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It seems like you all like making stuff
I recently had some fun with pencils and rubber bands. It seemed like the kind of thing people in this forum would enjoy seeing.
Edit: It seems that I am bad at embedding images, so here are some links instead:
http://i.min.us/icQEaE.JPG
http://i.min.us/icVcNk.JPG
These two are based on Conway Models
http://i.min.us/icUDnC.JPG
http://i.min.us/icQBS6.JPG
These two are just for fun
http://i.min.us/icVaFc.JPG
Here is a picture of all five with a ruler for scale
Edit: It seems that I am bad at embedding images, so here are some links instead:
http://i.min.us/icQEaE.JPG
http://i.min.us/icVcNk.JPG
These two are based on Conway Models
http://i.min.us/icUDnC.JPG
http://i.min.us/icQBS6.JPG
These two are just for fun
http://i.min.us/icVaFc.JPG
Here is a picture of all five with a ruler for scale
Comments
<img src="http://i.min.us/icQEaE.JPG" />Anyway, that's really cool. I wish I were good at making... anything...
I'm going to do this in two parts, making 4-axis things, and making 3-axis things. The 4-axes can be thought of as the major diagonals of a cube, if it helps your visualization.
So first things first: the materials.
If you want to make the simplest possible 4-axis model, you are going to need 24 pencils, and 8 rubber bands. I highly advise you to have a least two extra pencils though for "scaffolding".
The first thing you are going to do is take six of your pencils,make a 2x3 rectangle in your fist, and put a rubber band at each end. Don't make the rubber band so tight that you can't fit more pencils in - you will have to do so.
Time for the second axis. If you look at your 2x3 from the side of 3, you will see two rows between pencils. You are going to take two sets of three pencils, and put each set in one of those spaces, like so. Again, make sure to rubber band off both sides, though somewhat loosely if possible. When you are done with this step, it should look somewhat like this.
Now it is time for the third axis. If you look down onto the structure so far so that it looks like an 'X', (like the last link shows it), and look at the imaginary spaces between the pencils, you will see two holes that you can stick pencils into. Do so. Now, we are going to keep having 6 pencils to an axis, so put the additional four pencils in the angles of the 'X' and rubber band this axis so it stays in place. It should look something like this.
This next part will discuss how to add a fourth axis. If you would rather have a cube, you don't need to read it. Place the structure as it is shown in the previous link, so that it is standing on three axes. Now with one hand, push down onto the three axes which are sticking up. Notice that there are now seven hexagonal holes. We are going to ignore the center, and just put pencils in the six outer holes.
Now, for uniformity, we are going to make all of the awkward parallelogram shaped sides look like the attractive hexagonal one. Take two extra pencils, and make the parallelogram look like this. Use your rubber bands to hold the new pencils in place. Now remove the two extra pencils so it looks like the pretty side. Use these two pencils to beautify the next side, and then the next side.
Notice that the places where you can put pencils form a honeycomb like pattern. If you want, you can build out in this pattern. You can make triangles, hexagons, 6-pointed stars, etc. You also aren't required to make it symmetrical. I'll leave you with a closing challenge. Note that the completed model has a small hollow space. If you enlarge it, that hollow space grows accordingly. Can you put something inside of it? (the answer is yes, though I can't show you a picture because my girlfriend has that one)
Back to the making of a cube:
For this shape, you will need many more pencils and rubber bands. I used 6 to an edge, so in total 72 pencils and 24 rubber bands were used. If you want to save pencils, you could use only 4 to an edge, but pencils come in boxes of 72, so you might as well go for 6.
Follow the instructions so that you have a structure with three axes. Instead of keeping the intersection of your axes towards the centers of all of your pencils, move it to the edges, like so. You don't need to do so at the eraser end if you don't want, I just happened to choose to do so. Now, follow the adding method to keep adding edges that belong in a cube. Order is not important, though I'll show you how I did it because it was pretty easy.
First, I completed a face of the cube.
Then I built the pillars coming up from the cube (not pictured)
Then I started working on the top.
And then I finished the top.
Again, there is tons you can do beyond these simple instructions. One thing pictured in the original post is the edges of a 2x2x2 cube. Also, you can combine 3 and 4 axis structures if you are clever about it.
Final words:
Rubber bands wear out eventually. If you want it to last forever, replace them regularly, or use twine.
All materials are relatively cheap, and after a few tries, the instructions aren't very hard to follow. Give these as kick-ass geek gifts.