Dodecahedron

Il solido platonico che preferisco

Pierre MEYER and the puzzle dodecahedron

Pierre Meyer is an artist who works with ivory.

https://www.maitresdart.com/pierre_meyer-40/parcours_et_realisations.html

Great his puzzle dodecahedron!

Chinese and European ivory puzzle balls

From Wikipedia: https://en.wikipedia.org/wiki/Ivory_carving

"By the 18th century China had a considerable market in items such as figures made for export to Europe, and from the Meiji Period Japan followed. Japanese ivory for the domestic market had traditionally mostly been small objects such as netsuke, for which ivory was used from the 17th century, or little inlays for sword-fittings and the like, but in the later 19th century, using African ivory, pieces became as large as the material would allow, and carved with virtuosic skill. A speciality was round puzzle balls of openwork that contained a series of smaller balls, freely rotating, inside them, a tribute to the patience of Asian craftsmen."

Usually, many of these balls have a decorated stand made of ivory too.

Chinese puzzle ball, with openwork and a series of twelve smaller balls, ivory, 19th century. British Museum. Original photograph from Ged Carroll

Form http://tinglefactor.typepad.com/thetinglefactorbox/2013/07/where-is-the-seam-chinese-puzzle-ball.html

"Originally, they (Chinese puzzle balls) were made almost exclusively from ivory, or the tusks of elephants and were the playthings of rich men because of the time and effort involved in making them. ... Usually, puzzle balls are symbols of good luck, and are decorated with a variety of feng shui symbols. The outermost layer often features the phoenix and dragon, symbols of yin and yang. The phoenix represents the wife while the dragon is the husband and emperor, and balls decorated with these symbols are thought to bring good luck and happiness to a marriage. In fact, almost all of the symbols most commonly associated with puzzle balls are associated with ensuring a long and happy marriage. Some balls even have different symbols on different layers, though the most common is a highly decorative outer ball and ‘latticed’ balls inside (with geometric patterns of holes)."

Detail of an ivory ball on show in the German Rautenstrauch-Joest Museum. It has 16 layers, which can spin. Courtesy Till Niermann , Wikipedia.

In the above image we see an example of Canton ivory carving. From Wikipedia (on the Lingnan culture or Cantonese culture). "Canton ivory woodcarving is another well-known product from Lingnan. With a history of 2000 years, it traditionally uses ivory as raw material to make sculptures, with the Canton-style renowned for being particularly delicate and detailed without being brittle. The Cantonese people have also successfully produced the legendary craft product - Ivory ball. After the 1980s, however, international ivory trade has been banned. This results in the Cantonese people now trying to find substitute materials - materials that look and feel like but are actually not ivory - in their attempt to pass on this ancient art."

From http://www.odditycentral.com/pics/chinese-puzzle-balls-the-rubiks-cube-of-the-ancient-world.html

"Chinese puzzle balls are ornate decorative items that consist of several concentric spheres, each of which rotates freely, carved from the same piece of material. ... These detailed works of art are usually made up of at least 3 to 7 layers, but the world’s largest puzzle ball is actually made of 42 concentric balls all enclosed one within the other. Although the inner balls can be manipulated to align all the holes, Chinese puzzle balls got their name from people who, through the ages, pondered the mystery of making such objects. So how exactly are puzzle balls made? .... Chinese masters rotate a solid ball on a lathe and start by drilling holes toward the center of the objects. Then, using special “L”-shaped tools, they begin to separate the innermost balls. ...  Because it is easier to work with, the exterior shell is the most elaborately carved, usually featuring an intertwined dragon and a phoenix."

Antikitera.net tells us that the first puzzle balls appeared during the Song Dynasty, around 1000 d.C.
http://www.antikitera.net/news.asp?ID=11753

After having shown the Chinese ivory balls, it seems that the puzzle balls became popular in Europe thanks to Chinese products of the later XIXth century. However, puzzle balls existed in Europe in XVI or XVII century. Here an example.

European puzzle ball, XVI-XVII Century (Image Courtesy: Maureen and Renato Bucci, Italy). It was exhibited with a rosary having the beads made in the same manner of the ball. 

