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THE GALLO-ROMAN DODECAHEDRON AND THE RECEPTACLE OF ALL BECOMING

Published online by Cambridge University Press:  17 November 2025

Michael Guggenberger  and
Stephen Leach
Michael Guggenberger
Affiliation:
Michael Guggenberger, Österreichischer Alpenverein, Olympiastraße 37, 6020 Innsbruck, Austria. Email: michael.guggenberger@alpenverein.at
Stephen Leach*
Affiliation:
Stephen Leach, 1 West Park Road, Derby, DE22 1GG, UK. Email: s.d.leach@outlook.com
*
*Corresponding author: Email s.d.leach@outlook.com
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Abstract

Discussions of the Gallo-Roman dodecahedron often note the significance of the dodecahedron in Platonic and Pythagorean philosophy, but they tend not to relate the archaeology to the textual evidence in any detail. We attempt to do that in this paper. We argue that, whilst it remains the case that there is no contemporaneous description of the Gallo-Roman dodecahedron, there are several texts – including an overlooked passage in Iamblichus’ On the Pythagorean Life – that point to its possible inspiration. We relate these texts to the location of dodecahedra in Gaul and Britain and to the interest of the Druids in Pythagoras, which was frequently remarked upon by Roman commentators.

Keywords

dodecahedronPlatoPythagorasIamblichusdivinationDruids

Information

Type
Research paper
Information
The Antiquaries Journal , Volume 105 , October 2025 , pp. 31 - 54
Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Society of Antiquaries of London

INTRODUCTION

‘what these trousered barbarians believe is the very faith of Greek Pythagoras himself’, Valerius Maximus

It has often been remarked that there is no more mysterious artefact in Roman archaeology than the dodecahedron.

The Gallo-Roman dodecahedron is a twelve-sided hollow object made of copper alloy (eg. bronze). It has thirty edges and twenty vertices. At every vertex there is a small ball or knob and at the centre of each of its twelve flat pentagonal faces there is a single hole of different size. These holes vary from 0.6cm to 4cm, the largest holes between 1.7cm and 4cm and the smallest between 0.6cm and 2.8cm.Footnote 1 Excluding the knobs, the diameter of these objects (from face to opposite face) varies from 4cm to c 10cm.Footnote 2

There are different types of Gallo-Roman dodecahedra, and there is no consistency in the pattern of circles and/or ring-and-dot motifs on their faces,Footnote 3 but the most common type by far (Greiner/Guggenberger type 1a) has ten perfectly round holes with usually three concentric circlesFootnote 4 engraved into the metalFootnote 5 and an additional pair of holes (opposite to each other) without circles. The latter are not so perfectly round and are often larger than the other holes.Footnote 6 In most cases this can be explained by the production process, but there may also be repercussions for its use.

About 134 Gallo-Roman dodecahedra have been found since the first, discovered at Aston in Hertfordshire, was presented to the Society of Antiquaries of London in 1739 (fig 1).Footnote 7 An ongoing catalogue has been compiled by Michael Guggenberger.Footnote 8 They are found almost exclusively in the north-western provinces of the Roman Empire, which are rich in Celtic cultural heritage. Their distribution is focused on the Gallic and Germanic provinces (c 70 per cent, especially on the territory of the former Gallia Comata)Footnote 9 and a large proportion (c 20 per cent) are from Britannia.Footnote 10 In total, around 90 per cent of all dodecahedra originate from areas that – for a short time – belonged to the Gallic Empire (ad 260–74). The easternmost is from Brigetio in Pannonia (Hungary, Guggenberger no. 92), one is from Deonica in Moesia superior (Serbia, Guggenberger no. 130Footnote 11), but none have been found in the Roman heartland (Italy), in Spain, Africa or in the eastern provinces of the Empire.Footnote 12 They were used from around ad 200Footnote 13 to the late fourth century ad, and it seems plausible that some of these were difficult to cast and thus for that reason alone were inherently valuable objects that were passed from one generation to the next. ‘Apparently they derived from an environment characterized by the mutual influence of the Roman and Celtic cultures’ (fig 2).Footnote 14

Fig 1.

Find report from 1739 of the Aston dodecahedron (Guggenberger no. 59). Photo: reproduced with kind permission of the SAL.

Fig 2.

Distribution map of the Gallo-Roman dodecahedra: find sites in yellow, repositories (site not known) in grey. Map: © Michael Guggenberger, based on NASA Visible Earth image.

Dodecahedra come from all kinds of environments,Footnote 15 but only very few have been recovered from archaeological excavations in stratified contexts. Of those dodecahedra with a recorded find location, more than half come from cities or other settlements (fig 3),Footnote 16 just under one-fifth from military camps,Footnote 17 c 8.5 per cent from find contexts with plausible sacred connections,Footnote 18 c 7 per cent from graves or necropolis areas,Footnote 19 c 5.5 per cent from well backfills or refuse pits without known sacred connections,Footnote 20 c 4 per cent from coin hoards or presumably non-sacred bronze hoardsFootnote 21 and c 4 per cent from rivers.Footnote 22 Given that the overwhelming majority of Gallo-Roman dodecahedra derive from civilian contexts and that their distribution within the Roman Empire is geographically limited (despite the mobility of Roman soldiers), a primary military purpose can be ruled out, although there is some concentration around the frontiers.Footnote 23 River finds may represent ritual depositions or accidental losses. That they are found in hoards or in graves – of both men and women – suggests that they were valued possessions. (Their presence in hoards might be explained by the intrinsic value of copper alloys, but this does not explain their presence in graves.) A very beautiful, until now unpublished, Gallo-Roman dodecahedron once belonged to the ‘Henryk Klunder collection, Mainz’ (fig 4).Footnote 24

Fig 3.

Dodecahedron Carmarthenshire (Guggenberger no. 60). Photo: reproduced with kind permission of the SAL.

Fig 4.

Dodecahedron Mainz 3 (Guggenberger no. 134): complete; diameter face to opposite face 5.5cm (without knobs); one pair of holes 1.5/1.7cm and 1.4/1.5cm, all other holes in a very small range (c 1.0–c 1.25cm); thickness c 1.5mm; diameter knobs c 0.5cm; 246g; all faces with five ring-and-dot motifs (Greiner/Guggenberger type 2a). Photo: © Michael Guggenberger.

One of the most recent finds is a well-preserved dodecahedron from Norton Disney (Lincolnshire; Guggenberger no. 132) discovered on the top of a large pit full of building debris 700m east of a villa rustica. Lorena Hitchens suggests that it could have been placed there to ritually close the pit.Footnote 25 It may originate from a shrine.Footnote 26 A fragmented specimen from the southern side of the Severn estuary, south-west of Gloucester (Guggenberger no. 122) was part of a cache identified as originating from a temple (perhaps of Diana at Gloucester).Footnote 27 The fragmented dodecahedron from Lydney (Guggenberger no. 68) comes from the site of the temple complex of the local god Nodens; however, the exact find context is unknown.Footnote 28 Another dodecahedron from the north of Paris, France (Guggenberger no. 110), was found by a metal detectorist in a ‘modest Gallo-Roman domestic structure’, only one metre away from a bronze statuette of a goddess (Juno?).Footnote 29 And a dodecahedron from Pfofeld, Germany (Guggenberger no. 20), was discovered along the Roman Limes, in the same area of a palisade trench (near a watchtower) as a bronze statuette of Mercury as Hermes-Thoth, the syncretic deity that gave rise to the mythical sage Hermes Trismegistus.Footnote 30 A further dodecahedron was found in Schwarzenacker, Germany (Guggenberger no. 21), ‘near’ the sacrificial shafts of an urban Gallo-Roman cult precinct.Footnote 31

Three dodecahedra come from richly furnished graves.Footnote 32 Of these, the one from Gelduba (Guggenberger no. 11), west of the Rhine at Gellep, Germany, was found in a grave of a wealthy woman, who died around ad 350. Its position immediately adjacent to an object of bone (length c 15cm, diameter c 3cm) suggests a functional connection between the two objects.Footnote 33 There may perhaps have been a temporary mounting of the dodecahedron upon a kind of handle passing through its pair of production holes (2.4cm and 2.3cm).Footnote 34

Because the design of the dodecahedron is almost unique, and because there is no contemporaneous description of it, nor even a depiction, there have been proposed all manner of speculations concerning its use, some brilliant, but most of them fantastic or even absurd.Footnote 35 (Its suggested use as a distance-measuring device must be rejected, as F H Thompson, FSA already conclusively demonstrated in The Antiquaries Journal in 1970.Footnote 36) Although new theories emerge continually among archaeologists, there is nowadays fairly broad consensus that the purpose of the Gallo-Roman dodecahedron cannot be found without considering the symbolism of its unchanging basic shape,Footnote 37 and it is often assumed to be some kind of ritual object, possibly used in divination (perhaps in combination with a light source).Footnote 38 Given the broad range of religious and philosophical beliefs, syncretic cults and divination rituals within Gallo-Roman culture, the presence of dodecahedra – as shown – in sacred contexts (and graves and rivers) fits this theory well. The aim of this paper is to try to advance from this vague description towards a description that is a little more focused and detailed.

