
The Spiegel has an interesting story on a polyhedron dran by Albrecht Duerer, who created in 1614
a chalcography engraving called "Melencolia I".
There article mentions a few speculations which
come with interpretations about the polyhedron in that picture. One gets this polyhedron
by taking a cube, stretching it along one side and cutting away two corners.
The Mathematician Friedrich Hirzebruch has compared it with the crystal form of "Calcit".
Ishizu Hideko tried to show that Duerer has hidden the "bisection of the cube"
into the engraving. Ernst Theodor Mayer, psychiatrist figured out that if one projects the
polyhedron onto a plane, one gets the David stars and the corners project
onto the grid points of the 4 x 4 magic square. Some claim that Duerer was a
freemason. There also Freudian explanations:
if a polyhedron has more vertices than faces, it is called "male" if it has more faces then
vertices, it is female. In this interpretation, the cube is male and the
octahedron is female. The Duerer polyhedron has f=8 faces and v=12 vertices and
e=18 edges leading to the formula ve+f=2 which holds for all convex polyhedra.
The Duerer polyhedron is female, having been obtained from the male cube by cutting
some corners.
A castrated cube ... ?
It would certainly be a reason to be melancholic, but
its probably a bit farfetched and indeed, this association
can not be found in the Spiegel article. Some figures which appear in the Spiegel article are by
Jan Schneider .
