, and was just practice for students. There are too many of them, in too many different places not to be an object with a practical, daily function. There are lots of ancient objects that are hard to make; that is not a reason to think they were just practice for students.
Now that you and others have done the hard work of actually quantifying the geometry, I am tempted to make a 3D file of this that can be printed on my 3D printer. It would probably have to be broken into a few pieces to print properly and assembled after printing.
Excellent! Can we see it tomorrow? 
You might feel differently if you tried making one. I’ve made a lot of different things - and quite unlike ever before, I experienced a distinct feeling that this thing is more complex, delicate and tricky to make than it needs to be - and some parts seem almost deliberately challenging (affixing the panels with the largest holes, cutting neat curves on the smallest holes, ensuring that the five upward-pointing ball corners don’t end up half filled in the casting, etc).
I’ve never encountered this as the null hypothesis (isn’t that usually ‘religious artifact’?), but in any case, I’m not saying this thing has no purpose at all - I’m saying that its purpose may be that of an apprentice completion piece - a portable demonstration of mastery of multiple, specific skills - not a challenge for students, but a sales tool - something a metalworker can show to clients to persuade them that he is up to the task.
It could be a fetish, unless that is covered by “religious artifact.” It’s certainly takng on aspects of one here.
The form looks awesome - good luck with the mould making and casting!
I think I have an idea on this, I think it may have been used in waterclocks to regulate flow, through the different sized holes - the holes correspond to how quickly/slowly the water should flow out, so you would attach this to a big water container and cover all but one hole, the size of which represents how long you want to time for.
The knobs on the vertices could have been used to hold it in place.
A water clock needs a hole far smaller than those on any Roman dodecahedron. You need drips, not gushes.