X-Git-Url: https://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FTests%2FCube.hs;h=11159b5bc6f668a6e14f0976646c5e50398d1236;hb=f07f76b231a3df623aab8b6035ac6000ce2a5eb2;hp=1df642fea96b6fab5163913a96fe735a168fcbfb;hpb=a73ad12eaff8510ae18ffafdefc0ae928603d5a5;p=spline3.git

diff --git a/src/Tests/Cube.hs b/src/Tests/Cube.hs
index 1df642f..11159b5 100644
--- a/src/Tests/Cube.hs
+++ b/src/Tests/Cube.hs
@@ -5,9 +5,10 @@ import Test.QuickCheck
 
 import Comparisons
 import Cube
-import FunctionValues (FunctionValues(FunctionValues))
-import Tests.FunctionValues
-import Tetrahedron (v0, volume)
+import FunctionValues (FunctionValues)
+import Tests.FunctionValues ()
+import Tetrahedron (b0, b1, b2, b3, c,
+                    v0, v1, v2, v3, volume)
 
 instance Arbitrary Cube where
     arbitrary = do
@@ -28,10 +29,10 @@ instance Arbitrary Cube where
 --   (which comprise cubes of positive volume) must have positive volume
 --   as well.
 prop_all_volumes_positive :: Cube -> Bool
-prop_all_volumes_positive c =
+prop_all_volumes_positive cube =
     null nonpositive_volumes
     where
-      ts = tetrahedrons c
+      ts = tetrahedrons cube
       volumes = map volume ts
       nonpositive_volumes = filter (<= 0) volumes
 
@@ -39,174 +40,457 @@ prop_all_volumes_positive c =
 --   already know their volumes. There's 24 tetrahedra to a cube, so
 --   we'd expect the volume of each one to be (1/24)*h^3.
 prop_tetrahedron0_volumes_exact :: Cube -> Bool
-prop_tetrahedron0_volumes_exact c =
-    volume (tetrahedron0 c) ~= (1/24)*(delta^(3::Int))
+prop_tetrahedron0_volumes_exact cube =
+    volume (tetrahedron0 cube) ~= (1/24)*(delta^(3::Int))
     where
-      delta = h c
+      delta = h cube
 
 -- | In fact, since all of the tetrahedra are identical, we should
 --   already know their volumes. There's 24 tetrahedra to a cube, so
 --   we'd expect the volume of each one to be (1/24)*h^3.
 prop_tetrahedron1_volumes_exact :: Cube -> Bool
-prop_tetrahedron1_volumes_exact c =
-    volume (tetrahedron1 c) ~= (1/24)*(delta^(3::Int))
+prop_tetrahedron1_volumes_exact cube =
+    volume (tetrahedron1 cube) ~= (1/24)*(delta^(3::Int))
     where
-      delta = h c
+      delta = h cube
 
 -- | In fact, since all of the tetrahedra are identical, we should
 --   already know their volumes. There's 24 tetrahedra to a cube, so
 --   we'd expect the volume of each one to be (1/24)*h^3.
 prop_tetrahedron2_volumes_exact :: Cube -> Bool
-prop_tetrahedron2_volumes_exact c =
-    volume (tetrahedron2 c) ~= (1/24)*(delta^(3::Int))
+prop_tetrahedron2_volumes_exact cube =
+    volume (tetrahedron2 cube) ~= (1/24)*(delta^(3::Int))
     where
-      delta = h c
+      delta = h cube
 
 -- | In fact, since all of the tetrahedra are identical, we should
 --   already know their volumes. There's 24 tetrahedra to a cube, so
 --   we'd expect the volume of each one to be (1/24)*h^3.
 prop_tetrahedron3_volumes_exact :: Cube -> Bool
-prop_tetrahedron3_volumes_exact c =
-    volume (tetrahedron3 c) ~= (1/24)*(delta^(3::Int))
+prop_tetrahedron3_volumes_exact cube =
+    volume (tetrahedron3 cube) ~= (1/24)*(delta^(3::Int))
     where
-      delta = h c
+      delta = h cube
 
