More Menger

Posted in Arcana on April 29, 2008

By Wizards of the Coast

Ever since we brought up Dave Guskin's Menger Sponge a couple of weeks ago, there has been a lot of interest in the concept. Well, "a lot" might be overstating it, but as far as topology is concerned, any amount of interest is good. Also, even a small amount of interest is isomorphic to a large amount, as long as both have the same amount of holes.

Topology jokes aside, people in the forums rushed to create their own sponges. Special credit goes to FolkenFanel42, KingPoo, and Ezra from New York for creating Level 2 Sponges:

FolkenFanel42's Level 2 Menger SpongeKingPoo's Level 2 Menger Sponge
Ezra's Level 2 Menger Sponge

Sadly, FolkenFanel42's sponge is no more, because it was used as a piñata. It's a good thing it was, in fact, filled with delicious candy!

Here at the office, Monty Ashley was idly making a Level One Menger Sponge (with the card backs facing out, and a cube of rares imprisoned in the middle), when he decided he was actually more interested in the Level Zero part. The cubes, he decided, could interlock to create almost anything. So why not build something besides a sponge?

Hence, a set of soma cubes built out of cubes built out of Magic cards:

Monty Ashley's Soma Cubes

Soma cubes are essentially a building block puzzle, which can be assembled to create a wide variety of shapes. Here are some of the shapes that have been visible on Monty's desk, including the inevitable 3X3X3 Cube, made from Soma Cubes, made from cubes, made from Magic cards:

The CrystalThe Cube
The KnotThe Dog

Note that the faces have all been "capped", with a card added on the outside to hide the unsightly flaps. This added to the stability of the shapes, and also made the final product much more handsome.

Next, Monty's thinking of trying to construct sculptures made of Menger Cubes. It seems like Mario would look good, since he's already pixelated. Of course, that will involve making cubes of specific colors to match each pixel...

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