THE DODECAHEDRON AS A PLATONIC SOLID

Whilst it is true that there is no contemporaneous description of the Gallo-Roman dodecahedron, it is possible that its inspiration can be found in Plato. In his Timaeus (c 360 bc) he explains how the universe is constructed from four elements, each of which is made up of a different shape: fire is made up of tetrahedra, earth is made up of hexahedra (cubes), air is made up of octahedra and water is made up of icosahedra; but there is a fifth regular polyhedron, the pentagonal dodecahedron. Plato, through the mouthpiece of the astronomer Timaeus, suggests that it encapsulates all other shapes and is the basic structure of the whole universe itself as it approaches the shape of the perfect sphere: ‘Yet there remained a fifth construction, which the God used for the universe [to pan] […].’Footnote 39

The Timaeus was translated into Latin in the first century bc, and Plato’s views on the dodecahedron continued to exert influence. Thus, for example, in De Defectu Oraculorum, the Middle Platonist Plutarch (ad c 45–c 125) states through Lamprias that the ‘nature of the dodecahedron […] may well seem to be an image of all being [tou ontos eikón] with reference to all the corporeal that has becomeFootnote 40 [to somatikón gegonénai]’.Footnote 41

Indisputably, in the classical world, from Plato onwards, the dodecahedron was viewed as a shape of great cosmological significanceFootnote 42 – and, almost without exception, every interesting account of Gallo-Roman dodecahedra will mention this. The finding of a hollow Gallo-Roman icosahedron at Arloff (30km south-west of Bonn, Germany),Footnote 43 from a grave dating to around ad 200, underlines the point of taking into account the significance of the Platonic solids. Moreover, the dodecahedron and the icosahedron form a dual geometric pair.

But there may be more that Plato can tell us about these mysterious objects.

THE RECEPTACLE OF ALL BECOMING

Plato has a threefold ontology. There are the forms (perfect and unchanging) and there are the sensible things (the imperfect and changing copies of the forms); but less well-known is that Plato posits a third kind: the receptacle of all becoming that decides upon the way that the sensible things manifest the forms. The receptacle ‘is the condition that allows the elements to exist as sensible things by being that in which they can appear and change’.Footnote 44 Here is Plato introducing the concept:

Let the new starting point of our account of the universe be a fuller division than the previous; we then distinguished two kinds – we must now point out a third. Two were enough at an earlier stage, when we postulated one kind for the intelligible and unchanging model and another or the imitation of the model which comes into being and is visible. We did not distinguish a third kind, considering two would be enough; but now the argument seems to compel us to try to bring to light in words a kind that is difficult and obscure. What must we suppose its powers and nature to be? Most of all something like this: it is the receptacle [hypodoché] and, as it were, the nurse of all becoming.Footnote 45

Plato tells us that the receptacle of all becoming ‘always has to be called (as) the same’ because it never alters its characteristics although appearing differently at different times,Footnote 46 yet in trying to convey its characteristics he reaches for a number of analogies. He compares it to a lump of gold that may be worked into different forms, to a mother and a nurse, and to the base that a perfumer uses when making different fragrances. Its main characteristic is that it is malleable and, although of a neutral character itself, by mixing the four elements it is able to impress a character upon that which enters it. He describes it as an invisible or unseen form,Footnote 47 a space (chora)Footnote 48 that provides a place or seat (hedra) for all becoming,Footnote 49 thus a spatial location for ‘all the bodies’ (ta panta […] somata) that it receives.Footnote 50

Understandably then, ‘[t]here has been considerable discussion about whether the receptacle is to be thought of as matter, or as space, and whether it is possible to think of it coherently as having both of those roles’Footnote 51 – and no doubt this was also a subject of discussion among Plato’s earliest readers.Footnote 52 The hollowed, and holed, and remarkably thin-walled (0.5–4mmFootnote 53) Gallo-Roman dodecahedron could be considered an ingenious compromise in that it combines both roles. Indeed, if there were going to be a physical model of the receptacle of all becoming then it would be difficult to conceive of one more suited than the Gallo-Roman dodecahedron.

Admittedly, Plato does not state that the receptacle takes the shape of a dodecahedron – he only says it is free from those forms it receives.Footnote 54 However, since he implies that everything in the universe must pass through the receptacle and everything is made up of the elements (somata) in the form of four of the five regular solidsFootnote 55 – if you were to recreate it – the fifth solid, the dodecahedron (the cosmic universal sphere)Footnote 56 would be its most appropriate shape. ‘[T]he receptacle seems to possess a specific extension in the created universe, in contrast to what we can say of it in the pre-cosmos. But yet again, the determination of this extension is derived from something else, namely the dodecahedron that Plato claims to be the form of the world as a whole.’Footnote 57 Moreover, remarkably, the second part of the ancient Greek word dodekahedron is derived from hedra and reminds us again of the place or seat of all becoming.Footnote 58

It is curious that the Gallo-Roman dodecahedra almost all have twenty knobs – one at each vertex. Was this perhaps to emphasise the twenty vertices? In his book De Vita Pythagorica (On the Pythagorean Life), written at a time when interest in Pythagoras was enormous, the Neoplatonist philosopher Iamblichus (ad c 245–c 325) calls the dodecahedron not only ‘the sphere of the twelve pentagons’ (sphaira he ek ton dodeka pentagónon),Footnote 59 but also ‘the construction of the twenty vertices’ (he tou eikosagónou systasis).Footnote 60 According to Diogenes Laërtius (fl third century ad), Pythagoras divided man’s life into quarters: twenty years as a boy, twenty years as a youth, twenty years as a young man, and twenty years as an old man.Footnote 61 And Plato suggests that the normal period of full physical and mental development is twenty years for women (and thirty – like the number of a dodecahedron’s edges – for men).Footnote 62

It is therefore possible that the number twenty has some significance for a supposed divinatory usage of the Gallo-Roman dodecahedron and that this was emphasised by the knobs, which are all of the same size – with a broad range of diameters from object to object.Footnote 63 But that there exists one example with three knobs at each vertex (Guggenberger no. 66) suggests that the knobs are assigned to the pentagonal faces and that they may emphasise their meaning.Footnote 64 This detail, combined with the fact that there is not one dodecahedron without knobs, indicates a purpose beyond decorationFootnote 65 and may underscore the protective function of the knobsFootnote 66 for the faces and holesFootnote 67 (and edges). It also hints at a usage distinct from that of Roman dice, which never feature knobs because they have no functional need for them.Footnote 68 Their primary function seems to be to provide support, stability and protection to the dodecahedronFootnote 69 in a way that would not compromise its Platonic-Pythagorean character.

We may imagine that, when not in use, the Gallo-Roman dodecahedron was handled with due reverence and placed somewhere where it might be contemplated and honoured as an object of wonder that ‘we look at indeed in a kind of dream’.Footnote 70 Is this perhaps another reason for the knobs: to enable the dodecahedron to be elevated above the earth?