 -- | In fact, since all of the tetrahedra are identical, we should
 --   already know their volumes. There's 24 tetrahedra to a cube, so
 --   we'd expect the volume of each one to be (1/24)*h^3.
 prop_tetrahedron4_volumes_exact :: Cube -> Bool
-prop_tetrahedron4_volumes_exact c =
-    volume (tetrahedron4 c) ~= (1/24)*(delta^(3::Int))
+prop_tetrahedron4_volumes_exact cube =
+    volume (tetrahedron4 cube) ~= (1/24)*(delta^(3::Int))
     where
-      delta = h c
+      delta = h cube
 
 -- | In fact, since all of the tetrahedra are identical, we should
 --   already know their volumes. There's 24 tetrahedra to a cube, so
 --   we'd expect the volume of each one to be (1/24)*h^3.
 prop_tetrahedron5_volumes_exact :: Cube -> Bool
-prop_tetrahedron5_volumes_exact c =
-    volume (tetrahedron5 c) ~= (1/24)*(delta^(3::Int))
+prop_tetrahedron5_volumes_exact cube =
+    volume (tetrahedron5 cube) ~= (1/24)*(delta^(3::Int))
     where
-      delta = h c
+      delta = h cube
 
 -- | In fact, since all of the tetrahedra are identical, we should
 --   already know their volumes. There's 24 tetrahedra to a cube, so
 --   we'd expect the volume of each one to be (1/24)*h^3.
 prop_tetrahedron6_volumes_exact :: Cube -> Bool
-prop_tetrahedron6_volumes_exact c =
-    volume (tetrahedron6 c) ~= (1/24)*(delta^(3::Int))
+prop_tetrahedron6_volumes_exact cube =
+    volume (tetrahedron6 cube) ~= (1/24)*(delta^(3::Int))
     where
-      delta = h c
+      delta = h cube
 
 -- | In fact, since all of the tetrahedra are identical, we should
 --   already know their volumes. There's 24 tetrahedra to a cube, so
 --   we'd expect the volume of each one to be (1/24)*h^3.
 prop_tetrahedron7_volumes_exact :: Cube -> Bool
-prop_tetrahedron7_volumes_exact c =
-    volume (tetrahedron7 c) ~= (1/24)*(delta^(3::Int))
+prop_tetrahedron7_volumes_exact cube =
+    volume (tetrahedron7 cube) ~= (1/24)*(delta^(3::Int))
     where
-      delta = h c
+      delta = h cube
 
 -- | All tetrahedron should have their v0 located at the center of the cube.
 prop_v0_all_equal :: Cube -> Bool
-prop_v0_all_equal c = (v0 t0) == (v0 t1)
+prop_v0_all_equal cube = (v0 t0) == (v0 t1)
     where
-      t0 = head (tetrahedrons c) -- Doesn't matter which two we choose.
-      t1 = head $ tail (tetrahedrons c)
+      t0 = head (tetrahedrons cube) -- Doesn't matter which two we choose.
+      t1 = head $ tail (tetrahedrons cube)
 
 
 -- | This pretty much repeats the prop_all_volumes_positive property,
 --   but will let me know which tetrahedrons's vertices are disoriented.
 prop_tetrahedron0_volumes_positive :: Cube -> Bool
-prop_tetrahedron0_volumes_positive c =
-    volume (tetrahedron0 c) > 0
+prop_tetrahedron0_volumes_positive cube =
+    volume (tetrahedron0 cube) > 0
 
 -- | This pretty much repeats the prop_all_volumes_positive property,
 --   but will let me know which tetrahedrons's vertices are disoriented.
 prop_tetrahedron1_volumes_positive :: Cube -> Bool
-prop_tetrahedron1_volumes_positive c =
-    volume (tetrahedron1 c) > 0
+prop_tetrahedron1_volumes_positive cube =
+    volume (tetrahedron1 cube) > 0
 
 -- | This pretty much repeats the prop_all_volumes_positive property,
 --   but will let me know which tetrahedrons's vertices are disoriented.
 prop_tetrahedron2_volumes_positive :: Cube -> Bool
-prop_tetrahedron2_volumes_positive c =
-    volume (tetrahedron2 c) > 0
+prop_tetrahedron2_volumes_positive cube =
+    volume (tetrahedron2 cube) > 0
 
