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

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. [4]

Instances range in size from 4 to 11 centimetres (1.6 to 4.3 in). 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. [5]

Purpose

No mention of dodecahedrons has been found in contemporary accounts or pictures of the time. 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; [6] as spool knitting devices for making gloves [3] (though the earliest known reference to spool knitting is from 1535, [7] [8] [9] and this would neither explain the use of bronze, nor the apparently similar icosahedron which is missing the holes necessary for spool knitting); as part of a child's toy; [3] or for decorative purposes. [10]

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. [11] 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. [12] [13] 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

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. [14] Similar decorative gold dodecahedrons have been found in the Pyu city-states and Khao Sam Kaeo. [10] [15]

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">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> Polyhedron with 20 regular 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.

In geometry, a Johnson solid, sometimes also known as a Johnson–Zalgaller solid, is a strictly convex polyhedron whose faces are regular polygons. They are sometimes defined to exclude the uniform polyhedrons. There are ninety-two solids with such a property: the first solids are the pyramids, cupolas. and a rotunda; some of the solids may be constructed by attaching with those previous solids, whereas others may not. These solids are named after mathematicians Norman Johnson and Victor Zalgaller.

<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.

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:

<span class="mw-page-title-main">Stellation</span> Extending the elements of a polytope to form a new figure

In geometry, stellation is the process of extending a polygon in two dimensions, a polyhedron in three dimensions, or, in general, a polytope in n dimensions to form a new figure. Starting with an original figure, the process extends specific elements such as its edges or face planes, usually in a symmetrical way, until they meet each other again to form the closed boundary of a new figure. The new figure is a stellation of the original. The word stellation comes from the Latin stellātus, "starred", which in turn comes from the Latin stella, "star". Stellation is the reciprocal or dual process to faceting.

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 jn.

<span class="mw-page-title-main">Triakis icosahedron</span> Catalan solid with 60 faces

In geometry, the triakis icosahedron is an Archimedean dual solid, or a Catalan solid, with 60 isosceles triangle faces. Its dual is the truncated dodecahedron. It has also been called the kisicosahedron. It was first depicted, in a non-convex form with equilateral triangle faces, by Leonardo da Vinci in Luca Pacioli's Divina proportione, where it was named the icosahedron elevatum. The capsid of the Hepatitis A virus has the shape of a triakis icosahedron.

<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; these names mean the 12-sided polyhedron.

<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.

<span class="mw-page-title-main">Carved stone balls</span> Petrospheres from late Neolithic Scotland

Carved stone balls are petrospheres dated from the late Neolithic, to possibly as late as the Iron Age, mainly found in Scotland, but also elsewhere in Britain and Ireland. They are usually round and rarely oval, and of fairly uniform size at around 2+34 inches or 7 cm across, with anything between 3 and 160 protruding knobs on the surface. They range from having no ornamentation to extensive and highly varied engraved patterns. A wide range of theories has been produced to explain their use or significance, with none gaining very wide acceptance.

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.

<span class="mw-page-title-main">Decagram (geometry)</span> 10-pointed star polygon

In geometry, a decagram is a 10-point star polygon. There is one regular decagram, containing the vertices of a regular decagon, but connected by every third point. Its Schläfli symbol is {10/3}.

<span class="mw-page-title-main">Turicum</span> Former Gallo-Roman settlement in Switzerland

Turicum was a Gallo-Roman settlement at the lower end of Lake Zurich, and precursor of the city of Zürich. It was situated within the Roman province of Germania Superior) and near the border to the province of Raetia; there was a tax-collecting point for goods traffic on the waterway Walensee–Obersee-Zürichsee–Limmat–Aare–Rhine.

<span class="mw-page-title-main">Cattigara</span> Vietnamese port city described in antiquity

Cattigara is the name of a major port city located on the Magnus Sinus described by various antiquity sources. Modern scholars have linked Cattigara to the archaeological site of Óc Eo in present-day Vietnam.

References

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  11. Greiner, Bernhard A. (1996). "Römische Dodekaeder: Untersuchungen zur Typologie, Herstellung, Verbreitung, und Funktion". Carnuntum Jahrbuch 1995 (in German). pp. 9–44.
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  14. 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.
  15. 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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