THE DIVINE RECEPTACLES OF IAMBLICHUS

But let us now take a closer look at another passage from De Vita Pythagorica by Iamblichus. This passage is suggestive of there having been an association between the Gallo-Roman dodecahedron and the receptacle of all becoming. Its significance has not previously been noticed:

ὅλως δέ φασι Πυθαγόραν ζηλωτὴν γϵνέσθαι τῆς Ὀρφέως ἑρμηνϵίας τϵ καὶ διαθέσϵως καὶ τιμᾶν τοᾶς θϵοᾶς Ὀρφϵῖ παραπλησίως͵ ἱσταμένους αὐτοᾶς ἐν τοῖς ἀγάλμασι καὶ τῷ χαλκῷ͵ οὐ ταῖς ἡμϵτέραις συνϵζϵυγμένους μορφαῖς͵ ἀλλὰ τοῖς ἱδρύμασι τοῖς θϵίοις͵ πάντα πϵριέχοντας καὶ πάντων προνοοῦντας καὶ τῷ παντὶ τὴν φύσιν καὶ τὴν μορφὴν ὁμοίαν ἔχοντας

In general, Pythagoras is said to have emulated the Orphic mode of expression as well as [pious] disposition and honoured the Gods in a way similar to Orpheus, placing them in images and bronze, not bound to our [human] shapes but to divine receptacles [hidrýmasi Footnote 71], [because the Gods] encompass all and provide for all things, resembling the universe in growth and form.Footnote 72

The concept of the receptacle (hypodoché), borrowed from Plato, plays an important part in Iamblichus’ philosophy. Influenced by the late second century Chaldean Oracles, he uses the word for all kinds of images that enable the reception of a deity in theurgic practices – practices that re-enacted, through some physical means, the divine creative process. Much remains mysterious about these practices, but they seem to have typically involved figurative and hollow human-shaped statues.Footnote 73 In Plato’s Timaeus, hypodoché describes ‘the raw material that, having received the divine outpouring, made possible the world that we now know. As such, hypodochê is an apt term for a physical statue that will receive a god’.Footnote 74 Iamblichus’ notion hídryma Footnote 75 therefore may well be linked to his understanding of a theurgic hypodoché; for the quote suggests that Pythagoras, the supposed originator of theurgy, used a physical object of reception and veneration not resembling our human shapes but ‘resembling the universe [All] in growth and form’, a divine receptacle that encompasses all and provides for all things.

Like Iamblichus, the Neoplatonist Porphyry (ad c 234–c 305) also pondered the problem of divine representation. He states that the Gods had informed us:

what sort of figure should be given to their statues, and in what shapes they themselves appear […] they themselves suggested how even their statues ought to be made, and of what kind of material […] Moreover they have themselves indicated how they appear with regard to their forms, and from these their images were set up as they are.Footnote 76

In the above passage Porphyry refers to anthropomorphic statues, but in another passage he contemplates the possibility of Zeus’ non-figurative representation, as follows:

The authors of the Orphic hymns supposed Zeus to be the mind of the world, and that he created all things therein, containing the world in himself. Therefore in their theological systems they have handed down their opinions concerning him thus: ‘Zeus was the first, Zeus last, the lightning’s lord, /Zeus head, Zeus centre, all things are from Zeus. /Zeus born a male, Zeus virgin undefiled; /Zeus the firm base of earth and starry heaven; /Zeus sovereign, Zeus alone first cause of all: /One power divine, great ruler of the world, /One kingly form, encircling all things here, /Fire, water, earth, and ether, night and day; […] The god’s broad-spreading shoulders, breast, and back /Air’s wide expanse displays; on either side /Grow wings, wherewith throughout all space he flies. […]’ Zeus, therefore, is the whole world, animal of animals, and god of gods; but Zeus, that is, inasmuch as he is the mind from which he brings forth all things, and by his thoughts creates them. When the theologians had explained the nature of god in this manner, to make an image such as their description indicated was neither possible, nor, if any one thought of it, could he show the look of life, and intelligence, and forethought by the figure of a sphere. But they have made the representation of Zeus in human form […].Footnote 77

In this passage, Porphyry dismisses the possibility of creating an image of God (Zeus/Jupiter) that shows ‘the look of life, and intelligence, and forethought by the figure of a sphere’, but nonetheless the idea of a non-figurative representation had evidently crossed his mind. And

[a]fter all, the Hebrew God used the Ark of the Covenant as his earthly abode when he came down to visit, as the theurgists undoubtedly knew. Stories such as Solomon’s incarceration of demons in bottles were also known to the Greeks and Romans of this period, to say nothing of the Hesiodic story of Pandora’s jar.Footnote 78

In his Vita Pythagorae (Life of Pythagoras), Porphyry tells us that Pythagoras called ‘the sound produced from bronze being struck a daimon’s voice enclosed in the bronze’.Footnote 79 Here he uses the same term as Iamblichus: chalkós (bronze) – and in this case it makes us think of some kind of vessel, a sound bowl (or cymbals).Footnote 80 For the Pythagoreans, bronze was obviously of divine significance.

Of course, the passages quoted – especially Iamblichus on the divine receptacle – remind us of Plato’s reflections on the shape of the universe (encompassing all) and of our earlier considerations about the shape of the receptacle of all becoming – all the more so as, elsewhere in De Vita Pythagorica, Iamblichus refers to the strict secret of the Pythagorean dodecahedron.Footnote 81 He tells the legend of Hippasos, who died because he made the secret of the dodecahedron public. Iamblichus does not explain the nature of this secret, but, according to him, Pythagoras ‘created a worship of the Gods that was based on number’ – everything equals number – so that it was ‘as close to the nature of the Gods as possible’.Footnote 82 Here we should mention that it was ‘at the end of the sixth century [bc] that the idea of a standardized group of twelve gods became accepted – the so-called Dodekatheon’.Footnote 83 This idea of twelve ruling Gods is also represented in Plato’s Phaedo Footnote 84 and it was common knowledge during the period in which the Gallo-Roman dodecahedron was ‘invented’.

Setting aside the question of the truth of Iamblichus’ claims about Pythagoras quoted above, it is important to emphasise that Iamblichus (like Porphyry) was writing during the period in which the Gallo-Roman dodecahedra were made, and he was himself considered a Pythagorean sage. He was drawing influence from the late second century Chaldean Oracles. These were the texts that introduced the term ‘theurgist’ from which in turn the Neoplatonists derived ‘theurgy’.

The short passage in Iamblichus could be the closest we have to a contemporaneous ‘description’ of the Gallo-Roman dodecahedron. It might be objected that the quotation for Iamblichus could be as well interpreted in another way: that Pythagoras honoured the Gods in human-shaped statues, but at the same time, he thought that the Gods were not bound to them because their real form was similar to the universe. Nevertheless, if a Gallo-Roman scholar wanted to construct an object that resembled the real form of the Pythagorean Gods or of the cosmic receptacle of all becoming, for invoking the (twelve) Gods, then – assuming this scholar was familiar with texts and tradition upon which De Vita Pythagorica was based – the dodecahedron would be the obvious choice. To be clear, our argument is not that Iamblichus provided the template for the Gallo-Roman dodecahedron – he was writing at a time the first of these dodecahedra had already been constructed – but that the Gallo-Roman dodecahedron is part of the same tradition as Iamblichus’ remarks about Pythagorean receptacles.Footnote 85 In summary, the Gallo-Roman dodecahedron may be part of the tradition of animating statues in order to make contact with the divine that is discussed by Neoplatonists such as Iamblichus and Proclus and that was inspired by Plato’s Timaeus.

