|Fig. 901.03 Basic Right Triangle of Geodesic Sphere:
Shown here is the basic data for the 31 great circles
of the spherical icosahedron, which is the basis for
all geodesic dome calculations. The basic right
triangle as the lowest common denominator of a sphere's
surface includes all the data for the entire
sphere. It is precisely 1/120th of the sphere's surface
and is shown as shaded on the 31-great-circle-
sphere (A). An enlarged view of the same triangle is
shown (B) with all of the basic data denoted. There
are three different external edges and three different
internal edges for a total of six different edges.
There are six different internal angles other than 60º
or 90º. Note that all data given is spherical data,
edges are given as central angles and face angles are
for spherical triangles. No chord factors are shown.
Those not already indicated elsewhere are given by the
equation 2 sin(theta/2), where theta is the central angle.
Solid lines denote the set of 15 great circles. Dashed
lines denote the set of 10 great circles. Dotted lines
denote the set of 6 great circles.
Copyright © 1997 Estate of R. Buckminster Fuller