**Photography by Carlos Dorce**

The Berlin Papyrus 6619 s not the only mathematical “paper” of the Neues Museum of Berlin because we can see two more documents on exhibition. The first of them is a Greek papyrus (139 AD) with some geometrical problems and their solutions (first picture).

The second is a table with Greek fractions from the Byzantine epoch (7th century):

Photography by Carlos Dorce

Finally, we find this ceramic piece which is part of a more complete catalogue composed of pieces P 11999, P 12000, P 12002, P 12007, P 12008, P 12609 and P 12611 from the 3rd and 2nd centuries BC, all of them found in Elefantina.

**Photography by Carlos Dorce**

These pieces contain one of the most difficult problems of the Greek mathematics: the construction of a regular icosahedron. This P12609 was translated and analised by Jürgen Mau and Wolfgang Müller (`Mathematische Ostraka aus der Berliner Sammlung’, *Archiv für Papyrusforschung* XVII (1962), 1-10.), and we find some words which help us to understand the text. For example, word σφαιρας suggests that we are studying a tridimensional figure, τριγωνων πλευρον refers to equilateral triangles and δεκαγων is used by Euclid in some propositions of the *Elements*.

We can think about the transmission of the Greek science from Alexandria to other Greek cities because of these pieces were found in Elefantina and not in Alexandria. After Euclid’s *Elements*, the only reference to a construction of a regular icosahedron is found in the work of Hypsicles (c. 190 BC-c.120 BC) who explains that his father and Basilides of Tyrus discussed in Alexandria about Apollonius’ construction of the regular dodecahedron and icosahedron.

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