I Discover Polyhedra
 In
the early 1970's I was back from Vietnam and searching for my place in
the world. Things which had seemed so certain before the war were no
longer so. I returned to Penn State as a graduate student to sort things
out and to get an advanced degree at Uncle Sam's expense. Mostly I
worked hard, but there came those times when I was ready for something
completely different.
One day when I was poking around at the local hippy news stand, I found
a strange counter-culture newspaper called The Dome Cookbook. Here the
authors explained why it was better to live in a geodesic dome than in a
traditional house. Pictures of dome communities out west were
accompanied by articles critical of local building codes which preferred
structures with vertical walls. When I came to the step-by-step
instructions for building a dome house, I laughed out loud and bought
the paper. Back at my apartment I read how it was done. A dome house is
shaped roughly like half of a very large ping-pong ball. The framework
of the structure is made from wooden triangles. The article said that
this framework was very similar to half of an icosahedron. Once you have
the framework you go to a junk yard and cut the roofs off of a dozen
cars. These are then used to cover the wooden skeleton of the dome.
I was amused and intrigued ---- what a strange idea. I decided to build
a little cardboard model of a dome house just to see what it would look
like. To do this I needed to find out something about icosahedrons, so I
went to the campus library in search of information on the subject. What
I found there was knowledge, truth and an enduring pastime.
What I found that day, tucked away in its proper place in a low
ceilinged, dusty and dimly lit room filled with obscure texts on
mathematics, was a book called Mathematical Models. Sure enough, here
was information on how to build an icosahedron, but that only took a
single page! Why limit myself to a dome when here were instructions for
creating dozens of polyhedron models ---- everything from the
tetrahedron and the cube to the wondrous "great stellated
triacontahedron". I was fascinated by the perfect 3D symmetry of all
these models, as well as by their tongue-twisting names. I HAD to make
some of them; I ended up making more than twenty.
Drawing the patterns of pieces on computer cards and using white glue
and scotch tape, I assembled my first model ---- a "great icosahedron."
This was truly great! The assembly process was fascinating and the truth
inherent in the models was comforting at that turbulent time in my life.
Imagine an alien being named Klang who lives on a planet in a far away
part of the universe. Klang teaches mathematics in a small education
dome. The dome is made out of two-by-fours and car tops. Klang is
certain to know about the same exact polyhedra that I do. For over two
thousand years men have known of the basic polyhedra, and these will not
change in another ten thousand years. To know about polyhedra is to know
one thing at least that is true for ever and for always. I like that.
I built cubes and dodecahedrons, icosahedrons and snub cubes. I built
models out of cardboard, models out of wood and models out of glass. I
still build them occasionally even after 20 years, and it is always the
same. Drawing the parts to cut out is tedious, but assembling the
finished model is an interesting adventure in craftsmanship. I longed
for a computer program to print the parts for me, but back then all I
had access to were slow typewriter-like terminals connected to a
ponderous IBM mainframe. My little "parts printing" program would just
have to wait. And wait and wait.
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Books:
Mathematical Models, H. M. Cundy and A. P. Rollett, 2nd
ed.
Oxford: Oxford University Press, 1961
Polyhedron Models, Magnus J. Wenninger, New York
Cambridge University Press, 1971
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