diff --git a/python/tests/test_Orientation.py b/python/tests/test_Orientation.py
index bb8810c49..8dc526325 100644
--- a/python/tests/test_Orientation.py
+++ b/python/tests/test_Orientation.py
@@ -8,13 +8,8 @@ import damask
 from damask import Rotation
 from damask import Orientation
 from damask import Lattice
-   
-n = 1000
 
-@pytest.fixture
-def default():
-    """A set of n random rotations."""
-    return [Rotation.from_random() for r in range(n)]
+n = 1000
 
 @pytest.fixture
 def reference_dir(reference_dir_base):
@@ -28,10 +23,10 @@ class TestOrientation:
                                       {'label':'green','RGB':[0,1,0],'direction':[0,1,1]},
                                       {'label':'blue', 'RGB':[0,0,1],'direction':[1,1,1]}])
     @pytest.mark.parametrize('lattice',['fcc','bcc'])
-    def test_IPF_cubic(self,default,color,lattice):
+    def test_IPF_cubic(self,color,lattice):
         cube = damask.Orientation(damask.Rotation(),lattice)
         for direction in set(permutations(np.array(color['direction']))):
-            assert np.allclose(cube.IPFcolor(direction),np.array(color['RGB']))
+            assert np.allclose(cube.IPFcolor(np.array(direction)),np.array(color['RGB']))
 
     @pytest.mark.parametrize('lattice',Lattice.lattices)
     def test_IPF(self,lattice):
@@ -57,7 +52,7 @@ class TestOrientation:
         reference = os.path.join(reference_dir,'{}_{}.txt'.format(lattice,model))
         ori = Orientation(Rotation(),lattice)
         eu = np.array([o.rotation.asEulers(degrees=True) for o in ori.relatedOrientations(model)])
-        if update: 
+        if update:
             coords = np.array([(1,i+1) for i,x in enumerate(eu)])
             table = damask.Table(eu,{'Eulers':(3,)})
             table.add('pos',coords)
diff --git a/python/tests/test_Rotation.py b/python/tests/test_Rotation.py
index ffa1548d7..23ab03ff6 100644
--- a/python/tests/test_Rotation.py
+++ b/python/tests/test_Rotation.py
@@ -177,7 +177,7 @@ class TestRotation:
                                                  (Rotation.from_Rodrigues,  np.array([1,0,0,-1])),
                                                  (Rotation.from_Rodrigues,  np.array([1,1,0,1])),
                                                  (Rotation.from_homochoric, np.array([2,2,2]))  ])
-    def test_invalid(self,function,invalid):
+    def test_invalid_value(self,function,invalid):
         with pytest.raises(ValueError):
             function(invalid)
 
@@ -302,8 +302,42 @@ class TestRotation:
         assert np.all(np.take_along_axis(np.take_along_axis(a,f,-1),b,-1) == a)
 
 
-    @pytest.mark.parametrize('x',[np.random.rand(3),
-                                  np.random.rand(3,3)])
-    def test_rotation_identity(self,x):
+    @pytest.mark.parametrize('data',[np.random.rand(3),
+                                     np.random.rand(3,3),
+                                     np.random.rand(3,3,3,3)])
+    def test_rotate_identity(self,data):
         R = Rotation()
-        assert np.allclose(x,R*x)
+        assert np.allclose(data,R*data)
+
+    @pytest.mark.parametrize('data',[np.random.rand(3),
+                                     np.random.rand(3,3),
+                                     np.random.rand(3,3,3,3)])
+    def test_rotate_360deg(self,data):
+        phi_1 = np.random.random() * np.pi
+        phi_2 = 2*np.pi - phi_1
+        R_1 = Rotation.from_Eulers(np.array([phi_1,0.,0.]))
+        R_2 = Rotation.from_Eulers(np.array([0.,0.,phi_2]))
+        assert np.allclose(data,R_2*(R_1*data))
+
+    @pytest.mark.parametrize('data',[np.random.rand(3),
+                                     np.random.rand(3,3),
+                                     np.random.rand(3,3,3,3)])
+    def test_rotate_inverse(self,data):
+        R = Rotation.from_random()
+        assert np.allclose(data,R.inversed()*(R*data))
+
+    @pytest.mark.parametrize('data',[np.random.rand(4),
+                                     np.random.rand(3,2),
+                                     np.random.rand(3,2,3,3)])
+    def test_rotate_invalid_shape(self,data):
+        R = Rotation.from_random()
+        with pytest.raises(ValueError):
+            R*data
+
+    @pytest.mark.parametrize('data',['does_not_work',
+                                     (1,2),
+                                     5])
+    def test_rotate_invalid_type(self,data):
+        R = Rotation.from_random()
+        with pytest.raises(TypeError):
+            R*data