Scattered through museums across Europe you can find 40 to 50 strange bronze objects, hollow, about the size of a fist, with a dodecahedral shape (a dodecahedron has twelve sides, all identical pentagons). In the center of each face is a round hole, and each corner has a small knobby foot. In all, we know of 77 such objects found since 1739, always in Celtic areas, usually at Roman sites. As far as anyone can tell, they're of Celtic make and date from the first century or two A.D.
Their original distribution runs something like this:
No matter how many books you've pored over about the Celts and their religion, you probably have never heard of these dodecahedra. And, outside of Widdershins, you'll have a hard time learning much more.
C.W. Ceram, in the introduction to his popular Gods, Graves and Scholars, included a drawing of a Celtic dodecahedron without identifying it, noting only that no one knows what they were. Walter Burkert discussed these dodecahedra briefly in his Lore and Science in Ancient Pythagoreanism. You'd be lucky, however, to find even a passing mention of them in popular works about the Celts. And yet, Celtic dodecahedra present us with a characteristically beautiful, frustrating and suggestive mystery about the past.
What do we actually know about these objects?
They were cast of bronze with great skill using the lost-wax method. In many cases, the feet were attached after casting, but a few were cast with the feet integral.
No two are the same. The whole ones that have come down to us vary in height from about 11/2 to 41/4 inches, and in weight from as little as an ounce to well over two pounds. Most are around 21/2 inches high and weigh less than half a pound.
In a few, all the holes in the faces are the same size, but in most, the holes vary in diameter from under half an inch to over an inch. The smallest recorded hole is about a quarter-inch in diameter, and the largest about an inch and a half.
One was found in a woman's grave. Many show signs of having been in fire. It has been suggested that because pyrite, a fire-starting rock like flint, occasionally turns up in the form of a dodecahedral crystal, the dodecahedron may naturally have been associated with fire.
No one, however, has found any mention of Celtic dodecahedra in any surviving ancient Roman or Greek text.
In speculating what these enigmatic objects were for, archaeologists and antiquarians have suggested the following uses, among others:
Let's take a look at these options. As mace weights, the dodecahedra would have been silly. Not only are they generally light and fragile, they have little rounded feet, not the long, sharp, skull-splitting spikes you'd want in your mace.
It is just possible the dodecahedra could have been used as staff or scepter decorations. The only common pattern among the layout of holes in the dodecahedra's faces is that most have at least one pair of fairly large holes (around an inch in diameter) that are opposite each other and close to the same size. The problem is, the scepter decorations that exist from the period are plainly made to mount firmly on the end of a staff. The dodecahedra would have been harder to make, harder to mount and less impressive looking.
They would make great candleholders, though. They stand very nicely on their little feet no matter which side faces up, so you can easily choose a hole that fits your candle. In fact, wax residue has been found inside one of them. The problem is, if this was their use, why are the dodecahedra so much alike? A candleholder could equally well be a cube or any number of other shapes, and most shapes would be easier to make than a regular dodecahedron. In spite of variations in size and configuration, all of these objects look very, very similar.
As for their use in measurement, the differences in the dodecahedra's hole size does suggest some sort of measuring device. However, none of the holes or faces on any dodecahedron have identifying markings, so there's no way to tell the holes apart. In most cases, several of the holes are close enough to the same size that, without markings, you would easily confuse them. And again, these dodecahedra were very hard to make; if you simply wanted an object with standard-sized holes in it, why insist on this particular shape?
With great ingenuity, several scholars have developed a theory about how the dodecahedra could have been used to measure distances. If you look through a smaller hole and a larger hole in such a way that the circles line up, and you look at a stake marked with measurements so that it crosses the superimposed circle, you can calculate your distance from the stake based on how much stake is visible across the lined-up holes. Again, though, there are no markings on the dodecahedra to help you remember which holes to look through, and no pattern in hole sizes to tell you how to interpret your results. Also, if you were inventing a surveying instrument, you would probably not come up with a small, confusing bronze object that is extremely hard to fabricate. Larger, more easily created shapes would work better, where a dodecahedron would compromise accuracy and send costs through the roof.
Because the dodecahedra must have taken enormous skill to create, some people have suggested that their purpose was to serve as a proof of mastery in bronze casting. Too many of them survive, however, scattered over too large an area to make this very plausible. Why would this one particular object be chosen as a master piece by so many bronze casters across Britain, France, Switzerland and even into Austria and beyond? And why would people preserve them, if they had no other significance or use?
