For reference wiki says they range in size from 4 to 11 centimetres (I assume they mean diameter). A ping-pong ball is about 4 centimetres in diameter, and a softball is 10 centimeters
Ping pong ball:
Hand holding soft-ball:
A little large for my idea (jacks) but the smallest is definitely too small for a spool knitter
Zodiac, 12 months, Platonic solid. We run into the strong law of small numbers.
There aren’t enough numbers to avoid a legion of coincidences.
That the moon has a period of 29.5 days, and divides the year almost perfectly into 12 is coincidence enough. Tying that to the number of faces of one of the five Platonic solids is a stretch.
Especially as 12 has a useful number of divisors, so it crops up everywhere.
Lost wax casting isn’t a mass production technique, because the wax is, well, lost.
Lost wax casting is a mass production technique still in use today. It is a type of investment casting. Many mass production molds are temporary. Everything from Candy Corn to jet turbine blades are made using temporary molds. The wax is not lost either. Molds are preheated before molten metal is poured into them and the wax drains out of a little hole and is reused.
The substance of the wax isn’t lost, but that’s irrelevant. What matters about the wax is its shape, and that is lost.
I suppose that you could use lost wax to make a reusable mold, if you took care in your design and included thin sheets of something to separate the mold pieces, but it’s usually used for molds that couldn’t be easily separated, and where you remove the mold from the finished piece by breaking it away.
Yeah, you could make shallow moulds of lead or soapstone for casting the wax forms for the pentagonal faces and two-part moulds for casting the knobs in wax, then assemble those into the whole wax form for the dodecahedron - and that’s what you’d probably do (or something else like it) if you had to make hundreds or thousands of identical copies of these objects (and if you still wanted to use the lost wax method) but there doesn’t seem to be any reason to believe this ever happened.
They were game tools, to play the Icosian game!
I only play the Icosian game for money with a doubling cube.
It can be. In model railroading intricate bits that are a PITA to make by hand are available as lost wax castings.
A master is made then a silicone mold is made from it. The silicone mold is used to make the wax investment piece, many of them are joined together with sprues, and the whole assembly submerged into plaster encased in a cylinder four inches or so in diameter. The plaster is baked, hardening it and making the wax melt and get absorbed, then the cylinder is put into a spinning apparatus and the brass poured into the cavity. After it cools, the plaster is washed and broken away, then the individual parts are clipped from the sprues.
It is useful for moderate-sized runs and cheaper than machining a die for molding plastic parts, although that is becoming more common. I suspect CNC machining is the reason for that. The multi-step process is necessary because the silicone molds don’t stand up to the hot brass but last long enough with the wax. They do wear out and have to be remade from time to time.
There are also 3D printers that work in wax. Lost wax is the usual method for “3D printed brass”.
Although i have some cool doodads that were made on a 3d printer by first sintering stainless steel dust and then soaking the thing in molten brass to fill in the holes and coat it. Looks like slightly smoothed 3d printed brass.
In that process, the steel particles aren’t actually sintered together; they’re bound with a sort of glue. There are metal sintering processes, but they don’t need the brass dip finishing step.
The woman who sold them to me, whom i trust to be accurate on that sort of detail, told me it was sintered. And i don’t think it needed the brass, i think that was to improve the appearance.
Also, this was perhaps 20 years ago, when 3D printing of any type was fairly new.
The Enigma of the Roman Dodecahedron is Revealed !
This video just showed up in my YouTube feed. The guy makes a very strong case that the dodecahedrons were used to encode and decode messages.
They’d need to be standardized for that. Have we ever found any two that match?
I confess that I only skimmed the video, but if I’m understanding his proposal, it doesn’t sound very persuasive to me. Essentially, he proposes that each dodecahedron had a set of up to 12 encoding wheels associated with it, along with one plaintext wheel. To encode a message, you put the plaintext wheel on one side of the dodecahedron, then overlay one of the coding wheels on it (the one whose central shaft matches the hole on that side of the dodecahedron). Then read off the code by matching each letter on the plaintext wheel to the corresponding letter on the encoding wheel. He also shifts the wheel after each letter to make it a polyalphabetic substitution cipher. He then makes a wax imprint of the dodecahedron face to identify which cipher wheel was used.
My question is, so what’s the point of the dodecahedron in this process? You could just put the wheels on top of each other without any dodecahedron involved, and identify which of the 12 cipher wheels is used by sending a number. Adding the dodecahedron to the cipher wheels complicates the process entirely unnecessarily.
Well, they don’t ALL need to be standardized. They just need to be manufactured in matching pairs. Having each pair be different from other pairs would actually be better than having them all identical from a security standpoint (in a very minor way).
For this theory to work, though, each dodecahedron would need to have 12 different sized holes. I know that the holes are of different sizes, but do they all actually have 12 distinct sizes in all existing samples?
We would also need there to be pairs. Have any identical dodecahedra ever been found? AFAIK each one is unique.
Also, never found with an alphabet wheel, never mind sets of them.
Then of course the eternal question of why only in Gaul and Germania…
Given the ancients seem to have effectively baffled their enemies in the secret message stakes by such clever ruses as shaving someone’s head, tattooing a message and letting them fuzz up again before sending them through enemy lines [actual footage here], and wrapping a strip message around a stick I think this sounds like massive explanatory overkill. And the small detail that the dodecahedra are entirely superfluous to the exercise doesn’t help convince me.