import itertools
import numpy as np
from scipy.spatial.transform import Rotation

out = []
for perm in itertools.permutations(range(3)):
    for signs in itertools.product([1, -1], repeat=3):
        M = np.zeros((3, 3))
        for i, p in enumerate(perm):
            M[i, p] = signs[i]
        if abs(np.linalg.det(M) - 1.0) < 1e-6:
            out.append(M)

print("всего разворотов: %d" % len(out))
for idx in (22, 18, 19, 15):
    M = out[idx]
    R = Rotation.from_matrix(M)
    rv = R.as_rotvec()
    ang = float(np.linalg.norm(rv))
    ax = np.round(rv / ang, 3) if ang > 1e-9 else np.zeros(3)
    print("")
    print("#%d" % idx)
    print(M.astype(int))
    print("   ось %s  угол %.1f градусов" % (ax, np.degrees(ang)))
    print("   кватернион xyzw %s" % np.round(R.as_quat(), 4))