When it comes to divinatory dice, though, I think we're getting somewhere. Medieval and Renaissance sources do mention dodecahedral dice being used for divinatory purposes. A silver-plated solid lead dodecahedron of this sort, with signs of the zodiac inscribed on its faces, was excavated recently in Geneva. When it comes to the Celtic dodecahedra, however, we come back to the problem that the faces are not marked, making their use in divination seem less likely. And why go to the extra trouble of making them hollow, with different sized holes? And why add the little feet, which might break off if you threw the dodecahedra like dice?
Which brings us and most other scholars to the idea that these dodecahedra were religious objects of some sort, with mysterious mythical significance.
On the subject of mythical significance, we are on firmer ground. The dodecahedron is what is known as a regular solid. Regular solids are three-dimensional forms all of whose edges have the same length and all of whose faces have the same shape. With some subtle thought you can prove, as the Greek mathematicians Theaetetus and Euclid did, that only the following five regular solids can exist:
What, you may ask, would the Celts or their religious leaders the Druids have known or cared about Greeks, Plato or the regular solids? A lot, quite possibly. The Greeks and the Celts were in close contact for centuries, beginning before 400 B.C. The modern city of Marseilles, for example, started out as the Greek colony of Massilia, in the middle of Celtic lands.
Furthermore, the Greeks perceived the Druids to have been strongly linked to Pythagorean ideas from early on. Pythagoras himself, a mystic numerologist and Greek political leader of the seventh century B.C., was thought to have studied not only in Egypt and Babylon, but also among Druids. The Greek historian Hippolytus reported that Pythagoras' slave Zalmoxis also carried Pythagoras' teachings back to the Druids. While these stories are unlikely, originating as they did centuries after Pythagoras' death, they reflect the widespread Greek view that Druids and Pythagoreans shared important intellectual territory.
The Neo-Pythagoreans of the late classical period formed a secret magickal brotherhood that adopted the pentagram as its symbol. The pentagram is closely associated both with the pentagon (one side of a dodecahedron) and with the so-called golden section, which the Greeks believed to have powerful mystical and aesthetic properties, and used to design the Parthenon in Athens and Phidias' statuary.
The dodecahedron, then, was a form having enormous significance for Neo-Pythagoreans, and quite possibly for the Druids as well. It was the atomic shape of cosmic spirit, with the twelve pentagonal faces corresponding to the signs of the zodiac while also outlining hidden pentagrams that everywhere revealed the golden section.
For Druids, the form had the added significance of having 20 corners - as students of French learn in their first year, the Celts used a base-20 number system (remember quatre-vingt?). This significance may help to explain the prominent knobby little feet the Druids attached to each corner of their dodecahedra.
Having said all this, and accepting the hypothesis that the dodecahedra were ritual or divinatory magickal tools, we're not really any closer than before to answering the question we started with: How are these objects used?
Because so little reliable information has come down to us about the Druids, long-standing pagan tradition encourages us to excavate our imaginations for artifacts of that lost age. A fine tradition! I am drifting back across the gulf of time to a smoky village in the foothills of the Alps....
---
I see a young woman leaning out the window of a hut, talking to a man. "No," she says, "I don't have a mind to."
"Oh, my love," he says, "believe me, I am the one in your dreams, the one for you, only for you."
"Really?" she says. "Well, perhaps I'll ask my father's little magick ball."
The man looks abashed. "No, no, don't disturb your father!" But it's too late, she's gone. A minute later, she reappears and drags him inside. Reaching under his tunic, she grabs a good handful and with a pretty smile soon makes it larger.
"Now," she says, "let's see." She holds up the merciless little bronze globe. Most of those holes are so small! Squatting on the hard earth floor, she spins it on one of its many little feet. The man watches it twirl with real apprehension. Using pig fat and her long fingernails, she has the right to make an excruciating effort to work him into whatever hole lands upright, until she's satisfied he can't fit.
The spinning dodecahedron slows and suddenly a foot catches in the dirt. Bouncing, it comes to rest. The man's face lights up. The girl slowly lifts it and slips the large holes easily over what she's been teasing in her hands. He looks in her eyes, and she grins at him.
"You're right," she says. "I guess it's meant to be. At least this once, anyway." She leads him back to the straw in the corner.
---
The winds of time blow sideways across the night, stretching me into a wraith of mist among others drifting on the heath.
The old Druid, lean and stringy, is wrapped in skins, his white hair a wild tangle down his back. He sits alone just upwind of the small fire, taking its heat and light, intent on what he's doing.
With knobby fingers, he is meticulously poking a small stick through one of the holes in a bronze dodecahedron that he holds.