 -- | This pretty much repeats the prop_all_volumes_positive property,
 --   but will let me know which tetrahedrons's vertices are disoriented.
 prop_tetrahedron3_volumes_positive :: Cube -> Bool
-prop_tetrahedron3_volumes_positive c =
-    volume (tetrahedron3 c) > 0
+prop_tetrahedron3_volumes_positive cube =
+    volume (tetrahedron3 cube) > 0
 
 -- | This pretty much repeats the prop_all_volumes_positive property,
 --   but will let me know which tetrahedrons's vertices are disoriented.
 prop_tetrahedron4_volumes_positive :: Cube -> Bool
-prop_tetrahedron4_volumes_positive c =
-    volume (tetrahedron4 c) > 0
+prop_tetrahedron4_volumes_positive cube =
+    volume (tetrahedron4 cube) > 0
 
 -- | This pretty much repeats the prop_all_volumes_positive property,
 --   but will let me know which tetrahedrons's vertices are disoriented.
 prop_tetrahedron5_volumes_positive :: Cube -> Bool
-prop_tetrahedron5_volumes_positive c =
-    volume (tetrahedron5 c) > 0
+prop_tetrahedron5_volumes_positive cube =
+    volume (tetrahedron5 cube) > 0
 
 -- | This pretty much repeats the prop_all_volumes_positive property,
 --   but will let me know which tetrahedrons's vertices are disoriented.
 prop_tetrahedron6_volumes_positive :: Cube -> Bool
-prop_tetrahedron6_volumes_positive c =
-    volume (tetrahedron6 c) > 0
+prop_tetrahedron6_volumes_positive cube =
+    volume (tetrahedron6 cube) > 0
 
 -- | This pretty much repeats the prop_all_volumes_positive property,
 --   but will let me know which tetrahedrons's vertices are disoriented.
 prop_tetrahedron7_volumes_positive :: Cube -> Bool
-prop_tetrahedron7_volumes_positive c =
-    volume (tetrahedron7 c) > 0
+prop_tetrahedron7_volumes_positive cube =
+    volume (tetrahedron7 cube) > 0
 
 -- | This pretty much repeats the prop_all_volumes_positive property,
 --   but will let me know which tetrahedrons's vertices are disoriented.
 prop_tetrahedron8_volumes_positive :: Cube -> Bool
-prop_tetrahedron8_volumes_positive c =
-    volume (tetrahedron8 c) > 0
+prop_tetrahedron8_volumes_positive cube =
+    volume (tetrahedron8 cube) > 0
 
 -- | This pretty much repeats the prop_all_volumes_positive property,
 --   but will let me know which tetrahedrons's vertices are disoriented.
 prop_tetrahedron9_volumes_positive :: Cube -> Bool
-prop_tetrahedron9_volumes_positive c =
-    volume (tetrahedron9 c) > 0
+prop_tetrahedron9_volumes_positive cube =
+    volume (tetrahedron9 cube) > 0
 
 -- | This pretty much repeats the prop_all_volumes_positive property,
 --   but will let me know which tetrahedrons's vertices are disoriented.
 prop_tetrahedron10_volumes_positive :: Cube -> Bool
-prop_tetrahedron10_volumes_positive c =
-    volume (tetrahedron10 c) > 0
+prop_tetrahedron10_volumes_positive cube =
+    volume (tetrahedron10 cube) > 0
 
 -- | This pretty much repeats the prop_all_volumes_positive property,
 --   but will let me know which tetrahedrons's vertices are disoriented.
 prop_tetrahedron11_volumes_positive :: Cube -> Bool
-prop_tetrahedron11_volumes_positive c =
-    volume (tetrahedron11 c) > 0
+prop_tetrahedron11_volumes_positive cube =
+    volume (tetrahedron11 cube) > 0
 
 -- | This pretty much repeats the prop_all_volumes_positive property,
 --   but will let me know which tetrahedrons's vertices are disoriented.
 prop_tetrahedron12_volumes_positive :: Cube -> Bool
-prop_tetrahedron12_volumes_positive c =
-    volume (tetrahedron12 c) > 0
+prop_tetrahedron12_volumes_positive cube =
+    volume (tetrahedron12 cube) > 0
 
