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Funding for this project generously provided by Overdeck Family Foundation

around 250–150 BCE

Pottery Sherd Icosahedron Construction

Icosahedron construction on ancient pottery fragments

Six pottery sherds ("sherd" is the preferred archaeological term for a broken pieces of pottery—as opposed to the more common form "shard") found on the island of Elephantine appear to contain a number of exercises concerned with the construction of the regular icosahedron, one of the most sophisticated topics of ancient Greek mathematics.

Pottery Sherd Icosahedron Construction

Pottery sherds containing a mathematical diagram and accompanying text were found on Elephantine Island in Egypt by German archeological expeditions headed by Otto Rubensohn in 1906–1908. They have been dated to around 250–150 BCE and consist of six sherds, known to the Greeks as ostraka. Unlike papyri, whose contents generally recorded things wishing to be preserved, ostraka were scraps that were generally used to record ephemeral information such as tax receipts. Sherd P 12609 in particular contains strong indications that the ostrakon concerned construction of the regular icosahedron as described in Proposition XVI of Euclid's Elements.

Artifact format

Various; tallest sherd is about 14 cm high

Artifact origin

Elephantine, Egypt

Current artifact location

Egyptian Museum of Berlin, Berlin

Catalog number

P 11999, P 12002, P 12007, P 12008, P 12609, P 12611


Polyhedra timeline Burnt City Dice Euclid's Elements Pottery Sherd Icosahedron Construction Serpentinite Icosahedral Die Icosahedral Die with Divine Entities Da Vinci's Polyhedra Kepler's Planetary System

Interactive Content

Computational Explanation

Other Resources

Additional Reading

  • Mau, J. and Müller, W. "Mathematische Ostraka aus der Berliner Sammlung." Archiv für Papyrusforschung, No. XVII, pp. 1–10, 1962.