Model Maker
 When
I first began making polyhedra, I built my models out of colored file
folders. After selecting the model that I wanted to make from
Mathematical Models, I would draw the required parts on a large index
card, and then use a needle to prick through this master copy onto the
colored file folder beneath. Once I had the required number of
duplicates, I connected the prick marks using a straight edge and a
pencil, cut out the parts and assembled the model. I soon had about a
dozen such models, and was beginning to think myself pretty good at
building them, when I discovered a book called Polyhedron Models written
by Magnus J. Wenninger. In 1959, Wenninger became interested in building
polyhedra. Over the next few years, he built all of those shown in
Mathematical Models, but he did not stop there. By collecting books on
polyhedra and by doing a great deal of exploration on his own, Wenninger
eventually built a collection of well over 100 models that he displayed
on the back wall of his mathematics classroom. His book, Polyhedron
Models, contains photographs of 119 of these ---- everything from a
tetrahedron to a small inverted retrosnub icosicosidodecahedron, which
took over 100 hours to construct. I was entranced by the beauty of
Wenninger's work, but as I set about building some of his simpler
models, I knew that I would never have his monomania for the subject.
The best I could hope for was to be able to build models that looked as
good as his.
On a gusty Friday in June 1980, Pam and I sought refuge from the wind by
exploring the Science Museum in South Kensington, London. There we saw
the first locomotive, The Rocket, and Charles Babbage's Difference
Engine, an early attempt at a mechanical computer. As we turned away
from Babbage's creation, we saw a glass case filled with polyhedron
models ---- the first such models, other than my own, that I had ever
seen in the flesh. These were the work of one of the men who wrote
Mathematical Models, and this made me feel that I was looking at the
work of a friend. My friend could certainly build polyhedron models ----
they were colorful, very neatly done, and much, much more complicated
than anything I was ever likely to attempt. As I walked away, I found
myself dissatisfied that my own models were really just pale imitations
of the work of master model builders. What could I do to make my
polyhedron models distinctively mine?
Back home in Delaware, Pam and I tried a new idea ---- we built a great
dodecahedron out of window glass. We began by making a triangle of the
correct shape out of cardboard, then traced around this with a glass
marking pen. Guided by these lines, Pam then cut the required sixty
pieces of glass. To hold the pieces together, we used a plastic grouting
compound that was originally intended for caulking bathroom tiles and
tubs. This stuff started out very gooey, but after a time turned into a
sort of tough rubber. Assembling the model was a messy and slow process,
but when the excess rubber had been trimmed off with a razor blade, and
the glass had been polished inside and out, we had the beautiful model
that you see above. Here was a polyhedron model that was different and
distinctively ours!
In my next attempt at a distinctive model, I used a piece of glass from
the Crystal Palace to make a great dodecahedron out of photographs. The
piece of glass had a symmetric star pattern pressed into it. When you
placed pieces of colored paper behind it and held it up to the light,
various pleasingly symmetric color patterns emerged. I put my camera on
a tripod and took twelve pictures of each of five different color
patterns. I glued these sixty pictures to index cards, and then cut out
the parts that I would need to make a great dodecahedron. It took an
evening spent with scotch tape straps and Elmer's Glue to assembled the
pictures into a model. The finished polyhedron was unique and visually
interesting, but it took too much time and money to create.
For years I admired the polyhedra of M. C. Escher, which he decorated
with interlocking patterns of lizards, starfish, and other creatures. I
wanted to make my own decorated polyhedra, but could not puzzle out how
to make the patterns interlock. SymmeToy changed that. Now I have built
over a dozen decorated models, each distinctively mine, yet each with
the underlying truth and beauty of form that all polyhedra share. |
 
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