Roman dodecahedron

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Roman bronze dodecahedron found in Tongeren, Gallo-Roman Museum, Tongeren Pentagon-dodecaeder in brons, 150 tot 400 NC, vindplaats- Tongeren, Leopoldwal, 1939, collectie Gallo-Romeins Museum Tongeren, 4002.jpg
Roman bronze dodecahedron found in Tongeren, Gallo-Roman Museum, Tongeren

A Roman dodecahedron or Gallo-Roman dodecahedron [1] [2] is a small hollow object made of copper alloy which has been cast into a regular dodecahedral shape with twelve flat pentagonal faces. Each face has a circular hole of varying diameter in the middle, the holes connecting to the hollow center, and each corner has a protruding knob. [1] Roman dodecahedra date from the 2nd to 4th centuries AD and their purpose remains unknown. [1] They rarely show signs of wear, and do not have any inscribed numbers or letters. [3]

Contents

Description

Roman dodecahedra are cast in metal, [4] usually a copper alloy, although one silver example is known. [5] They are in the shape of regular dodecahedra, with the addition of a small metal ball at each vertex; each face has a circular hole in the centre. The dodecahedra vary in size from 4 to 11 cm; the holes in their faces have diameters ranging from 6 mm to 40 mm. [6] The lightest known example weighs 35 grams; the heaviest 1000 grams. [7] Most are decorated with circles, lines, and dots, but no letters or numbers are known to be marked on any of the objects. [8] One dodecahedron was found in a tomb alongside a bone object which might have been a kind of handle; however it was in too bad a condition to excavate and preserve. [9]

History

Two dodecahedra and an icosahedron on display in the Rheinisches Landesmuseum Bonn, Germany 2018 Rheinisches Landesmuseum Bonn, Dodekaeder & Ikosaeder.jpg
Two dodecahedra and an icosahedron on display in the Rheinisches Landesmuseum Bonn, Germany

The first dodecahedron was found in 1739. Since then, at least 130 similar objects have been found in Austria, Belgium, France, Germany, Hungary, Luxembourg, the Netherlands, Switzerland and the United Kingdom, but not in the Roman heartland in Italy. [1] In 2023, a dodecahedron in excellent condition was found by amateur archeologists in the small village of Norton Disney in Lincolnshire, UK, bringing the total to 33 of such objects found on the territory of Roman Britain. [10] It is on exhibition at the Lincoln Museum, Lincolnshire until October 2024. [11]

Purpose

The purpose of Roman dodecahedra has been much debated: [12] more than fifty possible explanations have been published. [13] Identifying their purpose with certainty is made more difficult as no mention of dodecahedra has been found in contemporary accounts or pictures of the time. [14] Speculative uses include as a survey instrument for estimating distances to (or sizes of) distant objects, though this is questioned as there are no markings to indicate that they would be a mathematical instrument; [15] as spool knitting devices for making gloves [3] (though the earliest known reference to spool knitting is from 1535, [16] [17] [18] and this would neither explain the use of bronze, nor the apparently similar icosahedron which is missing the holes necessary for spool knitting); or as part of a child's toy. [3]

Several dodecahedra were found in coin hoards, suggesting either that their owners considered them valuable objects, or that their use was connected with coins — as, for example, for easily checking coins fit a certain diameter and were not clipped. [19] It has been suggested that they might have been religious artifacts, or even fortune-telling devices. This latter speculation is based on the fact that most of the examples have been found in Gallo-Roman sites. [20] [21] It has also been suggested that they might have been an object to test the skill of a metalsmith, perhaps as part of a portfolio to demonstrate their capabilities to customers or as a way to qualify for a certain status in a collegium (guild). This speculation is based on the historic cost of bronze and the level of skill necessary to cast such an object. [3] Some 19th-century antiquarians speculated that they might be weapons, such as the head of a mace or a metal bullet, but other scholars have suggested that the dodecahedra are too light to make an effective weapon. [3]

Similar objects

A Roman icosahedron has also been discovered after having long been misclassified as a dodecahedron. This icosahedron was excavated near Arloff in Germany and is currently on display in the Rheinisches Landesmuseum in Bonn. [22] In 2009, metal-detectorists in France reported the discovery of an object at Saint-Trivier-de-Courtes, similar to the Roman dodecahedra but spherical with triangular and pentagonal holes. [23]

Smaller dodecahedra with the same features (holes and knobs) and made from gold have been found in South-East Asia along the Maritime Silk Road and the earliest items appear to be from the Roman epoch. Examples include those uncovered in Óc Eo, Vietnam, by Louis Malleret, who concluded that the objects represented the influence of Mediterranean trade on the Funan economy. [24] Similar decorative gold dodecahedra have been found in the Pyu city-states and Khao Sam Kaeo. [25] [26]

Related Research Articles

In geometry, a dodecahedron or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid. There are also three regular star dodecahedra, which are constructed as stellations of the convex form. All of these have icosahedral symmetry, order 120.

