The enigma of the dodecahedron

HUNGARIAN POLIS STUDIES Nr. 22

FROM POLITES TO MAGOS

Studia György Németh sexagenario dedicata

BUDAPEST - DEBRECEN

2016HPS22

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HPS-22-fedel.indd 1HPS-22-fedel.indd 1 2016.06.20. 15:28:262016.06.20. 15:28:26

HUNGARIAN POLIS STUDIES (HPS)

University of Debrecen Dept. of Ancient History and Class. Phil.

H–4010 Debrecen, Egyetem tér 1.

Nr. 22 ..........

...............

Editor Ádám Szabó

Managing Editor Edina Gradvohl

Contributors Dániel Bajnok, Péter Forisek, Péter Kató,

Ádám Lőrincz, Attila Marosi, Anna Mihalik, András Patay-Horváth

Supporters Hungarian Society for Antique Studies; Kódex Könyvgyártó Kft.;

Non Omnis Moriar Foundation; University of Debrecen

HU ISSN 1417-1708

2016

FROM POLITES TO MAGOS


BUDAPEST – DEBRECEN

HPS 22 From Polites to Magos


Redaction Ádám Szabó

© Authors © Editor of HPS

Cover photo: An image of the daimon Abraxas in bird-form inscribed on one of the six small lead containers found in the cistern of the Fountain of Anna Perenna, Rome in 1999-2000 (IV inscription on the body, ΙΧΝΟΦ/ΙΝΚΘ/ΘΘ has been resolved by Gy. Németh (2016) as a slightly inaccurate acronym for an invocation of Christ:

Ἰησοῦς Χριστὸς Ναζωραῖος ὁ [π]αῖς Ἰησοῦς Ναζωραῖος καὶ Θεός. Θεὸς, Θεός.

The container is in the Museo Nazionale Romano delle Terme, Dipartimento Epigrafico, inv. no. SAR 475555. Drawing based on Blänsdorf 2012, 624 no. IX.49.6.

ISBN .978-963-284-796-2

Printed by KÓDEX KÖNYVGYÁRTÓ KFT.

Leader: Attila Marosi Budapest

Prof. György Németh (25. June 1956)

CONTENTS Ádám Lőrincz Ỏ Διδάσκαλος ἡµῶν …………………….

………………….…..…….

……. 11

Béla Adamik Computerized Historical Linguistic Database of the Latin Inscriptions of the Imperial Age: Search and Charting Modules ………….

………………….……..….

……. 13

Silvia Alfayé Mind the bath! Magic at the Roman Bath-houses ………………

………………….……..….

……. 28

Radu Ardevan Die Domitii in der römisch-dakischen Lokalaristokratie ......

………………….…..…….

……. 38

Dániel Bajnok “Sympathy with the Practitioners”: Interview with Christopher A. Faraone ...

…………………...……….

……. 51

Andrea Barta New Remarks on the Latin Curse Tablet from Savaria .............

………………….……..….

……. 63

Giulia Baratta Zwei interessante römische Bleispiegel ..

………………….………...

……. 70

László Borhy Amphitheatralia Pannonica II: Deux amphithéâtres ...? Gedanken zu einer Bauinschrift aus Brigetio ……..

………………….…..…….

……. 83

Angelos Chaniotis Habent sua fata inscriptiones. A mortar impression of an inscription from Aphrodisias ..................

………………….……..….

……. 95

Christopher A. Faraone Some Further Remarks on Greek Magical Gems ..........................

………………….………….

……. 105

Tamás Gesztelyi Eine cretula aus Pergamon: Löwe mit Tropaion ...................

………………….………….

……. 116

Richard Gordon An enigmatic magical disk: Revisiting IG XIV 2276 = DTAudollent 123 (Bordighera) …………

………………….…….…….

……. 123

Edina Gradvohl The Ancient Name for Cravings (kissa) ..

………………….………….

……. 139

Tibor Grüll The Enigma of the Dodecahedron ..........

