Sunday, June 8, 2014

Roman Dodecahedron I suspect is a Ball Guage

Roman Dodecahedron
Is it a Spherical Ball Gauge?
I just learned about these interesting historical artifacts known as a Roman Dodecahedron yesterday (June, 7th 2014) and started to research them. Seems no one can agree on what they must have been used for.  Here's my guess.

It's a ball gauge!

That is, it's a gauge for checking the spherical curvature of balls.  Used most likely, for carving round balls from stone, such as the roman stone ballista balls. I did not see any other suggestions for this possible answer.

The holes of different sizes with the knobs of the same size, will allow each face of the 12 sided device to match a different sized ball.  It would allow the stone carver to check the ball to find the high spots that still need to be carved down further. If anyone has ever tried to carve a sphere, without the help of a tool like a lathe, you would know how hard it is to get an accurate round ball created.  A tool like this, would allow the stone carver to start on one spot of the rock, and establish the curvature of that spot, without first having to rough out the entire sphere. Once the curvature was started, they could continue working around the rock to form the entire ball.

The 12 sided shape is also very easy to make highly accurately, using only a compass and a straight edge. One side could be laid out and cut with a compass, and then 11 matching pieces could be made. The accuracy of the pentagrams are easily checked by rotating, and flipping the pieces to make sure they all align perfectly with each other no matter which they they turned. Each one, only needed a different sized hole in the middle. The actual size of the hole was not critical, as long as it was round, and well centered, which would be easy to lay out and cut with just a compass. 
Once the sides are all assembled, the dodecahedron is easily constructed and guaranteed accurate by geometry. No extra alignment tools are needed.

The balls can be brazed onto each corner, and checked for accuracy of length, against a flat surface.  Each side of the gauge must have all 5 corners aligned in a flat plane.  By checking and adjusting until all 12 sides are flat, it can be assured that all 20 corners are aligned into a perfect dodecahedron.

The resulting gauge will make 12 different sized but highly accurate round balls.

Though this technique would be very difficult if the goal was to make a highly accurate diameter sphere, say to fit inside a cannon bore.  It would be ideal however, if the exact diameter was not important, but the roundness of the sphere was important.  And that, as I understand it, is just what the roman's did need for the sling-shot like balsitis that would no doubt have maximum effect, and accuracy, if the balls were highly round, but where the precise diameter was not critical.

At the same time, there are other variations of this device, that have no holes in the structure at all, like this one:

This second form, seems to be for the same purpose -- to check the curvature of a sphere.  But instead of using a hole of a different size in each face, this device used nobs of different sizes on each corner to control the curvature of the sphere it was gauging.

Note also how the sides are decorated with round circles which is consistent with the concept that the device is associated with round objects.

Also note, how the sides curve inward, even though that's not needed.  But by making the sides curve inward, it reduces how far out the knobs need to stick, to create a given sized curvature.  All features seem logically consistent with using this device to check the curvature of a sphere.

Since this device only has three corners per side, different sized balls on the corners were guaranteed to produce different curvature gauges without needing to guarantee the accuracy of the alignment of the sides.  One could randomly place different sized balls on each corner and the device would still work to produce highly accurate spheres of many different sizes.

However, this style was probably harder to use, becuase it would require one to feel the rocking of the gauge on the work piece, but not to be able to see where it was touching and not touching. The style with the holes, would probably make it easier to see what parts needed to be carved down, and maybe even make it possible to mark the spots of the ball that needed more carving.

If my theory is correct, I suspect a closer examination of these devices would show tapered wear on the knobs consistent with it being placed against stone and dragged around to test the curve.  The alignment of each side could also be tested to verify that each face was correctly aligned to form an accurate spherical curvature gauge.

If one were to fight a war, where lots of stone Ballista balls had to be carved, and all tools needed to do the work had to be carried with you, this small hand tools seems idea for an army on the march.  I don't know much about Roman history, but if the location of where these were found in Europe were fairly consistent with where the Romans were using their Ballistas, that would be yet another verification of what these were.

Curt Welch


  1. Trying to understand a little more about Roman History, I've uncovered some data that is fairly consistent with the idea these could have been gauges for assisting in carving stone Ballast balls.

    First, the wikipedia page on these claim they date to the 2nd and 3rd Century.

    A map on this page, shows where they were found:

    Which seems roughly consistent with where the Roman Army might have been stationed and operating in this time period.

    On that same page, is mention that most of the objects found have no archaeological context, but a few have. And that context was:

    "Dodecahedrons are amongst others found in military camps (13), graves (3), near a sanctuary (1), in treasures (2) and as a river discovery (3)."

    A clear majority were found in Military Camps, making it consistent that these were tools carried around by the military.

    In addition, this page about the use of Roman siege engines:


    "According to Vegetius river stones were best, since they are round, smooth, and dense. Ballista stones found at the site of Masada were chiseled to make them as round as possible"

    So they were carved, at least some, to improve their roundness. And if the engineers were selecting and carving stones at a river, it's not unlikely that this tool could have been lost there, justifying the 3 river context findings above as well.

    Also on that same page, was the history indicating:

    "Every century (group of 60-100 men) in the Roman army had a ballista by the 1st century AD."

    So though the technology started to creep into use earlier, this type of weapon wasn't a common feature of the army use until the 1st century. The development of this sort of gauge as a standard tool used by the army could easily have not evolved until some time after the weapons become a standard part of the Roman Legion, which would explain why they date to the 2nd and 3rd century.

    Also, though most are made from bronze, some seem to be made from stone. Would it not be surprising if the stone carvers lost their tool, and attempted to duplicate one with the material they were experts at working with, in the field -- stone?

  2. Hi Curt, When I saw the first ball (on another site, which led me here in the comments) I immediately thought it might have been a drawplate for trichinopoly, but having now seen the second example you provided, I would concur that you are probably correct. Your example provides so much more sense and practicality that the gloves idea that was mentioned elsewhere. As a reenactor, and having had experience with both fibre arts and with carving techniques, I can immediately see the validity to your argument.

  3. Hello Curt, I'm the fellow whose model on Thingiverse you commented on. I would happily print out and send you one of these for the cost of filament and shipping if you wish to have one to test your theory, although I fear a plastic version won't be quite as hard-wearing as the original metal ones.

  4. Has anyone taken a variety of Ballista balls from an archeological source and gotten their dimensions? It would be interesting to see if they matched any devices or were roughly the right size. I know there are many variations to both but it might yield some interesting results

  5. Your close, but they are actually used to measure the displacement (size and shape) of sling shots for consistancy. By dropping the gauge in a bowl of water you can measure the water displacement of an object inside the dodecohedron, in this case sling shot, buy lining the surface of the water with the bottom of one of the holes and quantifying the amount of water, it gives you an accurate profile of the sling shot. This was key in making them accurate over long distances. A dodecohedron turns out to have just the right shape for doing this for an eliptical object.