What's a Generating Triangle?
All the Platonic solids and almost all the Archimedean solids
can be generated by reflecting a triangle across each of its edges
over and over. The triangle used to make the polyhedra is called
the generating triangle.
For the Platonic and Archimedean solids the set of angles at the corners
of the triangle is either (90,60,36), (90,60,45) or (90,60,60).
In the images below, the shape on the left is a three-color "bent"
triangle with angles of (90,60,36). When reflected across its edges
over and over, it generates the polyhedron on the right.