How do I determine the Tait-Bryan angles (yaw, pitch, and roll) of polyhedron faces to its center?

How do I determine the Tait-Bryan angles (yaw, pitch, and roll) of
polyhedron faces to its center?

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.