Porphyry, who himself was sceptical towards theurgy, nevertheless gives us further information about the use of certain materials, forms and patterns with statues: ‘As the deity is of the nature of light, and dwells in an atmosphere of ethereal fire, and is invisible to sense that is busy about mortal life, He [God] through translucent matter, as crystal or Parian marble or even ivory, led men on to the conception of his light […].’Footnote 86 Interestingly, a translucent crystal dodecahedronFootnote 87 (presumably used as a dice for fortune telling) was found in the Idaean Cave, a place in Crete associated with Zeus, and Porphyry explains that ‘the sphere and all things spherical’ are traditionally assigned ‘to the cosmos and to the sun and moon in particular, but sometimes also to fortune and to hope: and the circle and things circular to eternity, and to the motion of the heaven, and to the zones and cycles therein […]’.Footnote 88

Although we do not know in detail how a Gallo-Roman dodecahedron might have been used, assuming that its original inspiration was Plato’s Timaeus, then it would have most likely been used to gain divine visions based on numbers (or to ‘calculate’Footnote 89 the future). This is supported by the tradition that Pythagoras taught divination by numbers, rather than by consulting entrails etc, since ‘he considered this to be purer, more divine and more in keeping with the celestial numerical proportions of the Gods’.Footnote 90 The process of divination using the dodecahedra may have involved some form of movement or winnowing, for Plato tells us that this is how the receptacle mediates between the forms (the realm of being) and the sensible things (which are always in a state of becoming):

There are and were also before heaven came into being three distinct items: being [on], space [chora] and becoming [genesis]. As the nurse of becoming was made wet and fiery, and was receiving the shapes of earth and air, and suffering all the affections that go with them, its visual appearance varied; but as there was no homogeneity or balance in the forces that filled it, no part of it was in equilibrium, but it swayed unevenly in every direction as it was shaken by the forces, and being moved it in turn shook them. And the things that were moved were constantly being separated and carried in different directions like the contents of a winnowing basket [liknon] or a similar implement for cleaning corn, in which the solid and heavy stuff is sifted out and settles on one side, the light and insubstantial on another: so at that time were the four kinds shaken by the receptacle, which itself being moved acted as a kind of shaking implement.Footnote 91

Thus, the receptacle ‘is involved in (originally chaotic) motion and causation by being itself moved and causing the traces of the elements to move’.Footnote 92

The Gallo-Roman dodecahedra are all relatively light – about 35g to 580g, with just one example over 1000g,Footnote 93 and there is not one so large that it cannot be held in one hand and shakenFootnote 94 – prior to which some things (representing elements or Gods) may have been put into it as theurgic symbola (as was the case with the Neoplatonists’ hollow statues), and some of the holes may have been blocked.Footnote 95 The Neoplatonist Proclus tells us:

The telestic art establishes oracles and statues of the Gods on earth and through certain symbola makes them capable, they being made of portions of the perishable material world, to partake of the God and to be moved by him and to speak the future.Footnote 96

And Iamblichus goes into details:

in accordance with the properties of each of the Gods, the receptacles adapted to them, the theurgic art in many cases links together stones, plants, animals, aromatic substances and other such things that are sacred, perfect and godlike, and then from all these composes an integrated and pure receptacle.Footnote 97

The Platonic receptacle of all becoming was presumably created by the demiurge, the divine craftsman, who ‘constructs a world that is as excellent as its nature permits it to be’.Footnote 98 Plato compares it to wax that receives impressions and in so doing creates copies, but which is not itself permanently marked:

It always has to be called (as) the same: for [1] it does not in any way stand aside from its own capacity – for [2] it always receives everything, and it never takes on even one character that resembles any of the things coming into it, in any way whatsoever; for [3] it lies by nature as a wax mass [ekmageion] for all, being moved and reconfigured by the things coming into it, and because of them it appears different at different times – and the things coming into it and going out of it are always copies of the things that are, and are stamped from them in a manner that is hard to explain and fantastic.Footnote 99

The term ekmageion can also be translated alternatively as ‘matrix’Footnote 100 or ‘recipient’ of all impressions.Footnote 101 Either way, in the ancient world this description would have brought to mind the lost wax method of casting objects of gold, silver or bronze.Footnote 102 It is the method by which the Gallo-Roman dodecahedra were made, and it provides another analogy by which to explain how it might have been used. The dodecahedron may have offered two methods of divination: one way involving a kind of winnowing; and the other involving impressions made upon waxFootnote 103 – or a combination of both. The Timaeus is suggestive of light/heat, incense/fragrances, breeze/wind and vapor/mist permeating the receptacle and mingling, possibly representing the four elements and their mixtures.Footnote 104 None of these substances would leave traces in the form of scratches on the inner or outer surface of the receptacle. Note that the outer and inner surfaces of the Gallo-Roman dodecahedra – aside from a few exceptions and later destruction and corrosion – generally do not look worn.Footnote 105

Like the receptacle described by Plato, the Gallo-Roman dodecahedron never changes its unique characteristics, but it appears differently at different times because its basic geometric structure looks very different from different angles (fig 5), and its holes are all of different sizes.

Fig 5.

Another view of dodecahedron Mainz 3 (Guggenberger no. 134), showing a very different view perspective. Photo: © Michael Guggenberger.

It is probably also relevant for the understanding of the Gallo-Roman dodecahedron that Plato via his mouthpiece the astronomer Timaeus, before finally introducing the receptacle as space (chora) and seat (hedra) of all becoming, tells us that the demiurge, after constructing the cosmic soul,Footnote 106

proceeded to fashion the whole corporeal world within it, fitting the two together centre to centre; and the soul was woven right through from the centre to the outermost heaven, which it enveloped from the outside and, revolving on itself, provided a divine principle of unending and rational life for all time. The body of the heaven has come into being visible, but the soul is invisible and participating in reasoning and harmony.Footnote 107

As Plato finally answers the question of how the corporeal came into being by introducing the receptacle (hypodoché) as chora (space) and hedra (seat) of all becoming, this results in an analogy to the cosmic soul, since both receive somata (bodies/elements).Footnote 108 Whilst the circle of the Different is divided into smaller circles of different diameters, there is only one circle of the Same,Footnote 109 all together they anticipate the motions of the celestial bodies (sun, moon, planets and fixed stars).Footnote 110 These reflections on soul and body are related to the Pythagorean notion of universal harmony that may be somehow reflected in the circular holes (of different sizes) and circles (fig 6), and to the knobs (fixed to the vertices) of the Gallo-Roman dodecahedron.

Fig 6.

Dodecahedron Enns 1 (Guggenberger no. 99) with concentric circles around holes of varying sizes and two production holes. Drawing: © Michael Guggenberger.

Now, the objection might well be made that although, from Plato onwards, in the classical world the dodecahedron was acknowledged to have metaphysical and cosmological significance, and although the dodecahedron might be seen to embody both space (chora) and seat (hedra) – absence and presence – all of the above considerations are beside the point, if it is implausible that the group of people using Gallo-Roman dodecahedra in provinces such as the Tres Galliae (Belgica, Lugdunensis, Aquitania) and Britannia had knowledge of, or interest in Plato and the Pythagorean way of thinking. We turn to this objection in the following section.

PYTHAGOREAN DRUIDS

The objection can be answered by pointing to the number of classical sources that claim that the Druids (of the Tres Galliae and Britannia) most definitely were interested in philosophy.Footnote 111 One such source is Diogenes Laërtius (ad 180–240), who is here relying on earlier (lost) sources:

Some say that the study of philosophy originated with the barbarians. In that among the Persians there existed the Magi, and among the Babylonians or Assyrians the Chaldaei, among the Indians the Gymonsophistae, and among the Celts and Gauls men who were called Druids and Semnothei, as Aristotle relates in his book on magic, and Sotion [fl 200–170 bc] in the twenty-third book of his Succession of Philosophers.Footnote 112

According to Pomponius Mela, writing in about 43 bc, Gauls ‘have both their own eloquence and their own teachers of wisdom, the Druids. These men claim to know the size and shape of the earth and of the universe, the movements of the sky and of the stars, and what the gods intend. In secret, and for a long time (twenty years), they teach many things to the noblest males among their people, and they do it in a cave or in a hidden mountain defile.’Footnote 113 But, most interestingly, with regard to the argument of the present paper, a large proportion of the classical sources that mention the Druids associate them specifically with the philosophy of Pythagoras. This is significant: we have already noted the prominence given to the receptacle in the philosophy of the Pythagorean Neoplatonist Iamblichus; but, furthermore, it is generally agreed that the Timaeus is the most Pythagorean of all Plato’s dialogues.Footnote 114 Moreover, the reporting of Pythagorean beliefs ran counter to the obvious effort in many classical sources to emphasise the exotic ‘other-ness’ of conquered peoples. Indeed, some of these reports of Pythagorean beliefs are given in a tone of genuine surprise.

