I
did not have a logical framework for making decisions, or knowing what the
result would be. I was aware that the 12 pentagons in an icosahedron breakdown
are somehow crucial to getting a smooth curve, and also that the lengths of
struts get longer toward the centers of the spherical triangles of the
icosahedron. In this model,
everything was played by ear, except for constant radii for the inner and outer
frames.
At
a certain point, I found that there were four struts connected to a hub, and a
resulting angle which was clearly less than 180 degrees.
So at that point it seemed advisable to make this a pentagonal hub, and
attach only one additional strut, to make a 5strut pentagon hub, rather than
two, which would give a 6strut, hexagon hub.
It
is hard to explain the criteria for choosing where to place hubs, and so I began
thinking of it as ¡°spider math¡± Every
once in a while it seemed appropriate to have a pentagon. At one point, I found
that I had a hub with 5 struts attached, and a very obtuse angle remaining, and
so instead of adding a single strut to make a hexagonal vertex,
I added two more hubs, making
a heptagon, wondering if this would create major problems elsewhere.
It seemed not to matter, except that the decision to create heptagons
seemed to lead to the need for more pentagons in the vicinity.
The
system of folded connectors shown elsewhere on this web site makes it possible
to add or subtract connectors to any hub.
Some
questions come to mind.
The
model seems ¡°quite strong¡±. How
strong? Would this approach make any sense for a fullscale structure? Could it
possibly be ¡°engineered¡±?
Why
consider using the spidermath approach rather than going with
mathematicallyderived chord factors?

Is there a covering method which would be adaptable to the irregular polyhedra
of the outer frame?
