I'm modeling a pentagonal hexecontrahedron by placing faces and then rotating them.
I've determined the center of each face by using the Cartesian coordinates of the vertices of its dual polyhedron (a snub dodecahedron). Now I need to determine the rotation of these faces in terms of yaw, pitch, and roll ($-\pi..\pi$ radians). The pentagon is irregular, so all three are important.
This question probably has an obvious answer, but it has been 30 years since I've dealt with vectors and matrices. (My searches seem to all result in discussions of flying airplanes.)
This recently posted question may be relevant, although it mentions only pitch and yaw. I prefer this type of geometric solution.