 -- | This pretty much repeats the prop_all_volumes_positive property,
 --   but will let me know which tetrahedrons's vertices are disoriented.
 prop_tetrahedron13_volumes_positive :: Cube -> Bool
-prop_tetrahedron13_volumes_positive c =
-    volume (tetrahedron13 c) > 0
+prop_tetrahedron13_volumes_positive cube =
+    volume (tetrahedron13 cube) > 0
 
 -- | This pretty much repeats the prop_all_volumes_positive property,
 --   but will let me know which tetrahedrons's vertices are disoriented.
 prop_tetrahedron14_volumes_positive :: Cube -> Bool
-prop_tetrahedron14_volumes_positive c =
-    volume (tetrahedron14 c) > 0
+prop_tetrahedron14_volumes_positive cube =
+    volume (tetrahedron14 cube) > 0
 
 -- | This pretty much repeats the prop_all_volumes_positive property,
 --   but will let me know which tetrahedrons's vertices are disoriented.
 prop_tetrahedron15_volumes_positive :: Cube -> Bool
-prop_tetrahedron15_volumes_positive c =
-    volume (tetrahedron15 c) > 0
+prop_tetrahedron15_volumes_positive cube =
+    volume (tetrahedron15 cube) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+--   but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron16_volumes_positive :: Cube -> Bool
+prop_tetrahedron16_volumes_positive cube =
+    volume (tetrahedron16 cube) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+--   but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron17_volumes_positive :: Cube -> Bool
+prop_tetrahedron17_volumes_positive cube =
+    volume (tetrahedron17 cube) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+--   but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron18_volumes_positive :: Cube -> Bool
+prop_tetrahedron18_volumes_positive cube =
+    volume (tetrahedron18 cube) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+--   but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron19_volumes_positive :: Cube -> Bool
+prop_tetrahedron19_volumes_positive cube =
+    volume (tetrahedron19 cube) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+--   but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron20_volumes_positive :: Cube -> Bool
+prop_tetrahedron20_volumes_positive cube =
+    volume (tetrahedron20 cube) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+--   but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron21_volumes_positive :: Cube -> Bool
+prop_tetrahedron21_volumes_positive cube =
+    volume (tetrahedron21 cube) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+--   but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron22_volumes_positive :: Cube -> Bool
+prop_tetrahedron22_volumes_positive cube =
+    volume (tetrahedron22 cube) > 0
+
+-- | This pretty much repeats the prop_all_volumes_positive property,
+--   but will let me know which tetrahedrons's vertices are disoriented.
+prop_tetrahedron23_volumes_positive :: Cube -> Bool
+prop_tetrahedron23_volumes_positive cube =
+    volume (tetrahedron23 cube) > 0
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+--   fourth indices of c-t3 have been switched. This is because we
+--   store the triangles oriented such that their volume is
+--   positive. If T and T-tilde share <v0,v1,v2> and v3,v3-tilde point
+--   in opposite directions, one of them has to have negative volume!
+prop_c0120_identity1 :: Cube -> Bool
+prop_c0120_identity1 cube =
+   c t0 0 1 2 0 ~= (c t0 0 0 2 1 + c t3 0 0 1 2) / 2
+     where
+       t0 = tetrahedron0 cube
+       t3 = tetrahedron3 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+--   fourth indices of c-t3 have been switched. This is because we
+--   store the triangles oriented such that their volume is
+--   positive. If T and T-tilde share <v0,v1,v2> and v3,v3-tilde point
+--   in opposite directions, one of them has to have negative volume!
+prop_c0210_identity1 :: Cube -> Bool
+prop_c0210_identity1 cube =
+    c t0 0 2 1 0 ~= (c t0 0 1 1 1 + c t3 0 1 1 1) / 2