<span class="mw-page-title-main">Dual polyhedron</span> Polyhedron associated with another by swapping vertices for faces

In geometry, every polyhedron is associated with a second dual structure, where the vertices of one correspond to the faces of the other, and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other. Such dual figures remain combinatorial or abstract polyhedra, but not all can also be constructed as geometric polyhedra. Starting with any given polyhedron, the dual of its dual is the original polyhedron.

<span class="mw-page-title-main">Golden ratio</span> Number, approximately 1.618

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities ⁠⁠ and ⁠⁠ with ⁠⁠, ⁠⁠ is in a golden ratio to ⁠⁠ if

<span class="mw-page-title-main">Regular icosahedron</span> Convex polyhedron with 20 triangular faces

In geometry, the regular icosahedron is a convex polyhedron that can be constructed from pentagonal antiprism by attaching two pentagonal pyramids with regular faces to each of its pentagonal faces, or by putting points onto the cube. The resulting polyhedron has 20 equilateral triangles as its faces, 30 edges, and 12 vertices. It is an example of a Platonic solid and of a deltahedron. The icosahedral graph represents the skeleton of a regular icosahedron.

<span class="mw-page-title-main">Kepler–Poinsot polyhedron</span> Any of 4 regular star polyhedra

In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra.

<span class="mw-page-title-main">Polyhedron</span> Three-dimensional shape with flat faces, straight edges, and sharp corners

In geometry, a polyhedron is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices.

In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent regular polygons, and the same number of faces meet at each vertex. There are only five such polyhedra:

A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. A regular polyhedron is highly symmetrical, being all of edge-transitive, vertex-transitive and face-transitive. In classical contexts, many different equivalent definitions are used; a common one is that the faces are congruent regular polygons which are assembled in the same way around each vertex.

<span class="mw-page-title-main">Regular polytope</span> Polytope with highest degree of symmetry

In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. In particular, all its elements or j-faces — cells, faces and so on — are also transitive on the symmetries of the polytope, and are themselves regular polytopes of dimension j≤ n.

<span class="mw-page-title-main">Lucet</span> Tool for making cords or braids

A lucet is a tool used in cordmaking or braiding which is believed to date back to the Viking and Medieval periods, when it was used to create cords that were used on clothing, or to hang items from the belt. Lucet cord is square, strong, and slightly springy. It closely resembles knitted I-cord or the cord produced on a knitting spool. Lucet may unravel if cut, but is easily fixed with a small knot. Unlike other braiding techniques such as kumihimo, finger-loop braiding or plaiting, where the threads are of a finite length, lucetted braids can be created without pre-measuring threads and so it is a technique suited for very long cords.

<span class="mw-page-title-main">Hippasus</span> 5th-century BC Pythagorean philosopher

Hippasus of Metapontum was a Greek philosopher and early follower of Pythagoras. Little is known about his life or his beliefs, but he is sometimes credited with the discovery of the existence of irrational numbers. The discovery of irrational numbers is said to have been shocking to the Pythagoreans, and Hippasus is supposed to have drowned at sea, apparently as a punishment from the gods for divulging this and crediting it to himself instead of Pythagoras which was the norm in Pythagorean society. However, the few ancient sources who describe this story either do not mention Hippasus by name or alternatively tell that Hippasus drowned because he revealed how to construct a dodecahedron inside a sphere. The discovery of irrationality is not specifically ascribed to Hippasus by any ancient writer.

<span class="mw-page-title-main">Snub disphenoid</span> Convex polyhedron with 12 triangular faces

In geometry, the snub disphenoid is a convex polyhedron with 12 equilateral triangles as its faces. It is an example of deltahedron and Johnson solid. It can be constructed in different approaches. This shape also has alternative names called Siamese dodecahedron, triangular dodecahedron, trigonal dodecahedron, or dodecadeltahedron.