According to Diodorus Siculus (fl first century bc), ‘the belief of Pythagoras prevails among them [the Gauls], that the souls of men are immortal and that after a prescribed number of years they commence upon a new life, the soul entering another body’.Footnote 115 He adds that ‘Philosophers, as we may call them, and men learned in religious affairs are unusually honoured among them and called by them Druids’.Footnote 116

Strabo (64/63 bc–ad c 24) noted that the Druids studied not only natural philosophy but also moral philosophy: ‘Among all the Gallic peoples, generally speaking, there are three sets of men who are held in exceptional honour: the Bards, the Vates, diviners and natural philosophers; while the Druids, in addition to natural philosophy study also moral philosophy’.Footnote 117 The Vates mentioned by Strabo are probably the same as the Eubages mentioned by Ammianus Marcellinus (ad c 330–c 391/400), quoting a lost work by Timegenes of the first century ad. Here the Druids are identified emphatically as followers of Pythagoras:

Throughout these provinces, the people gradually becoming civilized, the study of liberal accomplishments flourished, having been first introduced by the Bards, the Eubages, and the Druids. The Bards were accustomed to employ themselves in celebrating the brave achievements of their illustrious men, in epic verse, accompanied with sweet airs on the lyre. The Eubages investigated the system and sublime secrets of nature and sought to explain them to their followers. Between these two came the Druids, men of loftier genius, bound in brotherhoods according to the precepts and example of Pythagoras; and their minds were elevated by investigations into secret and sublime matters, and from the contempt which they entertained for human affairs they pronounced the soul immortal.Footnote 118

The influence of Pythagoras is reaffirmed by Valerius Maximus (fl 14–37):

it is said they [the Gauls] lend each other sums that are repayable in the next world, so firmly are they convinced that the souls of men are immortal. And I would call them foolish indeed, if it were not that what these trousered barbarians believe is the very faith of Greek Pythagoras himself.Footnote 119

Lucian (c 120–c 180), who taught in Gaul for some time, tells us in Pro lapsu inter salutandum that the sýmbolon (mark of recognition) of the Pythagoreans was the pentágrammon, called hygieia (health, ie soundness of body and soul).Footnote 120 This pentagram (or pentalpha) refers to Plato’s cosmic soul and universal body (not affected by disease but healthy: Timaeus 33a) and to the Platonic-Pythagorean secret of the dodecahedron. According to Saint Hippolyte in the second century ad:

the Celtic Druids investigated to the very highest point the Pythagorean philosophy, after Zamolxis, by birth a Thracian, a servant of Pythagoras, became to them the originator of this discipline. Now after the death of Pythagoras, Zamolxis, repairing thither, became to them the originator of this philosophy. The Celts esteem these as prophets and seers, on account of foretelling to them certain [events], from calculations and numbers by the Pythagorean art.Footnote 121

Cicero confirms that the Druids, like other Pythagoreans, practised divination:

Nor is the practice of divination disregarded even among uncivilised tribes, if indeed there are Druids in Gaul – and there are, for I knew one myself, Diviaticus, the Aeduan, your guest and eulogist. He claimed to have that knowledge of nature which the Greeks call ‘physiologia’, and he used to make predictions, sometimes by means of augury and sometimes by means of conjecture.Footnote 122

But it is Caesar, in De bello Gallico, who provides some of the most telling details. He reveals that, although, like all followers of Pythagoras, they are devoted to secrecy, they do have a knowledge of written Greek:

Report says that in the schools of the Druids they learn by heart a great number of verses, and therefore some persons remain twenty years under training. And they do not think it proper to commit these utterances to writing, although in almost all other matters, and in their public and private accounts, they make use of Greek letters […] The cardinal doctrine which they seek to teach is that souls do not die, but after death pass from one to another; and this belief, as the fear of death is thereby cast aside, they hold to be the greatest incentive to valour. Besides this, they have many discussions as touching the stars and their movement, the size of the universe and of the earth, the order of nature, the strength and the powers of the immortal gods, and hand down their lore to the young men.Footnote 123

In summary, if there is any truth at all in the repeated claims of Druidic interest in Pythagoras then knowledge of Plato’s Timaeus and some beliefs held in common with Iamblichus would not be in the least unexpected. The notorious secrecy in which both the Pythagoreans and the Druids liked to cloak their knowledge would also explain why there is no contemporaneous description of the Gallo-Roman dodecahedron.Footnote 124

These Roman sources all predate the Gallo-Roman dodecahedra, but our argument is that the dodecahedra came into being through the increasing Romanisation of the Druids. Hence the dodecahedra are never found in Celtic regions outside of the Empire. The Druids were, according to these early sources, already interested in Pythagoras and able to read Greek; and so it is unsurprising that they developed a physical representation of the receptacle of all becoming. The proposed divinatory use of the Gallo-Roman dodecahedron parallels the use made of hollow statues in theurgy as practised by Neoplatonists such as Iamblichus.

It should also be noted that in Britain and Gaul the Gallo-Roman dodecahedron may not be entirely without parallels. Martin Henig suggests that meaning of the third- to fourth-century mosaics at Brading villa on the Isle of Wight, ‘can only be fully realized by one who, like the astronomer depicted on the threshold between them, was a practitioner of theurgy’. The mosaics include a depiction of Orpheus with a lyre surrounded by concentric circles with enchanted and encircling birds and animals. There is a similar mosaic at Woodchester villa (fourth century ad) in Gloucestershire, where ‘birds and mammals ever revolve in separate registers around the central and completely still image of Orpheus’.Footnote 125 This also applies to the mosaic at the Barton Farm villa in Gloucestershire. Both mosaics also feature an octagon, an allusion to the harmony of Orpheus’ music, structured upon the Pythagorean octave. Note that the Neoplatonists believed Pythagoras to have been an initiate of the cult of Orpheus and that Orpheus was the ultimate source of his wisdom (and so also much of Plato’s).

Polygonal structures occur in Gallo-Roman temple architecture as well, with examples including octagonal (eg Neuville-sur-Sarthe) and even pentagonal temples (Saint-Usage).Footnote 126 Also found at the religious complex of Neuville-sur-Sarthe, France, was a bronze box key (first century ad) with a pentagonal handle resembling the face of a Gallo-Roman dodecahedron – a design that seems appropriate to ‘unlocking secrets’. However, this similarity may well be a coincidence, as brooches show comparable patterns (but hardly any pentagon).Footnote 127

The dodecahedra may have had some pre-conquest precedents. Cage amulets with knobs and a pair of big holes have been surmised as precursors of the Gallo-Roman dodecahedron, but this remains speculative.Footnote 128 Moreover, there is the mysterious ovum anguinum Footnote 129 (‘snake egg’) that Pliny the Elder describes in his Naturalis historia as ‘held in high estimation’ by the people of the Gallic provinces, especially the Druids:

I have indeed seen such an egg the size of a moderate-sized round apple remarkable for its cartilaginous shell with numerous cup hollows resembling those of the arms of an octopus.Footnote 130

It is commonly identified with some kinds of sea urchin fossils that have a thin shell with ‘knobs’, holes and pentagonal or pentagram-like structures, and are similar in size and were found in cultic environments.Footnote 131 It even seems to have had a cosmological meaning.Footnote 132 There are some general similarities between the ovum anguinum and the Gallo-Roman dodecahedron. Indeed, the dodecahedra might even have replaced it, for the Roman emperors from Augustus onwards ‘fought increasingly bitterly against the religious doctrine of the Druids’.Footnote 133 Yet Druidism continued to thrive throughout the Roman period. After the suppression of autochthonous Celtic cults, the Druids found new fields of activity within the context of mixed Gallo-Roman beliefs and remained an important part of the local society.Footnote 134

Indeed, it might be argued that, with a greater familiarity with abstract art, the Druids were better able to realise Plato’s receptacle in physical form than were the Greek Neoplatonists, who were more accustomed to figurative art.