+      where
+        t0 = tetrahedron0 cube
+        t3 = tetrahedron3 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+--   fourth indices of c-t3 have been switched. This is because we
+--   store the triangles oriented such that their volume is
+--   positive. If T and T-tilde share <v0,v1,v2> and v3,v3-tilde point
+--   in opposite directions, one of them has to have negative volume!
+prop_c0300_identity1 :: Cube -> Bool
+prop_c0300_identity1 cube =
+    c t0 0 3 0 0 ~= (c t0 0 2 0 1 + c t3 0 2 1 0) / 2
+      where
+        t0 = tetrahedron0 cube
+        t3 = tetrahedron3 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+--   fourth indices of c-t3 have been switched. This is because we
+--   store the triangles oriented such that their volume is
+--   positive. If T and T-tilde share <v0,v1,v2> and v3,v3-tilde point
+--   in opposite directions, one of them has to have negative volume!
+prop_c1110_identity :: Cube -> Bool
+prop_c1110_identity cube =
+    c t0 1 1 1 0 ~= (c t0 1 0 1 1 + c t3 1 0 1 1) / 2
+      where
+        t0 = tetrahedron0 cube
+        t3 = tetrahedron3 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+--   fourth indices of c-t3 have been switched. This is because we
+--   store the triangles oriented such that their volume is
+--   positive. If T and T-tilde share <v0,v1,v2> and v3,v3-tilde point
+--   in opposite directions, one of them has to have negative volume!
+prop_c1200_identity1 :: Cube -> Bool
+prop_c1200_identity1 cube =
+    c t0 1 2 0 0 ~= (c t0 1 1 0 1 + c t3 1 1 1 0) / 2
+      where
+        t0 = tetrahedron0 cube
+        t3 = tetrahedron3 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+--   fourth indices of c-t3 have been switched. This is because we
+--   store the triangles oriented such that their volume is
+--   positive. If T and T-tilde share <v0,v1,v2> and v3,v3-tilde point
+--   in opposite directions, one of them has to have negative volume!
+prop_c2100_identity1 :: Cube -> Bool
+prop_c2100_identity1 cube =
+    c t0 2 1 0 0 ~= (c t0 2 0 0 1 + c t3 2 0 1 0) / 2
+      where
+        t0 = tetrahedron0 cube
+        t3 = tetrahedron3 cube
+
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+--   fourth indices of c-t1 have been switched. This is because we
+--   store the triangles oriented such that their volume is
+--   positive. If T and T-tilde share <v0,v1,v3> and v2,v2-tilde point
+--   in opposite directions, one of them has to have negative volume!
+prop_c0102_identity1 :: Cube -> Bool
+prop_c0102_identity1 cube =
+    c t0 0 1 0 2 ~= (c t0 0 0 1 2 + c t1 0 0 2 1) / 2
+      where
+        t0 = tetrahedron0 cube
+        t1 = tetrahedron1 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+--   fourth indices of c-t1 have been switched. This is because we
+--   store the triangles oriented such that their volume is
+--   positive. If T and T-tilde share <v0,v1,v3> and v2,v2-tilde point
+--   in opposite directions, one of them has to have negative volume!
+prop_c0201_identity1 :: Cube -> Bool
+prop_c0201_identity1 cube =
+    c t0 0 2 0 1 ~= (c t0 0 1 1 1 + c t1 0 1 1 1) / 2
+      where
+        t0 = tetrahedron0 cube
+        t1 = tetrahedron1 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+--   fourth indices of c-t1 have been switched. This is because we
+--   store the triangles oriented such that their volume is
+--   positive. If T and T-tilde share <v0,v1,v3> and v2,v2-tilde point
+--   in opposite directions, one of them has to have negative volume!
+prop_c0300_identity2 :: Cube -> Bool
+prop_c0300_identity2 cube =
+    c t0 0 3 0 0 ~= (c t0 0 2 1 0 + c t1 0 2 0 1) / 2
+      where
+        t0 = tetrahedron0 cube
+        t1 = tetrahedron1 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+--   fourth indices of c-t1 have been switched. This is because we
+--   store the triangles oriented such that their volume is
