Hans Weitzel: Zum Polyeder auf A.
DŸrers Stich
Melencolia I –
ein NŸrnberger Skizzenblatt mit
Darstellungen archimedischer Kšrper
New mathematical hypotheses are postulated concerning
the truncated rhombohedron in DŸrerÕs engraving
MelencoliaáI 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¡ 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 NŸrnberg-Codex of
DŸrerÕs 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
NŸrnberg, as the next after DŸrer, rediscovered a
further archimedean solid; this rediscovering has been attributed to D.
Barbaro until now.
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