Dodecahedral die

"In modern role-playing games, the dodecahedron is often used as a twelve-sided die, one of the more common polyhedral dice" http://en.wikipedia.org/wiki/Dodecahedron

http://en.wikipedia.org/wiki/Dice#Non-cubical_dice

Even in the past, the dodecahedron was used for dice.

Here an example form the site archéologique de la Cathédrale Saint-Pierre de Genève 

http://www.site-archeologique.ch/contenu.php?id-node=25&id-img=84

Copie d'un dé romain, en forme du dodécaèdre, datant du IVe siècle

Even older are the Etruscan dodecahedra:

More on the etruscan dodecahedron at sites:

https://sites.google.com/site/ancientdodecahedra/etruscan-dodecahedron

http://stretchingtheboundaries.blogspot.it/2012/05/etruscan-dodecahedron.html

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

Chimu Surveying

An Ancient Surveying Equipment of Chimu
The Chimu lives in the pre-Columbian Peru, struggling to survive in one of the world's driest desert.

They were therefore "hydraulic engineers". Some of their knowledge about the management of water came from their predecessors, the Mochica, who lived in the Peru's Moche Valley during the 1st millennium AD. Mochica built a network of canals to irrigate their fields. 

 Adapted from http://www.specialtyinterests.net/eop.html

This is a Chimu surveying instrument shows how calculate the slope of the land. "The device consisted of a ceramic bowl pierced by a hollow sighting tube passing through a calibrated, cross-shaped opening (inset). And artificial horizon was established by aligning water with the three dots in the bowl, which was leveled in a larger, sand-filled vessel atop a tripod (far left); when the sighting tube was in the center of the cross-shaped opening it was parallel to the artificial horizon. Chimu surveyors marked a rod at the height of the level sighting tube, then moved the rod a known distance along uneven ground and sighted the mark. The ground slope corresponded to the tube angle indicated by the calibrations inside the bowl." From

Feats and wisdom of the ancients

Time-Life Books

2 Reviews

Time-Life Books, Aug 1, 1990 - History - 143 pages

Surveying and Hydraulic Engineering of the Pre-Columbian Chimú State: ad 900–1450, Charles R. Ortloff, Cambridge Archaeological Journal, Volume 5 / Issue 01 / April 1995, pp 55-74
Abstract The Chimú state of northern coastal Peru (ad 900–1480) developed massive irrigation-based agricultural systems supplied by intricate networks of canals drawing water from river sources in coastal valleys under their political control. Further intervalley canal systems, some up to 50 miles in length, were constructed to shunt water between river valleys to augment intravalley supplies. A high degree of civil engineering skill was necessary to construct and maintain such complex systems; knowledge of surveying and of open channel flow hydraulics was paramount. Some of the technology used by the Chimú has been investigated: surveying instruments and calculating tools have been unearthed and analyzed to provide some understanding of the technical base used for canal design. Details of the hydraulics knowledge-base have been extracted from computer simulation of the functioning of ancient Chimú canal designs. This article assembles known pieces of information related to Chimú civil engineering practice and attempts to provide a plausible methodology that could have been implemented by the Chimú to survey the precise canal bed slopes necessary for proper hydraulic functioning of large canal systems through rugged Andean foothill and mountain areas.

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