Dürer's polyhedron: 5 theories that explain Melencolia's crazy cube

December 4, 2014 12:03 AM

Dürer's polyhedron: 5 theories that explain Melencolia's crazy cube

The distinctive three-dimensional shape in Albrecht Dürer’s 1514 engraving Melencolia I has been the subject of innumerous analyses and still no one is sure what it is or what it means. On the occasion of its 500th birthday, mathematician Günter M Ziegler looks again at art history’s most infamous truncated triangular trapezohedron

posted by ob1quixote (23 comments total)

The angel is just upset because bespoke die that was the centerpiece of its innovative RPG design is not working out at all.
posted by GenjiandProust at 12:31 AM on December 4, 2014 [18 favorites]

ob1quixote: "still no one is sure what it is or what it means."

I assume he was trying to imply the pentagon version of a platonic solid. Yea it isn't perfect, but you try drawing impossible mathematical objects.
posted by pwnguin at 12:46 AM on December 4, 2014

It seems to have a mark of some kind on it.

I imagine it is to be interpreted in the overall context of imaginative melancholia.

However, at the moment my tentative conclusion is that it's an Aztec Death Cube.
posted by Segundus at 1:33 AM on December 4, 2014 [7 favorites]

Ishizu Hideko (2009) has argued that Dürer has designed the proportion of his polyhedron to encode a solution to the classical Greek “Delian problem” to double the volume of a cube – for which one would need an expansion factor that is the cube root of 2. We now know (since the 19th century) that this problem cannot be solved exactly with compass and ruler alone – but there are very good approximate solutions, one of them due to Dürer in his Geometry book from 1525. But is this really encoded in the Melencolia polyhedron? It doesn’t convince me.

You have this theory, supported by Dürer actually creating a solution to that particular problem in a book he wrote, but you discard it because "it doesn't convince me", and then go on to theories about Freemasons and "Freudian symbolism"? Yeah, ok.
posted by Joakim Ziegler at 2:09 AM on December 4, 2014 [18 favorites]

I assume he was trying to imply the pentagon version of a platonic solid. Yea it isn't perfect, but you try drawing impossible mathematical objects.

OK.
posted by Wolfdog at 3:47 AM on December 4, 2014 [2 favorites]

MathWorld: Dürer's Solid.
posted by stebulus at 4:01 AM on December 4, 2014 [3 favorites]

Well, it's Masonic all right, but if I told you more I'd have to kill you.
posted by Curious Artificer at 4:01 AM on December 4, 2014

I think he just got really bummed out one day and decided to invent some impossible polyhedra. Like everybody doesn't have some days like that, right?
posted by newdaddy at 4:42 AM on December 4, 2014 [5 favorites]

Figured it out.
posted by condour75 at 5:26 AM on December 4, 2014 [9 favorites]

You have this theory, supported by Dürer actually creating a solution to that particular problem in a book he wrote, but you discard it because "it doesn't convince me", and then go on to theories about Freemasons and "Freudian symbolism"? Yeah, ok.

But... but... not trying to explain everything in terms of Freemasons and Freudian symbolism makes the world immeasurably poorer. I do this with my breakfast most mornings, and it's really fun. Of course, it's easier, since I eat my toast wearing trousers with only one leg while standing on a cube, but you can try it, too!
posted by GenjiandProust at 5:47 AM on December 4, 2014

I think it's a broken basalt formation which unfortunately doesn't exactly put the Masonic thing to rest. It even has a smudgey lichen spot on it.
posted by fiercekitten at 7:45 AM on December 4, 2014 [1 favorite]

Segundus: "However, at the moment my tentative conclusion is that it's an Aztec Death Cube."

I'm gonna need some audio with the beating of a horde of horses and such.

I suppose Death Cube K is about the closest I'll get. But that's nowhere near as scary as Aztec Death Cube.

Which is nowhere near as scary as the Death Cube known as the Pontiac Aztek
posted by symbioid at 9:17 AM on December 4, 2014

condour75: Figured it out.

Needs a Batman mask to complete the joke.
posted by IAmBroom at 9:41 AM on December 4, 2014 [1 favorite]

GenjiandProust: Of course, it's easier, since I eat my toast wearing trousers with only one leg while standing on a cube, but you can try it, too!

Your mudder zee cube... tell me more about her...
posted by IAmBroom at 9:42 AM on December 4, 2014 [1 favorite]

Wolfdog: OK.

Well, I was meaning a five sided polygon. But reviewing the article, the Delian problem is probably the most correct explanation.
posted by pwnguin at 10:20 AM on December 4, 2014

Well, I was meaning a five sided polygon.

OK.
posted by Wolfdog at 10:36 AM on December 4, 2014 [1 favorite]

OK, Wolfdog. Now do a five-sided polyhedron.
posted by Anticipation Of A New Lover's Arrival, The at 12:12 PM on December 4, 2014

OK, Wolfdog. Now do a five-sided polyhedron.

OK.
posted by Wolfdog at 12:15 PM on December 4, 2014 [1 favorite]

Now do a duck, a rabbit, and a man wearing a hat.
posted by IAmBroom at 2:06 PM on December 4, 2014 [2 favorites]

It's like "if you give a mouse a polyhedron" or something, good grief.
posted by Wolfdog at 2:48 PM on December 4, 2014 [3 favorites]

I fail at life so hard. I meant polyhedron, but it was like... early or something. Like 10am or something ridiculous.
posted by pwnguin at 5:09 PM on December 4, 2014 [4 favorites]

GenjiandProust: "But... but... not trying to explain everything in terms of Freemasons and Freudian symbolism makes the world immeasurably poorer. I do this with my breakfast most mornings, and it's really fun."

He could still try, and just arrive at the most reasonable explanation at the end.
posted by Joakim Ziegler at 7:09 PM on December 4, 2014 [1 favorite]

GenjiandProust: "But... but... not trying to explain everything in terms of Freemasons and Freudian symbolism makes the world immeasurably poorer."

By the way, if you're into that kind of thing, you should really consider a career in film studies.
posted by Joakim Ziegler at 2:53 AM on December 5, 2014 [1 favorite]