………………….………….

……. 148

György W. Hegyi Augustus, Hercules and Horace ..............

………………….………….

……. 157

Péter Kovács Kaiser Julian in Pannonien, über Pannonien .....................

………………….………….

……. 169

Gyula Lindner ”Früher war alles besser” ‒ Religiöser Konservativismus bei Plutarch .

………………….……….….

……. 188

Marc Mayer i Olivé Notes on the Influence of Greek Formulae in Two Inscriptions from Tarraco CIL II2/14, 947 and 1108 …..…..

………………….………….

……. 199

Zsolt Mráv The statue base of Severus Alexander from Ulcisia (Szentendre, Pest county, Hungary) …….

………………….………….

……. 204

Levente Nagy Jenseitsvorstellungen und ihre Interpretationsprobleme im spätrömischen frühchristlichen Gräberfeld von Sopianae/Pécs .................

………………….………….

……. 210

Dóra Pataricza ”White blood” – An Evaluative Overview of Nursing Practices in Classical Antiquity …..

………………….………….

……. 230

András Patay-Horváth Lepreon during the 5th century BC ..........

………………….………….

……. 243

Ioan Piso Nochmals zur spätrömischen Inschrift von Gornea .......

………………….………….

……. 255

Zsigmond Ritoók Networks in Homer .................................

………………….………….

……. 263

Heikki Solin Briefe an die Unterwelt ...........................

………………….………….

……. 287

Tamás Szabadváry An ’old-new’ Late Roman mirror from the Collection of the Hungarian National Museum .............

………………….………….

……. 293

András Szabó Magic prism from the Roman Collection of the Hungarian National Museum ...................

………………….………….

……. 299

Ádám Szabó Aquilae et Genio legionis. Beschriftete Bronzeplatte aus Brigetio in der Römersammlung des Ungarischen Nationalmuseums .........

………………….………….

……. 309

Levente Takács The color of Roman slaves – a short note to Cicero’s In Pisonem ..........

………………….………….

……. 318

Zsuzsa Várhelyi Women, couples and sacrifice in the Roman Empire ................

………………….………….

……. 325

Javier Velaza Neither Christians nor Poets: a Note on AEp 1974, 503 ………..

………………….………….

……. 333

László Vilmos Who Pulled the Oars? Sailing the Seas in Early Archaic Greece ............

………………….………….

……. 338

Daniela Urbanová – Miroslav Frýdek Priscilla Caranti – Einige Bemerkungen zum Möglichen Entstehungsszenario des Fluchtäfelchens aus Gross-Gerau (Dfx. 5.1.3/1) ...........................................

………………….………….

……. 343

Authors of this volume ...........................

………………….…………. ……. 351

Hungarian Polis Studies (HPS) Recently published (1997-) ..............

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……. 354

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Tibor Grüll

THE ENIGMA OF THE DODECAHEDRON In his report sent to The Society of Antiquaries in 1739, a local historian described in detail a strange hollow object made of bronze, with a do-decahedral shape of twelve flat pentagonal faces he found at Aston (Hert-fordshire, England). Over the past three hundred years more than two hundred professional and amateur historians or experts have declared their opinion about the possible function and usage of this enigmatic object. Of them, the most well-known was Léopold Hugo–Victor Hugo’s nephew–who can be considered a pioneer in the research of the dodecahedron. The famous French archaeologist and historian, Julien de Saint-Venant (1847–1930) wrote the first monograph on this object. Among the mathematicians Moritz Cantor (1829–1920), Ferdinand von Lindemann (1852–1939), and Benno Artmann (1933–2010) found this enigma worthy of investigation.1 Precisely 116 pieces of dodecahedra have been found up until now in the territory of today’s Belgium, Croatia, France, Germany, Great-Britain, Hungary, Luxemburg, Netherlands, and Switzerland. The northernmost piece was found along Hadrian’s Wall, and the southernmost at Arles.2 The westernmost object turned up at Fishguard (Wales), and the easternmost at the legionary camp of Brigeto (Szőny, Hungary). It is very important to emphasize that not a single one has been found in Italy, Africa or in the eastern provinces of the Roman Empire. Dodecahedra found in the western part of the imperium Romanum are usually dated to the second/third, and fourth century AD on the basis of archaeological context. Unfortunately, most of these objects have surfaced in antiquity markets and consequently, we have no information about their origin.Now let us look at the appearance of this strange object. The dodecahedron is usually made out of copper alloy, its only sample made of silver was found at Geneva.3 The object has twelve flat pentagonal faces, thirty edges of equal length, and twenty vertices, on which we can find small knobs of varying sizes. (On a do-decahedron found in London three of these knobs were soldered to each other.)

