One dihedral angle is 15°, and the others are right.
Uses the construction of J-P Sydler (*Sur l'équivalence des polyèdres à dièdres rationnels*, Elemente der Mathematik 8, 1953), along with my [decahedron](https://sketchfab.com/3d-models/decahedron-e7b22b7e08084351acf1987243f045ab) to square off the resulting 45° edges.