I drift to his shoulder. The inside of the dodecahedron is packed with peat. In each hole, something different has been inserted. A holly leaf, a myrtle berry, a chip of bone, a blackthorn twig, an oak leaf, a child's tooth, a scrap of ash bark, a little feather, a crescent of fingernail, a smooth gray pebble, the broken dome of a robin's egg, the dried remnants of a human eye. Each is held in place by herbs and grasses carefully wedged at the edges of the holes. Around each foot, a person's hair has been carefully wrapped and tied. They are different colors, gray and black and red and blonde and brown. I can feel the many meanings, though I cannot grasp them.
I feel myself drifting away. He is dismissing us, calling out the round fullness of the moon above. He will scry, spinning the dodecahedron again and again on his wolf-skin cloak to the questions that he sets.
When he's done, he will place the bronze thing in the fire, releasing the magick, and in the morning lift it from the ashes again, warm and empty as the heart in death.
---
The Roman children pass shrieking as the game shifts, but Marcellus just leans back into the column, panting wildly, trying to catch his breath. Tibernius catches sight of him and trots over. "Come on, give us a hand."
Maro shakes his head grimly, like a centurion. Something of his seriousness communicates to Tibi. "What's up?"
"I was just at the market. Saw a fight."
Tibi raised an eyebrow. "So?"
"Both dead."
"Oh?" Tibi looks scared and interested. He doesn't like blood, but he does.
"It was two soldiers from the legion, fighting over a piece of bronze, a trophy thing, good luck charm. One of those things that shows you've killed an important Druid."
"Yeah? What happened."
"The bigger one, his guts were all over the ground, he was dragging them between his legs, but he cut the thick one's neck and knocked the trophy out of his hand on the backstroke. Blood spurting like a fountain."
Tibi licks his lips. "They scream?"
Maro shakes his head. "Nah, hardly any noise at all. But."
Tibi almost doesn't pick up the but; he's thinking about the death. Then he notices. "But what?"
Maro opens up his hand. "I got it. The trophy thing rolled under the bread stall. Nobody else saw it." The dull gleam of the bronze dodecahedron in his palm silences them both. For a moment it is luck, mystery, danger and death, savagery and barbarism and cruel ancient magick. Then, suddenly, it seems more like a Greek thing, precious and subtle in its beauty.
"You going to keep it?" asks Tibi.
Maro looks at him. "You tell and I'll kill you, I swear I will."
Tibi shakes his head silently.
Eleven years later, when Marcellus' body is pulled from under two dead cohorts and three Gauls, his officers find the dodecahedron in his canvas satchel, with a few gold coins.
---
So, perhaps these remarkable objects were Druidic magickal tools, mystical symbols of the cosmos, and maybe on occasion divinatory love dice. It is likely that we've found so many of them in Roman camps because the Romans seized them as spoils. But your guess is as good as mine. The Druids carried this and many other secrets to the grave.
Bibliographical Notes: Up until a few years ago, the most detailed catalog of Celtic dodecahedra was to be found in a very rare 54-page work by J. de Saint-Venant entitled Dodécaèdres perlés en bronze creux ajouré de l'époque gallo-romaine, published in 1907 in Nevers. The one copy of this work I could locate in the United States is in Harvard's Dumbarton Oaks library in Washington, D.C., and Dumbarton Oaks won't send it out on interlibrary loan. The other comprehensive analysis of the subject, Waldemar Deonna's "Les dodécaèdres gallo-romains en bronze, ajourés et bouletés," published in Bulletin de l'Association Pro Aventico, Vol.16 (1954), pp. 19-89, is not much easier to lay hands on.
Do not despair, however - in 1993, Robert Nouwen of Tongeren, Belgium, published the definitive work on the subject, entitled De Romeinse Pentagon-dodecaëder: mythe en enigma. It contains a complete catalog of known dodecahedra, some new metallurgical analysis and a thorough survey of earlier work on the subject. The good news is, you can still get a copy of this excellent monograph from the Provinciaal Gallo-Romeins Museum in Tongeren. The bad news is, it's in Flemish, with a summary in French. The museum's address, if you're interested, is Kielenstraat 15, 3700 Tongeren, Belgium; you can write to them in English, and a $25 check will cover the book and shipping.
For those of us whose Dutch is a little weak, there are a couple of brief articles in English by Benno Artmann, one in Mathematical Intelligencer, Vol. 15.2 (Spring 1993) p. 52, and one in American Mathematical Monthly, Vol. 103.2 (Feb. 1996), p. 132. There is also a good summary article by Christopher Hill in Antiquaries Journal, Vol. 74 (1994), p. 289. From these, you can also get pointers into the scattered earlier literature on the subject.
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