CONCLUSION

The fact that there exists no contemporaneous description of the Gallo-Roman dodecahedron has until now led to some significant written sources being overlooked. We have argued that the Gallo-Roman dodecahedron can hardly be understood without considering the philosophical-scientific background of its basic polyhedral shape; and that its ultimate inspiration and model may have been the receptacle of all becoming in Plato’s Timaeus, the most Pythagorean of all Plato’s dialogues. This argument is supported by Iamblichus’ claim that Pythagoras honoured the Gods in bronze and imagined them as ‘not bound to our shapes, but to divine receptacles’ because the Gods ‘encompass all and provide for all things, resembling the universe in growth and form’.Footnote 135 We have argued that the idea of a receptacle for the Gods – as mentioned and discussed by Neoplatonists – may be of some relevance in understanding the Gallo-Roman dodecahedra, for these precious objects were being made at the same time as Neoplatonists were promoting the supposedly Pythagorean practice of theurgy – the ritual re-enactment of the divine creative process involving the use of hollow statues. The Gallo-Roman dodecahedra may demonstrate an awareness of this theurgic ambition and a realisation of Plato’s receptacle in more abstract form – a form that is in fact closer to the Timaeus. The first dodecahedra coincide with the first allusion to theurgy (in the Chaldean Oracles) and then and subsequently they were made exclusively in Romanised Celtic areas where there was a documented pre-existent interest in the Pythagorean tradition. In this instance, what Greek philosophers merely conceived may have been brought into being by Gallo-Roman Druids, or by sages in the Druidic tradition, and subsequently used by a somewhat wider circle of initiates – men and women – as suggested by the quantity of finds and their contexts, including sacred spaces and graves.

To make further progress we are reliant upon archaeology, and the hope of finding more dodecahedra in situ. In suggesting that Gallo-Roman dodecahedra may have been used as receptacles in (theurgic) divination, this study has highlighted some of the questions that might be asked in future archaeological investigations: for example, is there any trace of another substance inside or outside of some dodecahedra; and are there any (microscopic) signs of wear; and, of those that are broken, were they deliberately or accidentally broken?Footnote 136

In all of these investigations, we battle against the ancient Pythagorean and Druidic habit of secrecy, but that there was a Pythagorean-Druidic aspect to the Gallo-Roman dodecahedron, whilst not yet proven, seems plausible.

Footnotes

1. Guggenberger Reference Guggenberger2000a and Reference Guggenberger2013, 56. For diameters of all holes and other measures and statistics concerning Gallo-Roman dodecahedra, see Guggenberger Reference Guggenberger1999, 193–207 and tabs 9–26, and Guggenberger Reference Guggenberger2000a, figs 1–3. The difference in the diameters of holes within pairs of holes (opposite to each other) is statistically between c 0.2cm and c 0.45cm; however, some dodecahedra have pairs of holes with approximately the same diameter, whereas others have very different diameters.

2. Guggenberger Reference Guggenberger1999, 34. Including the knobs, the diameter can be up to c 11cm. For (average) sizes, see Guggenberger Reference Guggenberger1999, Reference Guggenberger2000a, figs 1, 3.

3. See typology Guggenberger Reference Guggenberger1999, 50–4, Reference Guggenberger2000a, 68 with fig 1; Greiner Reference Greiner1996, 10–13.

4. Sometimes fewer, sometimes up to six circles, eg dodecahedron Guggenberger no. 11 shows two to five circles around ten of its twelve holes.

5. For further details, see Guggenberger Reference Guggenberger1999, 29, 36–7, 50–1.

6. In about 70 per cent of the cases with production holes/Produktionslöcher, as they are referred to in Guggenberger Reference Guggenberger1999, 28, 34, 50. See also Greiner Reference Greiner1996, 20.

7. For a comprehensive index of the literature on the subject up to 1999, see Guggenberger Reference Guggenberger1999, 207–26.

8. Guggenberger Reference Guggenberger2024, i–x, Reference Guggenberger2021 (http://saegewerk.org/laboratory/dodekaeder-dodecahedron), Reference Guggenberger1999, 149–87, Reference Guggenberger2000a, 77–82, Reference Guggenberger2000b, 16–17; compare De Saint-Venant Reference De Saint-Venant1907; Nouwen Reference Nouwen1993; Greiner Reference Greiner1996.

9. Less so in Gallia Narbonensis (Gallia Transalpina), which was conquered earlier.

10. Many dodecahedra with special features come from Roman Britain (Greiner Reference Greiner1996, 13), some of which do not appear to be so skilfully designed. They may point out to local imitations of ‘classic’ dodecahedra.

11. Vujović Reference Vujović2021.

12. Guggenberger Reference Guggenberger2013, 57, fig 1; Grüll Reference Grüll2016, 148.

13. The deposition of the stratified Jublains dodecahedron (Guggenberger no. 98) took place in the first half of the 3rd century (Guillier et al Reference Guillier, Delage and Besombes2008, 284). However, some dodecahedra may well date from the 2nd century, but their dating remains uncertain: Bachem, Feldberg, Zugmantel (Guggenberger nos 5, 10, 27; Barthel Reference Barthel and Jacobi1909, 94–5) and Bad Cannstatt 1 (Guggenberger no. 6; Nouwen Reference Nouwen1993, 32). See also Guggenberger Reference Guggenberger1999, 15–16, 168, Reference Guggenberger2000a, 68. Note that the somewhat related icosahedron from Arloff discussed below dates to around ad 200 (Letter from Ursula Heimberg to M Guggenberger, 29 Jan 1999).

14. Guggenberger Reference Guggenberger2013, 58.

15. See Guggenberger Reference Guggenberger1999, tab 8.

16. Dodecahedra Guggenberger nos 12, 21, 23, 26, 29–30, 35, 40, 47–8, 50, 54, 60, 65–6, 72–4, 81, 83–6, 89–90, 95–8, 100, 102, 105–7, 117, 123 and 131 (see list Guggenberger Reference Guggenberger2024, i–x).

17. Guggenberger nos 7–8, 10, 16, 25, 27, 32, 69–70, 78, 80, 99, 124 and 125 (see list Guggenberger Reference Guggenberger2024, i–x).

18. Guggenberger nos 20–1, 68, 110, 122 and 132 (see list Guggenberger Reference Guggenberger2024, i–x).

19. Guggenberger nos 2, 4–5, 11, 49 (see list Guggenberger Reference Guggenberger2024, i–x).

20. Guggenberger nos 12, 57, 109 and 112 (see list Guggenberger Reference Guggenberger2024, i–x).

21. Guggenberger nos 33, 53 and 60 (see list Guggenberger Reference Guggenberger2024, i–x).

22. Guggenberger nos 22, 77 and 91 (see list Guggenberger Reference Guggenberger2024, i–x).

23. Compare Herz Reference Herz, Lo Cascio and Tacoma2016. Note also the presence of male and female civilians in military camps (see Allison Reference Allison2008).

24. Now in a private Swiss collection in Winterthur.

25. Hitchens Reference Hitchens2023 in Parker and Tipper Reference Parker and Tipper2025, 33.

26. Guggenberger Reference Guggenberger2024, x; Henig Reference Henig2025, 29–30;.

27. Coombe and Henig Reference Coombe and Henig2020, 234, 238, fig 9, 259–60; Guggenberger Reference Guggenberger2024, ix.

28. Wheeler and Wheeler Reference Wheeler and Wheeler1932, 86, fig 20; Guggenberger Reference Guggenberger1999, 171; Coombe and Henig Reference Coombe and Henig2020, 234.

29. Berton Reference Berton2007; Guggenberger Reference Guggenberger2024, viii.

30. Winkelmann Reference Winkelmann1933, 137–8, tab 16; Guggenberger Reference Guggenberger1999, 20, 178. The Neoplatonists were among the recipients of Hermetic cosmology etc.

31. Kolling Reference Kolling1993, 124; Guggenberger Reference Guggenberger1999, 182.

32. Bassenge (Belgium), Bachem and Gellep (both Germany); Guggenberger nos 2, 5, 11: Barthel Reference Barthel and Jacobi1909, 94; Nouwen Reference Nouwen1993, 31, 32, 35; Guggenberger Reference Guggenberger1999, 152, 154, 163–4.