1 Artmann 1993, 1996. 2 Benoît 1957. 3 Cervi-Brunier 1985.

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Map: Béla Nagy

Each pentagonal face has a circular hole of varying diameter in the middle (the narrowest is 6 mm, the broadest is 40 mm), the holes are connected to the hollowed-out center. The dodecahedra are ranging from 4 cm to 11 cm in size (without the knobs), their weight is varying between 35 and 580 grams (we only know of one sample which weighs about 1000 grams).

Fig. 1.: The structure of the dodecahedron (http://shop.romansystems-engineering.com)

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Most of these dodecahedra bear surface decorations: circles around the holes, small circles with dots, lines parallel to the edges etc. We must stress that no letters, numbers, or similar characters can be found on any of these objects. As to the intended usage of these objects, nearly fifty different theories have been published in the scholarly literature, not to mention the fantastic “solutions” of hobby researchers and esoteric circles. The varied theories have been summarized many times in the past.4 Most scholars have put aside the assumption that the dodecahedron was a kind of weapon (e. g. mace). Much more current is the hypothesis that it was a sort of measuring device, rangefinder, calibration gauge, or an astronomical measuring device.5 It has also been suggested that the object was purely a decorative item: an extravagant household item, such as a candle-holder; a signum militare which was drawn up the rod for the army’s vexillum; an instrument of cosmic power; or merely a toy which resembles the very popular French cup-and-ball game, the so called bilboquet.

Fig. 2.: The icosahedron found at Arloff (source: www.dodecaeder.nl)

Regarding the function of the dodecahedron, Sjra Wagemans elaborated on a conception in which this enigmatic object was used for fixing the spring and 4 e. g. Nouwen 1993; Guggenberger 1999. 5 Kurzweil 1957; Sparavigna 2012.

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autumn equinoxes.6 The Dutch researcher compared the dodecahedra to the icosahedron (a convex polyhedron with twenty faces, thirty edges and twelve vertices) owned by the Rheinisches Landesmuseum of Bonn, Inv.-No. 53.356). The bronze icosahedron was excavated in 1953 in the village of Arloff (some 30 kms SW of Bonn), it weighs 465 grams and its overall diameter is about 8 cm. In this object we can find only two circular holes, and the knobs soldered to the vertices are of differing sizes. According to Wagemans, the Roman dodecahedron is a developed form of the icosahedron, and it was used as follows: “the dodecahedron was placed on a horizontal plate on a sunny day in autumn. Thereupon, around noon, when the sun reached its highest point of that day, one would measure the light falling through two openings opposite each other. Next, twenty measuring points would be examined for beams of light going through the hole. This all would be done according to a specific system”7. In the opinion of Amelia Carolina Spara-vigna, it was used as a dioptron (rangefinder): “dodecahedron was used as an ancient theodolite, placed on a tripod and with a range pole as a target ‒ may be painted as the modern ones ‒ for precise measurements”8. Research supported by astronomical and mathematical charts, geometrical formulae, however, fail the exam of common sense. If the dodecahedron was really used as a measuring instrument, why was its size not standardized, and why do we not find any signs or numbers on it? The main source of our uncertainty regarding the function of the dode-cahedra is that it is not mentioned in any ancient text, and we do not possess any visual representation yet. As mentioned above, most of these objects were not found in controlled archaeological excavations. Consequently, archaeology cannot help to determine its original function either. All we are aware of is that among the sites where these objects have been found there are five military camps, two public baths, one theater, one tomb, one hoard, and one filled well.9 A dodecahedron was found at the Gallo-Roman temple near Schwarzenacker|Homburg (Germany); and three objects were discovered in riverbeds near Nijmegen, Trier, and Zürich, which probably hints to some religious (votive) function.