+--   positive. If T and T-tilde share <v0,v1,v3> and v2,v2-tilde point
+--   in opposite directions, one of them has to have negative volume!
+prop_c1101_identity :: Cube -> Bool
+prop_c1101_identity cube =
+    c t0 1 1 0 1 ~= (c t0 1 0 1 1 + c t1 1 0 1 1) / 2
+      where
+        t0 = tetrahedron0 cube
+        t1 = tetrahedron1 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+--   fourth indices of c-t1 have been switched. This is because we
+--   store the triangles oriented such that their volume is
+--   positive. If T and T-tilde share <v0,v1,v3> and v2,v2-tilde point
+--   in opposite directions, one of them has to have negative volume!
+prop_c1200_identity2 :: Cube -> Bool
+prop_c1200_identity2 cube =
+    c t0 1 2 0 0 ~= (c t0 1 1 1 0 + c t1 1 1 0 1) / 2
+      where
+        t0 = tetrahedron0 cube
+        t1 = tetrahedron1 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+--   fourth indices of c-t1 have been switched. This is because we
+--   store the triangles oriented such that their volume is
+--   positive. If T and T-tilde share <v0,v1,v3> and v2,v2-tilde point
+--   in opposite directions, one of them has to have negative volume!
+prop_c2100_identity2 :: Cube -> Bool
+prop_c2100_identity2 cube =
+    c t0 2 1 0 0 ~= (c t0 2 0 1 0 + c t1 2 0 0 1) / 2
+      where
+        t0 = tetrahedron0 cube
+        t1 = tetrahedron1 cube
+
+
+prop_t0_shares_edge_with_t6 :: Cube -> Bool
+prop_t0_shares_edge_with_t6 cube =
+    (v2 t0) == (v3 t6) && (v3 t0) == (v2 t6)
+      where
+        t0 = tetrahedron0 cube
+        t6 = tetrahedron6 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c3000_identity :: Cube -> Bool
+prop_c3000_identity cube =
+    c t0 3 0 0 0 ~= c t0 2 1 0 0 + c t6 2 1 0 0 - ((c t0 2 0 1 0 + c t0 2 0 0 1)/ 2)
+      where
+        t0 = tetrahedron0 cube
+        t6 = tetrahedron6 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c2010_identity :: Cube -> Bool
+prop_c2010_identity cube =
+    c t0 2 0 1 0 ~= c t0 1 1 1 0 + c t6 1 1 1 0 - ((c t0 1 0 2 0 + c t0 1 0 1 1)/ 2)
+      where
+        t0 = tetrahedron0 cube
+        t6 = tetrahedron6 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c2001_identity :: Cube -> Bool
+prop_c2001_identity cube =
+    c t0 2 0 0 1 ~= c t0 1 1 0 1 + c t6 1 1 0 1 - ((c t0 1 0 0 2 + c t0 1 0 1 1)/ 2)
+      where
+        t0 = tetrahedron0 cube
+        t6 = tetrahedron6 cube
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c1020_identity :: Cube -> Bool
+prop_c1020_identity cube =
+    c t0 1 0 2 0 ~= c t0 0 1 2 0 + c t6 0 1 2 0 - ((c t0 0 0 3 0 + c t0 0 0 2 1)/ 2)
+      where
+        t0 = tetrahedron0 cube
+        t6 = tetrahedron6 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c1002_identity :: Cube -> Bool
+prop_c1002_identity cube =
+    c t0 1 0 0 2 ~= c t0 0 1 0 2 + c t6 0 1 0 2 - ((c t0 0 0 0 3 + c t0 0 0 1 2)/ 2)
+      where
+        t0 = tetrahedron0 cube
+        t6 = tetrahedron6 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c1011_identity :: Cube -> Bool
+prop_c1011_identity cube =
+    c t0 1 0 1 1 ~= c t0 0 1 1 1 + c t6 0 1 1 1 - ((c t0 0 0 1 2 + c t0 0 0 2 1)/ 2)
+      where
+        t0 = tetrahedron0 cube
+        t6 = tetrahedron6 cube
+
+
+
+-- | Given in Sorokina and Zeilfelder, p. 78.
+-- prop_cijk1_identity :: Cube -> Bool
+-- prop_cijk1_identity cube =
+--      and [ c t0 i j k 1 ~=
+--                  (c t1 (i+1) j k 0) * ((b0 t0) (v3 t1)) +
+--                  (c t1 i (j+1) k 0) * ((b1 t0) (v3 t1)) +
+--                  (c t1 i j (k+1) 0) * ((b2 t0) (v3 t1)) +
+--                  (c t1 i j k 1) * ((b3 t0) (v3 t1)) | i <- [0..2],
+--                                                       j <- [0..2],
+--                                                       k <- [0..2],
+--                                                       i + j + k == 2]
+--       where
+--         t0 = tetrahedron0 cube
+--         t1 = tetrahedron1 cube