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Your Da Vincis, your Michaelangelos, your Archimedii, they'd do the same thing if they had TiVo - Blather, Rinse, Repeat
May 22nd, 2006
10:51 pm


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Your Da Vincis, your Michaelangelos, your Archimedii, they'd do the same thing if they had TiVo
So, I was watching 24, and thinking about Geometric Sculpture, the kind made by George W. Hart, and thinking about 3d printing, and how it's a neat technique, but a very expensive one. Indeed, the site I recently linked to has comments to that effect - "Think of 3D printing as the last resort when you've dreamed up something that is flat-out impossible to make by conventional methods".

Which kind of took the wind out of my sails. I like technology, I like playing around with new stuff. I want to print out a thing that's never existed before into cornstarch, plaster, ABS plastic, or - hey, why not? - bronze. But Quicken has me on a short chain, so I can't really justify ordering a print run on a professional fabrication device just for my own amusement.

So, I was noodling with the idea of weaving and symmetry and the next thing you know, I ended up with a hand-woven icosahedron (20 sided die, for all you half-elf fighter/clerics out there). Made from a single sheet of 8 1/2" x 11" card stock (with some left over), this little thing holds itself together with no glue, tape, or telekinetic beams.

Just a little something I had fun with.

(2 comments | Leave a comment)

[User Picture]
Date:May 23rd, 2006 02:32 pm (UTC)
Wow! Are you going to publish how you did that?
[User Picture]
Date:May 23rd, 2006 03:08 pm (UTC)
I might make a pattern that you can cut out and assemble your own.

Here's a quick version:

All dimensions are in units that fit on a piece of letter paper. Feel free to scale to suit your own project.

  1. Cut 12 strips 11" x 1/2".
  2. For each strip:

    1. cut 1/4" notches 1/2" from each end, so that you can connect the ends of the strip and form a 10" loop.
    2. Draw lines across the strip at 1.5", 3.5", 5.5", 7.5", and 9.5" - these will be where the corners end up.
    3. For each line:

      1. Call the line you start with "h"
      2. Call the point where "h" meets the right hand side of the strip "p"
      3. Draw the two lines across the strip that intersect "p" and form a 60 degree angle with "h". These should look like an arrow or a crow's foot when you're done.
      4. Fold the strip along these new lines. I used a "valley" fold, which means that the pencil marks are on the inside or concave side of the fold. This hides my work as much as possible.

    4. Interlock the notched ends to form five-sided rings. You'll need to take them apart to weave them, below, but it's satisfying, and perhaps structurally beneficial, to have them in their final shapes at this point so you can see how they will ultimately lie.

  3. Start weaving the strips together, using paperclips as temporary structural supports. At each vertex, five strips meet, and on each face of that vertex, three strips overlap. If you hold the face with the vertex down (to match the first picture), you'll see three strips, (I) one going up and to the left, (II) one going horizontally, and (III) one going up and to the right. I used the rule that I wove over II, which wove over III. I expect that other rules would also work, but this one yielded good results. (I haven't tried other rules yet - I wonder if they don't support the structure as well, or if they end up looking any different. Maybe the next time I'm on the couch, I'll investigate.)
  4. Don't worry about getting the weave 100% correct at each juncture as you begin; by not using any adhesives, you've got the luxury of pulling pieces back out and reinserting them if they were in the wrong place. My early tests used tape, and that served to lock in mistakes I made. By the time you have about half your strips woven into place, the model will have enough integrity that your loops won't be flopping around. This is about the time I started ensuring that my weave rule was correct at each vertex.
  5. Towards the end, the weaving gets tricky. I used the pointy end of a compass to poke strips through the narrow openings at the end. Maybe a needlenose pliers would have worked as well or better.

I appreciate that some people will find these steps awfully sketchy in places, and if/when I create a pattern, I'll have pictures and diagrams that will clarify some steps. If you run ahead of me and try it yourself, let me know what your experiences are like.
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