The rosary, XVI-XVII Century (Image Courtesy: Maureen and Renato Bucci, Italy).  

The ball shown in the image is remarkable because it looks like a Roman Dodecahedron. Actually Renato Bucci was so kind to send me the picture because of this similarity. Probably, this was an object of a Wunderkammer (in italiano, camera delle meraviglie o gabinetto delle curiosità o delle meraviglie), encyclopedic collections of objects of the Reinassance Europe.  

From https://en.wikipedia.org/wiki/Cabinet_of_curiosities

"The Kunstkammer was regarded as a microcosm or theater of the world, and a memory theater. The Kunstkammer conveyed symbolically the patron's control of the world through its indoor, microscopic reproduction."

An example of Kunstkammer
http://wonder-cabinet.sites.gettysburg.edu/2017/cabinet/carved-ivory-puzzle-balls/

Besides the balls, we have also the polyhedra. Here the dodecahedra created by Egidius Lobenigk (1581 - 1584). From https://artsandculture.google.com/entity/m0t50361?categoryid=artist we can see them. 

These dodecahedra are at Staatliche Kunstsammlungen Dresden, (courtesy image from Jürgen Karpinski, photographer).

Let me conclude remarking that today puzzle balls are created too. Here the image of one of them, which is showing a contempoary "puzzle dodecahedra". The artist that created it is Pierre Meyer is an artist who works with ivory. https://www.maitresdart.com/pierre_meyer-40/parcours_et_realisations.html

Pierre Meyer's ivory "puzzle dodecahedron".

Also "new production of ornamental turning ivory of '600" is evidenced by the works of Andrea Pacciani, architect in Parma, by the web https://www.etsy.com/it/listing/225172225/tornitura-ornamentale-da-un-modello-in. A piece "is inspired by a piece of the museum's collection of Rosenborg in Denmark (*). Another piece is inspiered to the drawings of Grollier de Serviere, (1596–1689), French inventor and ornamental turner.
According to Andrea, "Thanks to the new generation of 3D technologies we could bring back the light of contemporary production about this object collection of great visual impact". That is, new technologies for creating objecs for our modern Wunderkammer.

(*) the reader can see the pieces at http://www.bobkatsjaunt.com/denmark.html.

A drawing from a book on the works of  Grollier de Serviere

CALCULI, COMPAS, DODECAEDRE

Very interesting page at http://www.alienor.org/Articles/ecriture/instrument3.htm
telling that "Les Gallo-Romains possédaient également différents instruments destinés aux disciplines scientifiques Pour compter, on utilisait des petits cailloux appelés calculi qui étaient placés dans des cases. On disposait aussi de compas se rapportant à la géométrie mais aussi au traçage des lignes d’écriture. ... Aujourd’hui, les avis convergent pour interpréter les dodécaèdres en bronze, creux, comme des instruments de géomètre."

Musée de Poitiers. Visit the site!

Les dodécaèdres gallo-romains (2)

Adapted from http://letarot.com/pages-vrac/pages/Truc-a-trous.html

Les dodécaèdres gallo-romains (1)

Adapted from http://letarot.com/pages-vrac/pages/Truc-a-trous.html

Vienne Roman Dodecahedron

Print! Cut! Fold! Glue!

Image obtained from some data in the paper:

Duval Paul-Marie. Comment décrire les dodécaèdres gallo-romains, en vue d'une étude

comparée. In: Gallia. Tome 39, fascicule 2, 1981. pp. 195-200, doi : 10.3406/galia.1981.1829

Bristol Roman Dodecahedron

Adapted from the paper:

Etwas Gewisses hievon zu bestimmen waere ein Gewagtes

260 Jahre Dodekaeder-Forschung, by Michael Guggenberger

Roman Dodecahedron replica

Print! Cut! Fold! Glue!

