While its nominal subject is melancholy, and while its aesthetic is crisp and clean, the true meaning of German Renaissance artist Albrecht Dürer’s famed print Melencolia I (1514) is anything but clear. It is one of his three “Master Engravings,” including Knight, Death and the Devil (1513) and Saint Jerome in His Study (1514), which are held to be among his greatest prints. 

Debate has continued for five centuries as to the artist’s true intention with the work, including with the title itself, since the significance of melancholy was up for debate in the Renaissance. The image is chock full of objects that may serve as symbols—a balance, an hourglass, a sphere, and calipers, to name just a few—which gives those who aim to decode it plenty of material to work with. While it has been interpreted to treat themes including alchemy and astronomy, it may also be a spiritual self-portrait, depicting the melancholy of the creative artist.

One object that has come in for extensive analysis is the truncated polyhedron that occupies the middle ground on the left side of the print. German mathematician Günter M. Ziegler has pointed out five theories (one for each century since the print was made!) that researchers have put forward as to the meaning of the polyhedron, some of which he finds more convincing than others but all of which deserve their moment in the sun.

1. Crystal

Some speculate that the object could represent a crystal, and in fact “there is a lively interplay between polyhedra and crystallography,” Ziegler writes. But alas, it was only in the 17th century that mathematical descriptions of crystals were developed, so this seems like a no-go, he opines.

2. Sphere

It is possible that the polyhedron’s vertices would all coincide with points on a sphere, and in fact there are drawings in a Dürer sketchbook that suggest this possibility. What’s more, the vertices of tetrahedrons, cubes, octahedrons, dodecahedrons, and icosahedrons—what are known as the platonic solids—all land on a sphere. 

3. Cube

The Delian problem sets forth a challenge: given the edge of a cube, one must construct the edge of a second cube with a volume double that of the first. Could Dürer have contained a solution to this problem in his polyhedron? Ziegler is unconvinced, and he’s a mathematician. We’re just art writers. 

4. Masonry

Things get a little more complicated here. Retired German psychiatrist Ernst Theodor Mayer points out that the vertices of the polyhedron, extended down to the ground, coincide with a star of David. Meanwhile, projected sideways, they would align with a magic square that hangs on the structure behind the winged figure, in which all rows and columns add up to 34. What exactly this would mean isn’t totally clear, though Ziegler points out that the freemasons hold Dürer as a hero. 

5. Freud

Finally, Ziegler points to a theory put forth by American mathematician-artist George Hart, that gets psychological. “One might speculate,” Hart writes, “that the cube represents masculinity and truncating one in an upright position may have some Freudian symbolism.” Sure, Freud wouldn’t be born for another 342 years, but there’s no reason his theories couldn’t explain Dürer’s psychology.

To see images illustrating these theories, see Ziegler’s article on the subject, dating from the print’s 500th anniversary.