Two cylinders in a cube

According to Archimedes (in the Method) this is a solid included between two cylinders, each of which is inscribed in one and the same cube so that its opposite

bases are in the two opposite faces of the cube and its surafes touches the other four

faces. The solid has four equal faces, four edges and two corners. If the radius of the

cylinders is R, the edges of the cube are 2R. The long diagonal is p R (= half the

cylinder circle) and the short diagonal is 2R (=the cube edge).

The volume of the solid is 2/3 of the cube volume.

(An Archimedean Palimpsest was discovered by JL Heiberg in 1907 in Constantinople.He

translated most of the Greek text. It contains transcriptions of Archimedes´ geometry,physics and writing ,eg. The Method) ( See http//www. omogenia.com/arch.htm and Physics Today,June 2000,p.32 and Th.L.Heath:The Method of Archimedes recently discovered by Heiberg, A supplement to the works of Archimedes 1897, The University Press Cambridge ,1912)