--- -- | 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 (face0 cube)
--- t1 = tetrahedron1 (face0 cube)
--- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--- t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
-
--- -- | Given in Sorokina and Zeilfelder, p. 79.
--- prop_c0120_identity1 :: Cube -> Bool
--- prop_c0120_identity1 cube =
--- c t0' 0 1 2 0 ~= (c t0' 0 0 2 1 + c t1' 0 0 2 1) / 2
--- where
--- t0 = tetrahedron0 (face0 cube)
--- t1 = tetrahedron1 (face0 cube)
--- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--- t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
-
-
--- -- | Given in Sorokina and Zeilfelder, p. 79.
--- prop_c0210_identity1 :: Cube -> Bool
--- prop_c0210_identity1 cube =
--- c t0' 0 2 1 0 ~= (c t0' 0 1 1 1 + c t1' 0 1 1 1) / 2
--- where
--- t0 = tetrahedron0 (face0 cube)
--- t1 = tetrahedron1 (face0 cube)
--- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--- t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
-
-
--- -- | Given in Sorokina and Zeilfelder, p. 79.
--- prop_c0300_identity1 :: Cube -> Bool
--- prop_c0300_identity1 cube =
--- c t0' 0 3 0 0 ~= (c t0' 0 2 0 1 + c t1' 0 2 0 1) / 2
--- where
--- t0 = tetrahedron0 (face0 cube)
--- t1 = tetrahedron1 (face0 cube)
--- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--- t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
-
--- -- | Given in Sorokina and Zeilfelder, p. 79.
--- prop_c1110_identity :: Cube -> Bool
--- prop_c1110_identity cube =
--- c t0' 1 1 1 0 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
--- where
--- t0 = tetrahedron0 (face0 cube)
--- t1 = tetrahedron1 (face0 cube)
--- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--- t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
-
-
--- -- | Given in Sorokina and Zeilfelder, p. 79.
--- prop_c1200_identity1 :: Cube -> Bool
--- prop_c1200_identity1 cube =
--- c t0' 1 2 0 0 ~= (c t0' 1 1 0 1 + c t1' 1 1 0 1) / 2
--- where
--- t0 = tetrahedron0 (face0 cube)
--- t1 = tetrahedron1 (face0 cube)
--- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--- t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
-
-
--- -- | Given in Sorokina and Zeilfelder, p. 79.
--- prop_c2100_identity1 :: Cube -> Bool
--- prop_c2100_identity1 cube =
--- c t0' 2 1 0 0 ~= (c t0' 2 0 0 1 + c t1' 2 0 0 1) / 2
--- where
--- t0 = tetrahedron0 (face0 cube)
--- t1 = tetrahedron1 (face0 cube)
--- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--- t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
-
-
--- -- | Given in Sorokina and Zeilfelder, p. 79.
--- prop_c0102_identity1 :: Cube -> Bool
--- prop_c0102_identity1 cube =
--- c t0' 0 1 0 2 ~= (c t0' 0 0 1 2 + c t3' 0 0 1 2) / 2
--- where
--- t0 = tetrahedron0 (face0 cube)
--- t3 = tetrahedron3 (face0 cube)
--- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--- t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
-
-
--- -- | Given in Sorokina and Zeilfelder, p. 79.
--- prop_c0201_identity1 :: Cube -> Bool
--- prop_c0201_identity1 cube =
--- c t0' 0 2 0 1 ~= (c t0' 0 1 1 1 + c t3' 0 1 1 1) / 2
--- where
--- t0 = tetrahedron0 (face0 cube)
--- t3 = tetrahedron3 (face0 cube)
--- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
--- t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)