33. Unfortunately, the ‘rod’ was in a very poor condition and could not be preserved. It is only known from a drawing of the grave.

34. Guggenberger Reference Guggenberger2013, 59, fig 7; see also Guggenberger Reference Guggenberger1999, 163, Reference Guggenberger2000a, 76–7. The production holes of some other dodecahedra show conditions and traces that might also indicate a temporary mounting (eg Guggenberger nos 2 and 101), but the evidence is not definitive (Guggenberger Reference Guggenberger1999, 34). Compare to icosahedron from Arloff, Germany (see n 43).

35. Dozens of theories have been published by experts from different fields as well as by non-experts (subject areas: symbol, divination device, candlestick/lamp, measuring device, knitting dolly, gaming, toy, weapon, masterpiece of an artisan, etc). See overview and discussion Guggenberger Reference Guggenberger1999, 55–113, 145–8, Reference Guggenberger2013, 59–60; Grüll Reference Grüll2016, 150–5.

36. Thompson Reference Thompson1970, 93–5. For various theories on its use as a measuring device, see Guggenberger Reference Guggenberger1999, 70–84.

37. Guggenberger Reference Guggenberger1999, particularly 49, 115–23, Reference Guggenberger2000a, 76–7, Reference Guggenberger2000b, 15–16, Reference Guggenberger2013, 57–8; see also eg Saint-Michel Reference Saint-Michel1951; Deonna Reference Deonna1954; Thompson Reference Thompson1970, 96; Nouwen Reference Nouwen1993; Hill Reference Hill1994; Greiner Reference Greiner1996; Grüll Reference Grüll2016, 154–5; compare also Henig Reference Henig2025.

38. See Thompson Reference Thompson1970, 95–6; Guggenberger Reference Guggenberger1999, 61–6, 86–100, 146–8, Reference Guggenberger2013; Grüll Reference Grüll2016, 155; Henig Reference Henig2025.

39. Plato 2008, 55c (trans Guggenberger). According to Socrates in Plato’s Phaedo, the basic structure of our planet is also linked to the dodecahedron: ‘the earth’s true surface, viewed from above, is supposed to look like one of those balls made of twelve pieces of skin’ (Plato 1993, 110b).

40. That is, having come into existence through generation.

41. Plutarch 1874, Moralis 428d (trans Guggenberger).

42. See Guggenberger Reference Guggenberger1999, 115–21.

43. See Nouwen Reference Nouwen1993, 58–9; Artmann Reference Artmann1996, Reference Artmann2005, 49–50; Guggenberger Reference Guggenberger1999, 124–6. It is the only one of its kind. Whereas the dodecahedron has 12 faces, 30 edges and 20 vertices, the icosahedron has 20 faces, 30 edges and 12 vertices. In geometry, the icosahedron and the dodecahedron are said to be duals – shapes in which the number of faces and vertices have been interchanged (Kotrč Reference Kotrč1981, 221); however, Plato assigns the element water to the icosahedron. Even if we were to set aside the Platonic role of the icosahedron, the function of the object from Arloff was different, as its knobs are not of the same diameter (three are larger than the others and arranged around the smaller of its only one pair of holes). This gives it a clear orientation (axis) and suggests defining its big knobs as feet, so that the larger hole is at the top and something (a candle?) can be put or placed inside; however, as both holes show traces of some other substance (Nouwen Reference Nouwen1993, 58), it might have been mounted (compare ‘sceptre mounts’ discussed by Guggenberger Reference Guggenberger1999, 92–4, 136–7; Grüll Reference Grüll2016, 153, fig 4, 154; Henig Reference Henig2025 – for other ancient polyhedric objects, see Guggenberger Reference Guggenberger1999, 126–39).

44. Sattler Reference Sattler2012, 173.

45. Plato 2008, 48e–49a.

46. Ibid, 50b (quote: trans Guggenberger).

47. Ibid, 51a.

48. Ibid, 52a and 52d.

49. Ibid, 52b.

50. Ibid, 50b.

51. Zeyl and Sattler Reference Zeyl, Sattler, Zalta and Nodelman2023.

52. Compare the widespread idea of Neoplatonists of the aetheric vehicle (ochema) of the soul, a light-like or etheric body located on the border between materiality and immateriality (Guggenberger Reference Guggenberger1999, 119–20; Shaw Reference Shaw, Afonasin, Dillon and Finamore2012, 94–102).

53. See Guggenberger Reference Guggenberger1999, 35.

54. Plato 2008, 50d.

55. Ibid, 50b and 53c–55c.

56. Ibid, 33b and 55c.

57. Sattler Reference Sattler2012, 190. Note also Socrates’ words in Phaedo: ‘There are many hollow places all round the earth, places of every shape and size, into which the water and mist and air have collected. But the earth’s true surface is as pure as the starry heaven in which it lies, and which is called “ether” by most of our authorities’ (Plato 1993, 9b).

58. Plato 2008, 50b.

59. Iamblichus 1963, xviii 88 (trans Guggenberger).

60. Ibid, xxxiv 247 (trans Guggenberger).

61. Joost-Gaugier Reference Joost-Gaugier2006, 208.

62. Plato, Republic 5.460d–461a.

63. Guggenberger Reference Guggenberger1999, 38.

64. Plutarch in De defectu Oraculorum (36) derives pente (five) from panta (all) and, among other things, points to the five parts of the soul and the five senses, and in De E apud Delphos (8) he points out that pente is called gámos (marriage) since it is the addition of the female number 2 and the male number 3 (Guggenberger Reference Guggenberger1999, 121). Wild Reference Wild2024 deals in detail with ‘wedding numbers’, which also play a role for Iamblichus.

65. Knob-like edge and border decoration is quite common – eg, on Roman plate brooches – but not always present.

66. Guggenberger Reference Guggenberger1999, 37–8, fig 17. The knobs come in a wide variety of shapes: from spheres and button-like forms (with conical neck) to club-like and rounded cylindrical forms. Sometimes the knobs and their necks are less carefully crafted. Many knobs are roughly spherical but they are never pointed or intentionally faceted.

67. For example, if the openings would have been filled with a mechanically sensitive substance that has not yet been detected (Greiner Reference Greiner1996, 17; Guggenberger Reference Guggenberger1999, 38).

68. Guggenberger Reference Guggenberger1999, 38–40, 94–105; compare Grüll Reference Grüll2016, 155.

69. Thompson Reference Thompson1970, 95; Guggenberger Reference Guggenberger1999, 38–9.

70. Plato 2008, 52b.

71. ‘Divine forms’ would be more general, but in this case the translation to ‘divine receptacles’ seems justified by the explanation that the Gods encompass all and by the resemblance to the universe.

72. Iamblichus 1963, 28.151 (trans Guggenberger).

73. Johnston Reference Johnston2008, 463.

74. Ibid, 462.

75. To hídryma = a thing founded or built, a stay, temple, shrine, but also a cult image, some kind of statue (eg of a daimon [daimónon hídryma]), here: receptacle. For a terminology of cult images, see Bremmer Reference Bremmer2013, 7–8.

76. Porphyry cited by Eusebius 1903, 5.11.199d–13.201b.

77. Porphyry cited by Eusebius 1903, 3.9. 100a-101c.

78. Johnston Reference Johnston2008, 463.

79. Porphyry 1816, 41 (trans Guggenberger).

80. In ch 26 of De Vita Pythagorica (about the invention of the harmonic science and ratios), Iamblichus also refers to the sound generated during metalsmithing.

81. De Vita Pythagorica 28.88 and 34.247. See Artmann Reference Artmann1984.

82. Iamblichus 1963, 28.147 (trans Guggenberger). See also 12.59 and 29.162, and Deonna Reference Deonna1954, 39–44.

83. Bremmer Reference Bremmer2013, 9.

84. Plato 1993, 247a.

85. However, Iamblichus might have provided some inspiration for later users of the dodecahedron.

86. Porphyry cited by Eusebius 1903, 3.7.98a.

87. Grüll 216, 155; for other Roman dodecahedral ‘dice’, especially from Geneva, Switzerland (referring to the zodiac; compare Alcinous 1993, 163, 40–169, 4; Plato 2008, 55c), and Patras (with numbers, from a grave), see Guggenberger Reference Guggenberger1999, 128–35.