6 Wagemans 2010. 7 Wagemans 2010. 8 Sparavigna 2012, 7. 9 Guillier et al. 2008.

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To this day, we have knowledge of only two dodecahedra which have been found in controlled scientific excavations. One of them is dated back to the fourth century AD, and was turned up in a richly equipped tomb of a woman in Krefeld-Gellep (Germany).10

Fig. 3.: Photo of the dodecahedron found at South Shields (Source: finds.org.uk)

The dodecahedron was found adjacent to an object of bone (diameter approximately 30 mm, length approximately 150 mm) which could have

10 Pirling–Siepen 2000; tab. 153.

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served as a kind of handle. Unfortunately, the condition of the handle was so poor it could not be relieved and preserved. Another dodecahedron was found during the excavation at the city of Noviodunum (Jublains, France) in 1995, in a building consisting of a room and a cellar which has been dated on the basis of ceramics and coins to the turn of the second–third century AD.11 The object was 59 mm in diameter (without the knobs), weighed 81 grams, and was made of bronze with lost wax casting technique. It can be considered a unique type because two of its opposite holes are ellipse-shaped (A side 26 x 21, 5 mm; B side 22,5 x 21,5 mm), all the other holes are geometrically perfect circles: the smallest is 10,5 mm, the largest is 22 mm in diameter.

Figs.: 4a-4b-4c. The unique dodecahedron found at Saint Trivier de Courtes (Source: www.la-detection.com/dp/ message-75691.htm)

11 Guillier et al. 2008.

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The knobs soldered to the vertices are 5-6 mm in diameter. According to the archaeologists, the room where the dodecahedron was found could have served as a shop where precious metal objects were sold. If it is true, it supports the assumption that the dodecahedron could be a precious object, and is in agreement with the fact that one piece was found in a coin-hoard.12 Although the dodecahedron as a geometrical form – the symbol of the Universe – was of great importance for the Pythagoreans and Platonists, it is conspicuous that the objects were “mostly found in the northwestern pro-vinces of the Roman Empire, with a focus on Gaul, that is, regions strongly influenced by Celtic traditions”.13 Michael Guggenberger proposed that the enigmatic bronze object “derived from an environment characterized by the mutual influence of the Roman and Celtic cultures”, but he also stressed that “there is no evidence of any comparable [ma-terial] tradition in the Celtic world”.14 On the internet, however, a strange object turned up in 2009 on a website operated by a group of French metal detectorists. In this year an anonymous hobby archaeologist found a metal object similar to known dodecahedra at Saint Trivier de Courtes (Ain department). But if we examine it closely, this object differs considerably from those we call dodecahedra: it does not consist of pentagonal faces, but it is globular; on which we find knobs arranged in circles: 6 above, 11 in the middle, and 6 below (23 altogether). Its holes are not circular either, but triangular and pentagonal, and they are not arranged diagonally. At the bottom of the sphere there is a flat base, with a hole in it.15 In summary, we cannot say that in the last three hundred years we have gotten closer to the solution of the enigma, in spite of the fact that we are in possession of more than a hundred dodecahedra. The most we can say about this object is that it belongs to the Gallo-Roman or Celto-Roman Kulturkreis,16 and it had a kind of a religious function. Notwithstanding, it is regarded as strange that such a sacred object

12 Greiner 1996. 13 Guggenberger 2013, 58. 14 Guggenberger 2013, 58. 15 Forum de discussion, identification trouvailles, detecteur de metaux, www.la-detection. com/dp/message-75691.htm (2009.04.06, no. 75691R1) – We can find a number of comments attached to the pictures, most of them absolutely useless to determine the function of the object. (I want to express my deep appreciation for the manifold help provided by my colleagues: to Mrs. Róza Füzi for translating French texts; to Mrs. Rita Kós for explaining mathematical problems; and to Mrs. Shelly Matos for revising my English.) 16 Saint-Michel 1951; Duval 1981.

