Breakdown Method

There are two different ways to break down the basic triangle on a regular polyhedron (e.g., on an octahedron or an icosahedron) in the process of turning it into a geodesic dome. Method 1 breaks that triangle down using equal geometric angles. Method 2 breaks the same triangle down using equal lengths. Ninety nine percent of the time, the difference between these two methods is miniscule, and you needn't bother yourself with it at all.

This picture illustrates the two breakdown methods superimposed on one another to show the slight differences. Method 1 is pictured in black, and Method 2 is pictured in red.