module Tests.Face
where
+import Control.Monad (unless)
+import Test.HUnit
import Test.QuickCheck
+import Assertions
import Comparisons
-import Cube (Cube(grid), top)
-import Face (face0,
- face2,
- face5,
- tetrahedron0,
- tetrahedron1,
- tetrahedron2,
- tetrahedron3,
- tetrahedrons)
-import Grid (Grid(h))
+import Face
+import Grid (Grid(h), make_grid)
+import Point
import Tetrahedron
--- QuickCheck Tests.
-
--- | Since the grid size is necessarily positive, all tetrahedrons
--- (which comprise cubes of positive volume) must have positive volume
--- as well.
-prop_all_volumes_positive :: Cube -> Property
-prop_all_volumes_positive c =
- (delta > 0) ==> (null nonpositive_volumes)
- where
- delta = h (grid c)
- ts = tetrahedrons c
- volumes = map volume ts
- nonpositive_volumes = filter (<= 0) volumes
-
-
--- | 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)
-
-
--- | Given in Sorokina and Zeilfelder, p. 79.
-prop_c0300_identity2 :: Cube -> Bool
-prop_c0300_identity2 cube =
- c t0' 3 0 0 0 ~= (c t0' 0 2 1 0 + c t3' 0 2 1 0) / 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_c1101_identity :: Cube -> Bool
-prop_c1101_identity cube =
- c t0' 1 1 0 1 ~= (c t0' 1 1 0 1 + c t3' 1 1 0 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)
-
-
--- | Given in Sorokina and Zeilfelder, p. 79.
-prop_c1200_identity2 :: Cube -> Bool
-prop_c1200_identity2 cube =
- c t0' 1 1 1 0 ~= (c t0' 1 1 1 0 + c t3' 1 1 1 0) / 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_c2100_identity2 :: Cube -> Bool
-prop_c2100_identity2 cube =
- c t0' 2 1 0 0 ~= (c t0' 2 0 1 0 + c t3' 2 0 1 0) / 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_c3000_identity :: Cube -> Bool
-prop_c3000_identity cube =
- c t0' 3 0 0 0 ~= c t0' 2 1 0 0 + c t2' 2 1 0 0 - ((c t0' 2 0 1 0 + c t0' 2 0 0 1)/ 2)
- where
- t0 = tetrahedron0 (face0 cube)
- t2 = tetrahedron2 (face5 cube)
- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
- t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
-
-
--- | 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 t2' 1 1 1 0 - ((c t0' 1 0 2 0 + c t0' 1 0 1 1)/ 2)
- where
- t0 = tetrahedron0 (face0 cube)
- t2 = tetrahedron2 (face5 cube)
- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
- t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
-
-
--- | 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 t2' 1 1 0 1 - ((c t0' 1 0 0 2 + c t0' 1 0 1 1)/ 2)
- where
- t0 = tetrahedron0 (face0 cube)
- t2 = tetrahedron2 (face5 cube)
- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
- t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
-
--- | 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 t2' 0 1 2 0 - ((c t0' 0 0 3 0 + c t0' 0 0 2 1)/ 2)
- where
- t0 = tetrahedron0 (face0 cube)
- t2 = tetrahedron2 (face5 cube)
- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
- t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
-
-
--- | 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 t2' 0 1 0 2 - ((c t0' 0 0 0 3 + c t0' 0 0 1 2)/ 2)
- where
- t0 = tetrahedron0 (face0 cube)
- t2 = tetrahedron2 (face5 cube)
- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
- t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
-
-
--- | 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 t2' 0 1 1 1 - ((c t0' 0 0 1 2 + c t0' 0 0 2 1)/ 2)
- where
- t0 = tetrahedron0 (face0 cube)
- t2 = tetrahedron2 (face5 cube)
- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
- t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
-
-
--- | Given in Sorokina and Zeilfelder, p. 80.
-prop_c0120_identity2 :: Cube -> Bool
-prop_c0120_identity2 cube =
- c t0' 0 1 2 0 ~= (c t0' 1 0 2 0 + c t1' 1 0 2 0) / 2
- where
- t0 = tetrahedron0 (face0 cube)
- t1 = tetrahedron0 (face2 (top 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. 80.
-prop_c0102_identity2 :: Cube -> Bool
-prop_c0102_identity2 cube =
- c t0' 0 1 0 2 ~= (c t0' 1 0 0 2 + c t1' 1 0 0 2) / 2
- where
- t0 = tetrahedron0 (face0 cube)
- t1 = tetrahedron0 (face2 (top 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. 80.
