Dear Jayadev and IGL members.

I plan to conduct IGL research on an interesting "architectural" problem
proposed by Tony Robbin (artist, New York) during his visit last week.

For this purpose, however, participants must know/learn Python/OpenGL
and I will spend the first half of the term conducting seminars on these
skills for people who want to learn Python from a geometrical viewpoint.
(Almost all Python tutorials "out there" are non-visual, 2-dimensional,
and inanimate.) This could be of independent interest to some of you
in connection with other projects.

The problem we will work on can be summarized: While we all know that
architectural structures made up of triangular framing are stable
(geodesic domes, trusses, etc). But framings made up of parallelograms
generally are not. But some (quasicrystalline ones) can be "stabilized" by
a small number of triangulations of the faces (how small? least number?
theorems, anyone?).

Much of contemporary architecture depends not on rod-and-node (tensile)
framings, but on concrete slabs (compressile) fastened by "hinges". Compare
a (single) cube: its one-skeleton (edges+vertices) is unstable,
you can squash it. But its two-skeleton (faces), even if hinged, is stable
because three slabs abut at each vertex. It's dual, the octahedron, is
just the other way around. The triangular faces make its 1-skeleton stable,
but it's 2-skeleton is collapsible. There's geometry here!

We propose to generalize this to quasicrystalline structures in space.

George Francis