I first became interested in solid geometry about twenty years ago when
I was looking after my daughter who was about thirteen at the time.
We were watching the Discovery Channel, and there was a scientist holding
up a model of a truncated icosahedron (also called a Buckminsterfullerine or Buckey ball).
He was flipping it around from face to face, letting us see the symmetry of it.
It hardly looked 'solid' though. It was just the outward shape of the thing showing
the faces, the corners, and the edges, but it was empty inside.
Like Buckminster Fuller I became interested in, and fixated on the spherical shapes,
and especially the truncated icosahedron (Bucky ball) which has the outward shape of a soccerball.
These can be joined together at their pentoganal faces to form a three-dimensional
matrix (or tessellation?) which fills all of space. The spaces in between them
have the shape of truncated tetrahedra which I call Bucky blocks.
If you were to construct the same matrix using truncated tetrahedra joined together
at their triangular faces, the spaces in between would be truncated icosahedra (Bucky balls).
The Bucky blocks and Bucky balls 'interface absolutely'.
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A dual project aspect:
"What good are they?" she asked as she gazed into my truncated tetrahedra expanded icosahedron.
Instead of feeling hurt, I blocked my emotions and thought objectively about what she said.
What good are they?... The answer came to me right away:
Space Frames!
They are used in the building industry. They can be used in building the same way that HTML
is used in web design: to provide a framework upon which work can be done to embellish and to
make more utilizable, functional, and aesthetically pleasing the systems being established.