-prop_c0111_identity :: Cube -> Bool
-prop_c0111_identity cube =
- c t0' 0 1 1 1 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
- where
- t0 = tetrahedron0 (face0 cube)
- t1 = tetrahedron0 (face2 (top 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. 80.
-prop_c0210_identity2 :: Cube -> Bool
-prop_c0210_identity2 cube =
- c t0 0 2 1 0 ~= (c t0 1 1 1 0 + c t1 1 1 1 0) / 2
- where
- t0 = tetrahedron0 (face0 cube)
- t1 = tetrahedron0 (face2 (top 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. 80.
-prop_c0201_identity2 :: Cube -> Bool
-prop_c0201_identity2 cube =
- c t0 0 2 0 1 ~= (c t0 1 1 0 1 + c t1 1 1 0 1) / 2
- where
- t0 = tetrahedron0 (face0 cube)
- t1 = tetrahedron0 (face2 (top 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. 80.
-prop_c0300_identity3 :: Cube -> Bool
-prop_c0300_identity3 cube =
- c t0 0 3 0 0 ~= (c t0 1 2 0 0 + c t1 1 2 0 0) / 2
- where
- t0 = tetrahedron0 (face0 cube)
- t1 = tetrahedron0 (face2 (top cube))
- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
- t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+
+-- HUnit tests.
+
+
+
+
+
+-- -- test_trilinear_f0_t0_v0 :: Test
+-- -- test_trilinear_f0_t0_v0 =
+-- -- TestCase $ assertClose "v0 is correct" (v0 t) (0.5, 1.5, 1.5)
+-- -- where
+-- -- g = make_grid 1 trilinear
+-- -- cube = cube_at g 1 1 1
+-- -- t = tetrahedron0 (face0 cube) -- Any one will do.
+
+
+-- -- test_trilinear_f0_t0_v1 :: Test
+-- -- test_trilinear_f0_t0_v1 =
+-- -- TestCase $ assertClose "v1 is correct" (v1 t) (1.5, 1.5, 1.5)
+-- -- where
+-- -- g = make_grid 1 trilinear
+-- -- cube = cube_at g 1 1 1
+-- -- t = tetrahedron0 (face0 cube) -- Any one will do.
+
+
+-- -- test_trilinear_f0_t0_v2 :: Test
+-- -- test_trilinear_f0_t0_v2 =
+-- -- TestCase $ assertClose "v2 is correct" (v2 t) (1, 1, 1.5)
+-- -- where
+-- -- g = make_grid 1 trilinear
+-- -- cube = cube_at g 1 1 1
+-- -- t = tetrahedron0 (face0 cube) -- Any one will do.
+
+
+
+-- -- test_trilinear_f0_t0_v3 :: Test
+-- -- test_trilinear_f0_t0_v3 =
+-- -- TestCase $ assertClose "v3 is correct" (v3 t) (1, 1, 1)
+-- -- where
+-- -- g = make_grid 1 trilinear
+-- -- cube = cube_at g 1 1 1
+-- -- t = tetrahedron0 (face0 cube) -- Any one will do.
+
+
+
+-- face_tests :: [Test]
+face_tests = []
+-- face_tests = [test_trilinear_c0030,
+-- test_trilinear_c0003,
+-- test_trilinear_c0021,
+-- test_trilinear_c0012,
+-- test_trilinear_c0120,
+-- test_trilinear_c0102,
+-- test_trilinear_c0111,
+-- test_trilinear_c0210,
+-- test_trilinear_c0201,
+-- test_trilinear_c0300,
+-- test_trilinear_c1020,
+-- test_trilinear_c1002,
+-- test_trilinear_c1011,
+-- test_trilinear_c1110,
+-- test_trilinear_c1101,
+-- test_trilinear_c1200,
+-- test_trilinear_c2010,
+-- test_trilinear_c2001,
+-- test_trilinear_c2100,
+-- test_trilinear_c3000,
+-- test_trilinear_f0_t0_v0,
+-- test_trilinear_f0_t0_v1,
+-- test_trilinear_f0_t0_v2,
+-- test_trilinear_f0_t0_v3]
+
+
+-- -- QuickCheck Tests.
+
+
+-- -- | 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)
+
+
+-- -- | Given in Sorokina and Zeilfelder, p. 79.
+-- prop_c0300_identity2 :: Cube -> Bool
+-- prop_c0300_identity2 cube =
+-- c t0' 3 0 0 0 ~= (c t0' 0 2 1 0 + c t3' 0 2 1 0) / 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_c1101_identity :: Cube -> Bool
+-- prop_c1101_identity cube =
+-- c t0' 1 1 0 1 ~= (c t0' 1 1 0 1 + c t3' 1 1 0 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)
+
+
+-- -- | Given in Sorokina and Zeilfelder, p. 79.