88. Porphyry cited by Eusebius 1903, 3.7.98C; compare sphere of Pythagoras/Apuleius.

89. Joost-Gaugier Reference Joost-Gaugier2006, 208 takes this literally and suggests that the knobs might have been used as ‘arithmetical balls’ for divinatory calculations.

90. Iamblichus 1963, 19.93 (trans Guggenberger).

91. Plato 2008, 52d–53a. The liknon (or winnowing basket) was a ritual object in the ancient Greek and Roman Dionysian mysteries. A wall painting in Pompeii, in the initiation chamber of the villa of mysteries, shows an initiate reaching for a liknon. Another shows Dionysus himself.

92. Sattler Reference Sattler2012, 193. There is an interesting discussion of sacred divination ‘rattles’ (3rd–4th century) in Esposito Reference Esposito2019, 54–6, with dodecahedra further listed as priestly regalia pp 56–7.

93. Guggenberger Reference Guggenberger1999 35–6, tabs 25–6, Reference Guggenberger2013, 56.

94. Note that the knobs (and edges) of some dodecahedra seem to look worn whereas others are in perfect condition: Guggenberger Reference Guggenberger1999, 34.

95. Note that in ancient magical papyri, the sun is represented as a disc that opens during a ritual, revealing a fireless circle and fiery, closed gates from which Helios finally emerges: Gundel Reference Gundel1968, 12 (see also Guggenberger Reference Guggenberger1999, 44).

96. Proclus, In Timaeum 3.155.18 (trans after Johnston Reference Johnston2008, 457). Telestike techne is the technical term for the theurgic ‘divinising’ of statues (ritualised animation) and for the rituals that purified the soul of the theurgist. For this and the term symbolon, see Johnston Reference Johnston2008. Compare the aetheric vehicle of the soul (see n 52).

97. Iamblichus 2003, 5.23 [233.9–13].

98. Zeyl and Sattler Reference Zeyl, Sattler, Zalta and Nodelman2023.

99. Plato, Timaeus 50b–c (trans first sentence by Guggenberger, following text by Buckels Reference Buckels2013, 3 with minor alterations).

100. Plato 2008.

101. Plato 1892.

102. See Petraki Reference Petraki2023.

103. This suggestion would make sense of the dodecahedron, found at Feldberg in 1892 (Guggenberger no. 10), that was recorded as having traces of yellow wax. However, it should be noted that this observation may not be fully reliable (see Guggenberger Reference Guggenberger1999, 61–2, 144, 162).

104. Plato 2008, 49bc. Iamblichus discusses the use of light in theurgy, photagogia (see Shaw Reference Shaw2024, 112–27).

105. See Guggenberger Reference Guggenberger1999, 33–4, 61–2. Note again the possible traces of wax inside the Feldberg dodecahedron; ibid, 61–2, 144, 162.

106. Here Plato changes the order compared to his earlier description, in which God ‘put soul in the centre [of the universe] and stretched it throughout the whole and covered the body within it’ (34b), but the order in this earlier description was made only for rhetorical reasons (Perger Reference Perger1997, 87–8, 119–20, 142).

107. Plato 2008, 36d–37a.

108. Perger Reference Perger1997, 127–48. ‘Opinion and knowledge are not simply a set of individual data but contain everything individual in its overall context. The circles [of the cosmic soul] thus perform a kind of incorporeal synaesthesia and topography of the universe. Thereby the two areas that initially came into question as patterns of becoming, the unchanging and the becoming, appear as reference values’ (Perger Reference Perger1997, 121, trans Guggenberger).

109. Plato 2008, 35a–36d.

110. Ibid, 38c–39e.

111. A possible Druidic connection has previously been discussed in Guggenberger Reference Guggenberger1999, 88–92, Reference Guggenberger2000a, 76, Reference Guggenberger2013, 58; and eg Deonna Reference Deonna1954; Saint-Michel Reference Saint-Michel1951.

112. Diogenes Laërtius Reference Laërtius1853, 3–4. In a number of works the archaeologist Jean-Louis Brunaux has argued that such claims have not received enough attention (eg Brunaux Reference Brunaux2006). He suggests Greek philosophy may have originally entered Gaul via the Phocaean colony of Massalia (Marseilles) founded in 600 bc.

113. Pomponius Mela Reference Mela1998, Bk 3, 18–19.

114. The Phaedo also has a Pythagorean connection in that it was an account of Socrates’ final hours narrated by Phaedo at the request of the Pythagorean philosopher Echecrates, but of all of Plato’s dialogues it is the Timaeus that is believed to be the most substantively Pythagorean.

115. Diodorus Siculus Reference Siculus1939, Bk 5, 28.

116. Ibid, Bk 5, 31.

117. Strabo 1929, Bk 4, ch 4, 245.

118. Ammianus Marcellinus Reference Marcellinus1862, 15.9.8.

119. Valerius Maximus 2.6.10 (after Kendrick Reference Kendrick2004, 106).

120. Lucian Reference Jacobitz1896.

121. Hippolytus 1868, Bk 1, 61.

122. Cicero 1923, 1.41.90.

123. Caesar 1917, 6.14.

124. Saint-Michel Reference Saint-Michel1951; Guggenberger Reference Guggenberger2013, 60.

125. Henig Reference Henig2003, 153.

126. Guggenberger Reference Guggenberger1999, 46 with fig 23; Inrap 2010.

127. See knob-like edge and border decoration of, eg, (enamelled) plate brooches (some variants of Riha Reference Riha1979, type 3 and 7; compare five-armed specimen (Riha Reference Riha1979, no. 1,539) and polygonal pattern on discs: eg, Mackreth Reference Mackreth2011, type 2b).

128. See Guggenberger Reference Guggenberger1999, 137–9; Davies and Crummy Reference Davies and Crummy2022; Henig Reference Henig2025, 30.

129. Also called ovum serpentium or urinum.

130. Pliny, Naturalis historia xxix.52–4 (trans Guggenberger).

131. For further information about sea urchins in archaeological contexts, see Demnard and Neraudeau Reference Demnard and Neraudeau2001; Georges et al Reference Georges, Philippe and Barthélémy2014.

132. See Saint-Michel Reference Saint-Michel1951; Guggenberger Reference Guggenberger1999, 90–1; Georges et al Reference Georges, Philippe and Barthélémy2014, 535, 537, 541.

133. Georges et al Reference Georges, Philippe and Barthélémy2014, 541 and 535; Esposito Reference Esposito2019, 8.

134. Birkhan Reference Birkhan1997, 908.

135. Iamblichus 1963, 28.151 (trans Guggenberger).

136. Plato describes the receptacle as indestructible (2008, 52a).

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Figure 0

Fig 1. Find report from 1739 of the Aston dodecahedron (Guggenberger no. 59). Photo: reproduced with kind permission of the SAL.

Figure 1

Fig 2. Distribution map of the Gallo-Roman dodecahedra: find sites in yellow, repositories (site not known) in grey. Map: © Michael Guggenberger, based on NASA Visible Earth image.

Figure 2

Fig 3. Dodecahedron Carmarthenshire (Guggenberger no. 60). Photo: reproduced with kind permission of the SAL.

Figure 3

Fig 4. Dodecahedron Mainz 3 (Guggenberger no. 134): complete; diameter face to opposite face 5.5cm (without knobs); one pair of holes 1.5/1.7cm and 1.4/1.5cm, all other holes in a very small range (c 1.0–c 1.25cm); thickness c 1.5mm; diameter knobs c 0.5cm; 246g; all faces with five ring-and-dot motifs (Greiner/Guggenberger type 2a). Photo: © Michael Guggenberger.

Figure 4

Fig 5. Another view of dodecahedron Mainz 3 (Guggenberger no. 134), showing a very different view perspective. Photo: © Michael Guggenberger.

Figure 5

Fig 6. Dodecahedron Enns 1 (Guggenberger no. 99) with concentric circles around holes of varying sizes and two production holes. Drawing: © Michael Guggenberger.