[Polyhedron of Dürer's engraving Melancholia. I--a Nürnberg sketch representing the Archimedean body].

New mathematical hypotheses are postulated concerning the truncated rhombohedron in Dürer's engraving Melencolia.I as well as the relation of the rhombohedron to the magic square. The two free parameters of a truncated rhombohedron have to be chosen in a way that (i) its front orthogonal elevation is nearly quadratical and with the form of the magic square, and that (ii) it possesses approximately a circumscribed sphere. Both conditions result in a value of 79.2 degrees for the angle of the rhombohedron. Measuring two lengths of the rhombohedron of the engraving yields the same value. In the magic square, the numbers are positioned in a way that the connection lines between four numbers give the sum 34 for lines which are the projection lines of the edges of the rhombohedron. In the Nürnberg-Codex of Dürer's manuscripts, exists a page with some sketches of mostly archimedean solids. One sketch represents a pentagon with approximately the measures of the six lateral faces of the truncated rhombohedron. It has to be looked upon as a preliminary sketch for the solid of the engraving. In 1543 Augustin Hirschvogel from Nürnberg, as the next after Dürer, rediscovered a further archimedean solid; this rediscovering has been attributed to D. Barbaro until now.