<span class="mw-page-title-main">Uniform polyhedron</span> Isogonal polyhedron with regular faces

In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive—there is an isometry mapping any vertex onto any other. It follows that all vertices are congruent. Uniform polyhedra may be regular, quasi-regular, or semi-regular. The faces and vertices don't need to be convex, so many of the uniform polyhedra are also star polyhedra.

<span class="mw-page-title-main">Final stellation of the icosahedron</span> Outermost stellation of the icosahedron

In geometry, the complete or final stellation of the icosahedron is the outermost stellation of the icosahedron, and is "complete" and "final" because it includes all of the cells in the icosahedron's stellation diagram. That is, every three intersecting face planes of the icosahedral core intersect either on a vertex of this polyhedron or inside of it. It was studied by Max Brückner after the discovery of Kepler–Poinsot polyhedron. It can be viewed as an irregular, simple, and star polyhedron.

<span class="mw-page-title-main">Chamfered dodecahedron</span> Goldberg polyhedron with 42 faces

In geometry, the chamfered dodecahedron is a convex polyhedron with 80 vertices, 120 edges, and 42 faces: 30 hexagons and 12 pentagons. It is constructed as a chamfer (edge-truncation) of a regular dodecahedron. The pentagons are reduced in size and new hexagonal faces are added in place of all the original edges. Its dual is the pentakis icosidodecahedron.

<span class="mw-page-title-main">Regular dodecahedron</span> Convex polyhedron with 12 regular pentagonal faces

A regular dodecahedron or pentagonal dodecahedron is a dodecahedron composed of regular pentagonal faces, three meeting at each vertex. It is an example of Platonic solids, described as cosmic stellation by Plato in his dialogues, and it was used as part of Solar System proposed by Johannes Kepler. However, the regular dodecahedron, including the other Platonic solids, has already been described by other philosophers since antiquity.

<span class="mw-page-title-main">Spool knitting</span> Form of knitting

Spool knitting,loom knitting, corking,French knitting, or tomboy knitting is a form of knitting that uses a spool with a number of nails or pegs around the rim to produce a tube or sheet of fabric. The spool knitting devices are called knitting spools, knitting nancys, knitting frame, knitting loom, or French knitters.

<span class="mw-page-title-main">Óc Eo</span> Township in Mekong Delta, Vietnam

Óc Eo (Vietnamese) is an archaeological site in modern-day Óc Eo commune of Thoại Sơn District in An Giang Province of southern Vietnam. Located in the Mekong Delta, Óc Eo was a busy port of the kingdom of Funan between the 2nd century BC and 12th century AD and it may have been the port known to the Greeks and Romans as Cattigara.

Hypsicles was an ancient Greek mathematician and astronomer known for authoring On Ascensions (Ἀναφορικός) and possibly the Book XIV of Euclid's Elements. Hypsicles lived in Alexandria.

<span class="mw-page-title-main">Icosian game</span> Game of finding cycles on a dodecahedron

The icosian game is a mathematical game invented in 1856 by Irish mathematician William Rowan Hamilton. It involves finding a Hamiltonian cycle on a dodecahedron, a polygon using edges of the dodecahedron that passes through all its vertices. Hamilton's invention of the game came from his studies of symmetry, and from his invention of the icosian calculus, a mathematical system describing the symmetries of the dodecahedron.