Dimensions for making a replica Roman Dodecahedron (3)

Let us prepare a copy of the Roman Dodecahedron of Jublains.
We can use the paper:
Une fouille en bordure des thermes de Jublains (Mayenne) : enfin un dodécaèdre en contexte archéologique !
Gérard Guillier, Richard Delage et Paul-André Besombes, at http://rao.revues.org/680

For the dimensions please see the image http://rao.revues.org/docannexe/image/680/img-16.png

Or print and cut

Dimensions for making a replica Roman Dodecahedron (2)

Let us suppose somebody wants to make a replica of a Roman dodecahedron,.
Here another recipe. Consider the image

Centered at the center of each face, draw a circle, which will be a hole. These circles usually have different diameters. Print and cut the image.
 If you want some figures, you can, for instance use the article by

Duval Paul-Marie. Comment décrire les dodécaèdres gallo-romains, en vue d'une étude
comparée. In: Gallia. Tome 39, fascicule 2, 1981. pp. 195-200, doi : 10.3406/galia.1981.1829

Here I reproduce an image.

You have the exact potions of holes.
According to the image of the dodecahedron, 1 is opposite 12, 2 opposite 11, 3 opposite 10, etc.

Dimensions for making a replica Roman dodecahedron (1)

Let us suppose somebody wants to make a replica of a Roman dodecahedron,
here a recipe. Consider the following image

Centered at the center of each face, draw a circle, which will be a hole. These circles usually have different diameters. Print and cut the image.
If you want some figures, you can, for instance use the article at the following link:
http://www.scribd.com/doc/116123429/The-Roman-Dodecahedron-of-Kadath
Here I am reproducing a table.

Here we have not the exact potions of the holes, but we have the diameters of holes on the opposite faces.
According to the image of the dodecahedron, 1 is opposite 12, 2 opposite 11, 3 opposite 10, etc.

See the next post too!

Roman Dodecahedron of Kadath

The web site http://www.kadath.be/ is publishing the review Kadath. The site tells that it is based on the "projet KADATH". "Dans l’œuvre de H.P. Lovecraft, Kadath est la cité légendaire des Grands Anciens, symbole de l’origine des civilisations. Notre quête, appliquée aux réalités archéologiques, est de remonter à pareilles sources, en cherchant à déchiffrer l’empreinte que laissèrent les premiers civilisateurs, dieux et ancêtres présents dans tous les mythes et toutes les traditions."

At the link http://www.scribd.com/doc/116123429/The-Roman-Dodecahedron-of-Kadath

the reader can find a paper from Kadath, written by Pierre Méreaux-Tanguy discussing the Roman Dodecahedron as an optical instrument. For other reference on the Roman Dodecaedron see the papers: Ancient and modern rangefinders at http://arxiv.org/abs/1205.2078 and http://arxiv.org/abs/1206.0946

Dodecahedral sundial

Dodecahedron With Sundial Faces 

Palazzo Madama, Torino

End  XVII Century

Aléria dodecahedron

This image is adapted from YouTube http://www.youtube.com/watch?v=x_2OrVzC46Y

It is showing a rock crystal dodecahedron found at Aléria Corisca

http://en.wikipedia.org/wiki/Al%C3%A9ria

An ancient rangefinder (Roman Dodecahedron)

According to Wikipedia, "a rangefinder is a device that measures distance from the observer to a target, for the purposes of surveying, determining focus in photography, or accurately aiming a weapon. Some devices use active methods to measure (such as sonar, laser, or radar); others measure distance using trigonometry (stadiametric rangefinders and parallax, or coincidence rangefinders). These methodologies use a set of known information, usually distances or target sizes, to make the measurement, and have been in regular use since the 18th century".
 It could be surprising, but probably the Roman Army had a rangefinder. It was the Roman Dodecahedron (I have already discussed it in some posts and papers: on arXiv, where I am explaining how  it can be used for measuring distance as a rangefinder, http://arxiv.org/abs/1204.6497 ).
For me, those dodecahedrons having a structure with holes of different sizes, are military instruments to evaluate distances for ballistics. It is simple to use. Of course, later, during the Middle Age, different instruments had been developed for surveying: the dodecahedron was of the Roman Army, and, probably, its use lost after the collpase of the Empire. See also "Ancient and Modern Rangefinders", on arXiv, http://arxiv.org/abs/1205.2078 and on SCIRP  http://www.scirp.org/journal/PaperInformation.aspx?PaperID=23245