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turns up in the second–fourth century AD without any antecedents of the Iron Age. (Unless we regard the unique “dodecahedron” found at Saint Trivier de Courtes as an antecedent.) Experts usually emphasize the importance of the dodecahedron excavated in the cemetery of Krefeld-Gellep, because it implies that this enigmatic object was a kind of a scepter with the symbolic meaning of cosmic-astral power. The Druids cannot be considered as potential owners in this late period, but persons somehow connected to the Druidic traditions can be imagined.17 The fact that we know of only one dodecahedron made of precious metal (silver), hints that it was not used by an elite and privileged circle of a handful of “initiated”. More probable is that it belonged to low-ranking astrology or divination. The twelve holes of varying diameters probably refer to astral symbolism, but without signs and characters they cannot be unambiguously identified with celestial bodies (Sun, Moon, planets, stars). It is also inexplicable why this form of soothsaying or divination was limited to the western half of the Roman Empire. Finally, we can attribute the dodecahedra some sort of religious function with cosmic-astral symbolism. Possibly it was used as a kind of an amulet (although it would be carried with much difficulty around somebody’s neck) or a scepter used in theurgical or astromantic fortune-telling as a practical device for inquiring of the celestial bodies or supernatural powers. Angelos Chaniotis has also related the dodecahedron found in the Idaean Cave (Crete) to astral magic. This peculiar object, however, was made of rock crystal and on its twelve faces we find Greek characters instead of holes.18 While it is obvious that the Idaean dodecahedron was used as a dice ‒ the Gallo-Roman dodecahedra could not be used as such because knobs soldered to the vertices hindered the bowling of the object. It is all the more interesting that we can probably detect the continued existence ‒ or at least influence ‒ of the Gallo-Roman dode-cahedra. The so-called Sortes Sangallenses survived on a composite palimpsest manuscript datable to circa AD 600 in the library of the Abbey of Saint Gall (St. Gallen). It is probably not just coincidence that in this collection the number of sortes is always twelve.19 It can only be hoped the conditions in which Gallo-Roman dodecahedra were found will be examined more carefully in the future, so that experts can, perhaps, finally find out what these peculiar objects were used for almost 2000 years ago.

