diff --git a/spatialmath/pose3d.py b/spatialmath/pose3d.py
index b8d8d5de..03641b92 100644
--- a/spatialmath/pose3d.py
+++ b/spatialmath/pose3d.py
@@ -769,7 +769,24 @@ def RotatedVector(cls, v1: ArrayLike3, v2: ArrayLike3, tol=20) -> Self:
         v = smb.cross(v1, v2)
         s = smb.norm(v)
         if abs(s) < tol * np.finfo(float).eps:
-            return cls(np.eye(3), check=False)
+            c = np.dot(v1, v2)
+            if c > 0:
+                # v1 and v2 already (anti)parallel in the same direction
+                return cls(np.eye(3), check=False)
+            # v1 and v2 point in opposite directions -- the formula below
+            # is singular here too (it divides by s**2), but unlike the
+            # c > 0 case the answer isn't identity: any 180 degree
+            # rotation about an axis perpendicular to v1 takes v1 to v2.
+            # Closed form for a 180 degree rotation about unit axis u:
+            # R = 2*u*u^T - I (Rodrigues at theta=pi, sin=0, cos=-1).
+            # Pick u by crossing v1 with whichever world axis it's least
+            # aligned with, so the cross product is never itself
+            # degenerate.
+            axis = np.zeros(3)
+            axis[np.argmin(np.abs(v1))] = 1.0
+            u = smb.unitvec(smb.cross(v1, axis))
+            R = 2 * np.outer(u, u) - np.eye(3)
+            return cls(R, check=False)
         else:
             c = np.dot(v1, v2)
             V = smb.skew(v)
diff --git a/tests/test_pose3d.py b/tests/test_pose3d.py
index cdb80fbd..7b0d2414 100755
--- a/tests/test_pose3d.py
+++ b/tests/test_pose3d.py
@@ -726,6 +726,19 @@ def test_rotatedvector(self):
         Re = SO3.RotatedVector(v1, v1)
         np.testing.assert_almost_equal(Re, np.eye(3))
 
+        # Antipodal case: v1 and v2 point in exactly opposite directions.
+        # The cross product used to find the rotation axis is zero here
+        # too, same as the parallel case above, but the correct answer is
+        # a 180 degree flip, not identity -- regression test for a bug
+        # where this silently returned identity instead.
+        for v1 in ([1, 0, 0], [0, 1, 0], [0, 0, 1], [1, 2, 3], [-3, 1, 2]):
+            v1 = unitvec(v1)
+            v2 = [-x for x in v1]
+            Re = SO3.RotatedVector(v1, v2)
+            np.testing.assert_almost_equal(np.asarray(Re * v1).flatten(), v2)
+            # must actually be a 180 degree rotation, not identity
+            assert not np.allclose(Re.A, np.eye(3))
+
         R = SO3()  # identity matrix case
 
         # Check log and exponential map