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This is a woodworking project that was inspired by the cover of the excellent book Gödel, Escher, Bach.  The idea is to make a shape which is the intersection of three block letters, such that its profile is a different letter from each of three axes.

I've done this twice now, and to make a proper one you may need to as well. I'll explain why in a minute, but if you'd like to try your hand you'll need:
  • Wood (I've made little ones out of packing styrofoam and a pocket knife as well, though)
  • A bandsaw
  • Sandpaper
  • Acrylic paint/sealer (optional)
Depending on which letters you want to make, you may also need:
  • A drill press
  • A coping saw

Step 1: Cut a Cube

You'll want to start with a cubic blank of wood. If you don't have one, you can easily make one with any cutting power tool and a stopper block. Say you want to cut a 2" cube. Set up a piece of wood on your machine so that 2" of it will be chopped off, and then clamp something up against it in that position. Make the cut, rotate the resulting piece and cut it again. Once more, and you'll have cut the wood to exactly the same length along all three axes. A cube!

Step 2: Imagine All the Letters...

Intersecting for one shape. Yeah, that was a poorly executed Beatles reference.

This step is actually the most important, but also probably the most difficult. All you need to do is draw your initials on each side of the cube, and imagine what shape will result when you cut them out. Some initials will cause problems in certain configurations. I've drawn a shoddy diagram in mspaint to try to help you visualize this.

Imagine that, like me, your first initial is a 'G'. You'll need one profile to have that shape, so you'll begin with a block letter 'G' that's as thick as your cube. Your final product must be contained within this form, or else your profile won't look like a 'G'! In order to form the other letters, you just need to remove material. You can remove as much as you want, as long as there is some wood at all points along the 'G' shape. 

In the diagram, I've shown two possible ways to create an 'I' profile from the front of the cube. The blue parts are the parts that need to be removed in order to form the 'I' in each case. On the left you can see that the shape is too narrow, and there will be no wood to create the 'G' on the sides. Even worse, the cube is now in three separate parts! On the right, you can see a successful design. The caps on the top and bottom of the 'I' provide enough material to keep all parts of the 'G' in place. Note however that the top and bottom of the resulting design are now only held together at those three places where the middle of the 'I' hits the 'G'.

Basically, what you'll need to do is ensure that each letter spans the full face of the cube from top to bottom and left to right. As long as there is some material at every point along these axes, the other shapes should be possible to produce. A more complex consideration is structural stability, as I mentioned above. The first time I tried this in wood, my initials came together in such a way that only a very thin piece of wood was left connecting two relatively massive parts of the design. This bit snapped in short order, and I had to glue it back together. You can see the bit of tape in the photo holding it together. The second time around, I rearranged the letters so that this would not occur and the result was much stronger.

Step 3: Cut Them Out!

Once you've drawn up all of your letters, pick one to start with and cut it out on the bandsaw. You may need to use a drill press or coping saw to form loops or tight bits of the letter. Think about which order will be easiest - I cut out the 'R' first because I didn't want to be drilling through the cube later when it might be more fragile.

After this shape is cut out, take stock of your letters again. You may have cut off some of the surfaces you had drawn on, so re-draw those bits of your template. Pick a second letter, and simply cut it out again while ignoring the first shape. Same for the third.

Step 4: Touch Up, Sand

Once you've cut all three shapes, you can check your profiles. Just hold the cube up to a window or something and see if each letter is visible. You might have to make some adjustments if any of your cuts weren't perfectly perpendicular. Use some sandpaper to round any corners you want rounded, and smooth off the tooth marks from the bandsaw. You can wrap some sandpaper around a pencil or something to get at those tough inside edges. I actually held a very thin strip of sandpaper tight along my coping saw's blade and used that to gently smooth the inside of the cut in the bottom of the 'G'.

Step 5: Add Color

I think adding color really improves the impact of these things. It guides the viewer to find each letter more easily while simultaneously highlighting the interesting ways the faces are used to make up each one.

The first stage is to paint all of the visible parts that make up each letter's profile. You'll have some edges left over after that which are not visible from any side (for example, all of the backs of the letters). These you can paint as you wish, I tried to continue the colors along perpendicular edges so that each letter kept its proper color from as many slight angles as possible. You can see this in the first picture, where part of the back of the 'G' is painted blue to keep the 'R' looking blue even if the cube is slightly rotated .

Step 6: Enjoy! (More Pictures)

I just wanted to include some photos showing of both versions together. You can get an idea of how the different way the letters were combined lead to to different shapes with particular structural stabilities.

As always, I'd love to see photos of your block! And by the way, for those wondering... my middle name is Jean. I'm half-Swiss =P
Great job! I've had this on my to-do list for some time (I read most of G-E-B and it blew my mind).
Soo Cool!
I want to try that
Oh this is pretty neat!
I need to make this
Wow, super cool project! It reminds me of the Playstation symbol.
I've seen this done with 3d software and printing, but it's cool to see it done by eye and hand.

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