Dürer's polyhedron: theories that explain Melencolia's crazy cube

I have a friend who's an artist, and he loves putting random weird things or vague symbology that doesn't particularly mean anything it his pictures. People always assume it does mean something, but since it's so vague (and he never tells them what it "means") they can never nail down exactly what it is. He's always praised as a deep and thoughtful artist because of it, and I think it's directly responsible for much of his success.

Given that it is an engraving, it might also be a plan for sharpening a burin.

There are many kinds of burins -- for a general impression of what I am after, see http://www.google.com/patents/US7032586

I love suggestion #4 (the Freemasonry/magic square one) but I suspect that the simpler first explanation is on the right track. This quibble from the article:

"But did Dürer study crystals? A systematic mathematical description of crystals begins only in the 17th century, so this theory comes at least 100 years too late."

Is really not particularly convincing when we consider what a polymath and all around genius Dürer was, and how interested he was in fine observations of nature (cf "The Great Patch of Turf.")

Seems like a compositional counterweight to the perfectly smooth sphere below.

Has anyone tried re-mapping the textures from the sphere amd the object onto a flat surface?