17 Guggenberger 2000, 74‒76. 18 Chaniotis 2006. 19 Klingshirn 2005.

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Bibliography Artmann 1993 = Artmann, B.: Roman Dodecahedra. Mathematical Intelligencer 15(2): 52‒53. Artmann 1996 = Artmann, B.: A Roman Icosahedron Discovered. American Mathematical Monthly 103(2): 132‒133. Benoît 1957 = Benoît, F.: Deux énigmes archéologiques: dodécaèdre perlé d’Arles et anneau octogonal bouleté de Vichy. OGAM 9(2): 104‒114, fig. 2‒8 et pl. IX-XII. Cervi-Brunier 1985 = Cervi-Brunier, I.: Le dodécaèdre en argent trouvé à Saint Pierre de Genève, Z. Revue Suisse d’Art et d’Archéologie | Schweizerische Archäologie Kunst-geschichte 42: 153‒156. Chaniotis 2006 = Chaniotis, A.: A dodecahedron of rock crystal from the Idaean cave and evidence for divination in the sacred cave of Zeus. In: Gabrilaki, I. ‒ Tzifopoulos, Y. (eds.), Actes of the International Symposium Mylopotamos, from Antiquity to our Days, vol. 3. Rethymnon, 205‒216. Déonna 1954 = Déonna, W.: Les dodécaèdres gallo-romains en bronze ajourés et bouletés. À propos du dodécaèdre d’Avenches. Bulletin de l’Association Pro Aventico 16, 18‒89. Duval 1981 = Duval, P. M.: Comment décrire les dodécaèdres galloromains en vue d’une étude comparée. Gallia 39: 195‒200. Greiner 1996 = Greiner, B. A.: Römische Dodekaeder. Untersuchungen zur Typologie, Herstellung, Verbreitung und Funktion. Carnuntum Jahrbuch 1995 [1996], 9‒44. Guggenberger 2000 = Guggenberger, M.: Etwas Gewisses hievon zu bestimmen waere ein Gewagtes. 260 Jahre Dodekaeder-Forschung, Veröffentlichungen des Tiroler Landesmuseum Ferdinandeum 80: 67‒84. Guggenberger 2013 = Guggenberger, M. 2013. The Gallo-Roman Dodecahedron. Mathema-tical Intelligencer 35(4): 56‒60. Guillier – Delage – Besombes 2008 = Guillier, G. – Delage, R. – Besombes, P. A.: Une fouille en bordure des thermes de Jublains (Mayenne): enfin un dodécaèdre en contexte archéologique, Revue Archéologique de l’Ouest 25: 269‒289. Klingshirn, W. E. 2005. Christian divination in late Roman Gaul: the Sortes Sangallenses. In: S. Iles Johnston, P. T. Struck (eds.): Mantikê. Studies in Ancient Divination. Brill, Leiden, 99-128. Kurzweil 1957 = Kurzweil, F.: Das Pentagondodekaeder des Museum Carnuntinum und seine Zweckbestimmung. Carnuntum Jahrbuch 1956 [1957], 23–29. Nouwen 1993 = Nouwen, R.: De Romeinse Pentagon-dodecaeder. Mythe en enigma. Publikaties van het Provinciaal Gallo-Romeins Museum te Tongeren 45. Hasselt: Museum Gallo-Romains Tongeren. Pirling – Siepen 2000 = Pirling, R. – Siepen, M.: Das römisch-fränkische Gräberfeld von Krefeld-Gellep 1983-1988. Stuttgart: Franz Steiner. Saint-Michel 1951 = Saint-Michel, L.: Situation des dodécaèdres celto-romains dans la tradition symbolique pythagoricienne. Bulletin de l’Association Guillaume Budé 4(2), 92– 116. Saint-Venant 1907 = Saint-Venant, J. de: Dodécaèdres perlés en bronze creux ajouré de l’époque gallo-romaine. Nevers: Mazeron. Sparavigna 2012 = Sparavigna, A. C.: Roman Dodecahedron as dioptron: analysis of freely available data. arXiv 1206.0946 29 (2012) [Downloaded at 28.04.2016.] Wagemans 2010 = Wagemans, S.: The Roman pentagon dodecahedron an astronomic measuring instrument for determining the optimal sowing date for winter grain. http://www.romandodecahedron.com/the-hypothesis [Downloaded at 21.04.2016.]

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From Polites to Magos

AUTHORS OF THIS VOLUME Béla Adamik scientific advisor Lendület (‘Momentum’) Research Group for Computational Latin Dialectology Research Institute for Linguistics of the Hungarian Academy of Sciences H-1068 Budapest, Benczúr u. 33. [email protected] Silvia Alfayé Profesor Contratado Doctor Departamento de Ciencias de la Antigüedad, Universidad de Zaragoza (Spain) [email protected] Radu Ardevan “Babeş-Bolyai” Universität zu Klausenburg Str. Kogălniceanu nr.1, 400084 Cluj-Napoca [email protected] Dániel Bajnok Eszterházy Károly College Department of Ancient and Medieval History H-3300 Eger, Eszterházy tér 1. [email protected] Andrea Barta research fellow Lendület (‘Momentum’) Research Group for Computational Latin Dialectology Research Institute for Linguistics, HAS 1068 Budapest, Benczúr u. 33. [email protected] Giulia Baratta, Università di Macerata, Dipartimento di Studi Umanistici. [email protected]