References

  1. 1 2 3 4 Guggenberger, Michael (2013-10-03). "The Gallo-Roman Dodecahedron". The Mathematical Intelligencer. 35 (4). Springer Science and Business Media LLC: 56–60. doi:10.1007/s00283-013-9403-7. ISSN   0343-6993. S2CID   122337773.
  2. ↑ Hill, Christopher (1994). "Gallo-Roman Dodecahedra: A Progress Report". The Antiquaries Journal. 74. Cambridge University Press (CUP): 289–292. doi:10.1017/s0003581500024458. ISSN   0003-5815. S2CID   161691752.
  3. 1 2 3 4 5 Metcalfe, Tom (August 6, 2018). "The Mysterious Bronze Objects that Have Baffled Archaeologists for Centuries". Pocket. Mental Floss. Retrieved 17 September 2019.
  4. ↑ Alexander, James (2023). "A Roman Villa at Newhall, Harlow, Essex". Archaeology International. 26: 212–213.
  5. ↑ Grüll, Tibor (2016). "The Enigma of the Dodecahedron". In Szabó, Ádám (ed.). From Polites to Magos. p. 148.
  6. ↑ Grüll, Tibor (2016). "The Enigma of the Dodecahedron". In Szabó, Ádám (ed.). From Polites to Magos. pp. 148–149.
  7. ↑ Grüll, Tibor (2016). "The Enigma of the Dodecahedron". In Szabó, Ádám (ed.). From Polites to Magos. p. 149.
  8. ↑ Grüll, Tibor (2016). "The Enigma of the Dodecahedron". In Szabó, Ádám (ed.). From Polites to Magos. p. 150.
  9. ↑ Grüll, Tibor (2016). "The Enigma of the Dodecahedron". In Szabó, Ádám (ed.). From Polites to Magos. pp. 152–153.
  10. ↑ Stavrou, A (20 January 2024). "Amateur archaeologist discovers bizarre Roman object that has baffled for centuries". The Independent . Retrieved 20 January 2024.
  11. ↑ "Roman dodecahedron that baffled experts stays on show in Lincoln". BBC News. 27 August 2024. Retrieved 28 August 2024.
  12. ↑ Coombe, Penny; Henig, Martin; Adams, Kurt; Gilmour, Brian; Pearce, John (2020). "The Gloucester Hoard of Roman Bronze". Britannia. 51: 260.
  13. ↑ Grüll, Tibor (2016). "The Enigma of the Dodecahedron". In Szabó, Ádám (ed.). From Polites to Magos. p. 150.
  14. ↑ Grüll, Tibor (2016). "The Enigma of the Dodecahedron". In Szabó, Ádám (ed.). From Polites to Magos. p. 151.
  15. ↑ Sparavigna, A. (2012). "Roman dodecahedron as dioptron: Analysis of freely available data". arXiv: 1206.0946 [physics.pop-ph].
  16. ↑ von Schmoller, Gustav (1879). "67. Rathsentscheidung in einem Streite der Tuchersunft und der Zunft zum Spiegel. dass das Hosenstricker-Handwerk ze der erstern gehöre. 1535.". Die Strassburger tucher- und weberzunft: Urkunden und darstellung nebst regesten und glossar. Ein beitrag zur geschichte der deutschen weberei und des deutschen gewerberechts vom XIII.-XVII. jahrhundert. Strassburg: Verlag von Karl J. Trübner. Retrieved 27 January 2023.
  17. ↑ Rutt, Richard (1987). A History of Hand Knitting (U.S. ed.). Loveland, Colo.: Interweave Press. ISBN   0934026351 . Retrieved 27 January 2023.
  18. ↑ Spencer, David J. (2001). Knitting technology : a comprehensive handbook and practical guide (3rd ed.). Lancaster, Pa.: Technomic. ISBN   9781855737556.
  19. ↑ Greiner, Bernhard A. (1996). "Römische Dodekaeder: Untersuchungen zur Typologie, Herstellung, Verbreitung, und Funktion". Carnuntum Jahrbuch 1995 (in German). pp. 9–44.
  20. ↑ Henig, Martin (1984). Religion in Roman Britain. Routledge. p. 128. ISBN   0-7134-6047-4.
  21. ↑ Kilford, L.J.P. (December 2004). "A mathematical tourist in Germany". Mathematics Today. Vol. 40, no. 6. p. 204.
  22. ↑ Artmann, Benno (1999). Euclid – the creation of mathematics. New York: Springer. p. 303. ISBN   978-0-387-98423-0.
  23. ↑ Grüll, Tibor (2016). "The Enigma of the Dodecahedron". In Szabó, Ádám (ed.). From Polites to Magos. p. 154.
  24. ↑ Malleret, Louis (1961). "Les dodecaedres d'or du site d'Oc-eo" [The gold dodecohedrons from the Oc-eo site]. Artibus Asiae (in French). 24 (3–4). JSTOR: 343–350. doi:10.2307/3249235. ISSN   0004-3648. JSTOR   3249235.
  25. ↑ Bennett, Anna T.N. (2009-12-31). "Gold in early Southeast Asia". ArchéoSciences (33). OpenEdition: 99–107. doi: 10.4000/archeosciences.2072 . ISSN   1960-1360.
  26. ↑ Xiong, Zhaoming (2014). "The Hepu Han tombs and the maritime Silk Road of the Han Dynasty". Antiquity. 88 (342). Cambridge University Press (CUP): 1229–1243. doi:10.1017/s0003598x0011542x. ISSN   0003-598X. S2CID   161059940.
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