To create a geodesic dome .
. .
. . . each of the basic triangles in a regular geometric
solid is broken down into smaller segments.
Here is a typical breakdown of an icosahedral dome,
with a berakdown frequency of 4. That means each side of the triangle
is broken up into 4 separate segments. Each of these segments
will be a strut, connected at each
end to a vertex. The Breakdown Triangle
Report provides details about which struts and verticies are needed
to form a broken-down triangle that is part of the dome. The actual
breakdown triangle, when built, does not lie flat. Rather, it
takes the shape of the dome quite naturally because of the different
sizes of the struts:
