Geometry Project of the Month
September 1998:
Building a Mobile

Here is the mysterious shape:

Because this shape has all right angles, it can be easily expressed by its coordinates in 3-D space. (In case you don't know, a point 3-D space is expressed by its X, Y, and Z coordinates, the former two being just like normal graphing, with the Z being the third dimension)

In X, Y, Z coordinates, it is: (0,0,1), (0,-1,1), (0,-1,0), (1,-1,0), (1,0,0), (1,0,-1), (0,0,-1), (0,1,-1), (0,1,0), (-1,1,0), (-1,0,0), (-1,0,1).

I figured out what it was by adding 3-dimensionality to the picture in my mind while constructing it with my Tinkertoys®:

Because I have described it in terms of coordinates, any view of it can be described by what coordinates to look from. In this case I'm using 5's, but you can look from any distance.
Here are the interesting views I found some of, and where to look from:

Star, from 5,5,5:

Rectangle, from 5,5,0:

Squares, from 5,0,0:

S shape, from 5,-5,0:

Diamond thing, from -10,-10,10: (needs to be farther away than others to look good because of perspective)

Anything, from anywhere:

I made the 3-D pictures with a ray-tracer program (one which makes 3-D scenes). Once I had figured out how to make the shape, I figured out the coordinates of each point, and put them into the ray-tracer. Part of the file, which defined the cylinders comprising the rods of the shape, looked like this:

cylinder 0.125   0  0  1   0 -1  1
cylinder 0.125   0 -1  1   0 -1  0
cylinder 0.125   0 -1  0  -1 -1  0
cylinder 0.125  -1 -1  0  -1  0  0
cylinder 0.125  -1  0  0  -1  0 -1
cylinder 0.125  -1  0 -1   0  0 -1
cylinder 0.125   0  0 -1   0  1 -1
cylinder 0.125   0  1 -1   0  1  0
cylinder 0.125   0  1  0   1  1  0
cylinder 0.125   1  1  0   1  0  0
cylinder 0.125   1  0  0   1  0  1
cylinder 0.125   1  0  1   0  0  1