László Borhy Eötvös Loránd University Faculty of Humanities Institute of Archaeological Sciences Department of Roman Provincial and Classical Archaeology H–1088 Budapest, Múzeum krt. 4B. [email protected] Angelos Chaniotis Institute for Advanced Study, Princeton [email protected] Christopher A. Faraone The University of Chichago Department of Classic 1115 E. 58th Street Chicago, IL 60637 [email protected] Miroslav Frýdek Fachassistent Philosophische Fakultät der Masaryk-Universität A. Nováka 1, 602 00 Brno Tschechische Republik [email protected] Tamás Gesztelyi University of Debrecen Department of Classical Philology and Ancient History H-4032 Debrecen, Egyetem tér 1. [email protected] Richard Gordon Max Weber Centre for Advanced Cultural and Social Research, University of Erfurt [email protected]

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Edina Gradvohl Semmelweis University Faculty of Health Sciences Department of Social Sciences H-1088 Budapest, Vas utca 17. [email protected] Tibor Grüll University of Pécs, Department of Ancient History H-7624 Pécs, Rókus utca 2. [email protected] György W. Hegyi Eötvös Lóránt University Faculty of Humanities Department of Ancient History H-1088 Budapest, Múzeum krt. 6–8. [email protected] Péter Kovács Pázmány Péter Catholic University H-2081 Piliscsaba, Egyetem utca 1. [email protected] Gyula Lindner Universität Pécs Philosophische Fakultät Institut für Geschichtswissenschaften Lehrstuhl für Alte Geschichte [email protected] Ádám Lőrincz King’s College, London [email protected] Marc Mayer i Olivé University of Barcelona Institut d’Estudis Catalans [email protected] Zsolt Mráv Hungarian National Museum Archaeological Department H-1088 Bp. Múzeum krt. 14-16 [email protected] [email protected]

Levente Nagy Universität Pécs Abteilung für Archäologie [email protected] Dóra Pataricza [email protected] András Patay-Horváth Eötvös Lóránt University Faculty of Humanities Department of Ancient History 1088 Budapest, Múzeum krt. 6-8. [email protected] Ioan Piso Facultatea de istorie şi filosofie Departamentul de Istorie Antică şi Arheologie Str. Kogălniceanu nr.1, 400084 Cluj-Napoca, România [email protected] Zsigmond Ritoók Hungarian Academy of Sciences H-1051 Bp. Széchenyi István tér 9. Heikki Solin Institutum Classicum Universitatis Helsingiensis PO.BOX 24 00014 Helsingin yliopisto [email protected] Tamás Szabadváry Institut of Archaeological Sciences Faculty of Humanities Eötvös Loránd University H-1088 Bp. Múzeum krt. 4/D. [email protected] András Szabó Hungarian National Museum Archaeological Department H-1088 Bp. Múzeum krt. 14-16. [email protected]

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Ádám Szabó Archaeological Department Hungarian National Museum University of Pécs [email protected] [email protected] Levente Takács University of Debrecen Department of Classical Philology and Ancient History H-4032 Debrecen, Egyetem tér 1. [email protected] Zsuzsa Várhelyi Associate Professor of Classical Studies Boston University 745 Commonwealth Avenue Boston, MA 02215 USA [email protected]

Javier Velaza Universitat de Barcelona, Departament de Filologia Llatina, [email protected] László Vilmos University of Pécs, Department of Ancient History, H-7624 Pécs, Rókus u. 2. [email protected] Daniela Urbanová Institut für Klassische Studien, Philosophische Fakultät der Masaryk-Universität A. Nováka 1, 602 00 Brno Tschechische Republik [email protected]

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The enigma of the dodecahedron