+-- prop_c1200_identity2 :: Cube -> Bool
+-- prop_c1200_identity2 cube =
+-- c t0' 1 1 1 0 ~= (c t0' 1 1 1 0 + c t3' 1 1 1 0) / 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_c2100_identity2 :: Cube -> Bool
+-- prop_c2100_identity2 cube =
+-- c t0' 2 1 0 0 ~= (c t0' 2 0 1 0 + c t3' 2 0 1 0) / 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_c3000_identity :: Cube -> Bool
+-- prop_c3000_identity cube =
+-- c t0' 3 0 0 0 ~= c t0' 2 1 0 0 + c t2' 2 1 0 0 - ((c t0' 2 0 1 0 + c t0' 2 0 0 1)/ 2)
+-- where
+-- t0 = tetrahedron0 (face0 cube)
+-- t2 = tetrahedron2 (face5 cube)
+-- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+-- t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
+
+
+-- -- | 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 t2' 1 1 1 0 - ((c t0' 1 0 2 0 + c t0' 1 0 1 1)/ 2)
+-- where
+-- t0 = tetrahedron0 (face0 cube)
+-- t2 = tetrahedron2 (face5 cube)
+-- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+-- t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
+
+
+-- -- | 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 t2' 1 1 0 1 - ((c t0' 1 0 0 2 + c t0' 1 0 1 1)/ 2)
+-- where
+-- t0 = tetrahedron0 (face0 cube)
+-- t2 = tetrahedron2 (face5 cube)
+-- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+-- t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
+
+-- -- | 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 t2' 0 1 2 0 - ((c t0' 0 0 3 0 + c t0' 0 0 2 1)/ 2)
+-- where
+-- t0 = tetrahedron0 (face0 cube)
+-- t2 = tetrahedron2 (face5 cube)
+-- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+-- t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
+
+
+-- -- | 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 t2' 0 1 0 2 - ((c t0' 0 0 0 3 + c t0' 0 0 1 2)/ 2)
+-- where
+-- t0 = tetrahedron0 (face0 cube)
+-- t2 = tetrahedron2 (face5 cube)
+-- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+-- t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
+
+
+-- -- | 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 t2' 0 1 1 1 - ((c t0' 0 0 1 2 + c t0' 0 0 2 1)/ 2)
+-- where
+-- t0 = tetrahedron0 (face0 cube)
+-- t2 = tetrahedron2 (face5 cube)
+-- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+-- t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
+
+
+-- -- | Given in Sorokina and Zeilfelder, p. 80.
+-- prop_c0120_identity2 :: Cube -> Bool
+-- prop_c0120_identity2 cube =
+-- c t0' 0 1 2 0 ~= (c t0' 1 0 2 0 + c t1' 1 0 2 0) / 2
+-- where
+-- t0 = tetrahedron0 (face0 cube)
+-- t1 = tetrahedron0 (face2 (top 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. 80.
+-- prop_c0102_identity2 :: Cube -> Bool
+-- prop_c0102_identity2 cube =
+-- c t0' 0 1 0 2 ~= (c t0' 1 0 0 2 + c t1' 1 0 0 2) / 2
+-- where
+-- t0 = tetrahedron0 (face0 cube)
+-- t1 = tetrahedron0 (face2 (top 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. 80.
+-- prop_c0111_identity :: Cube -> Bool
+-- prop_c0111_identity cube =
+-- c t0' 0 1 1 1 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
+-- where
+-- t0 = tetrahedron0 (face0 cube)
+-- t1 = tetrahedron0 (face2 (top 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. 80.
+-- prop_c0210_identity2 :: Cube -> Bool
+-- prop_c0210_identity2 cube =
+-- c t0 0 2 1 0 ~= (c t0 1 1 1 0 + c t1 1 1 1 0) / 2
+-- where
+-- t0 = tetrahedron0 (face0 cube)
+-- t1 = tetrahedron0 (face2 (top 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. 80.
+-- prop_c0201_identity2 :: Cube -> Bool
+-- prop_c0201_identity2 cube =
+-- c t0 0 2 0 1 ~= (c t0 1 1 0 1 + c t1 1 1 0 1) / 2
+-- where
+-- t0 = tetrahedron0 (face0 cube)
+-- t1 = tetrahedron0 (face2 (top 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. 80.
+-- prop_c0300_identity3 :: Cube -> Bool
+-- prop_c0300_identity3 cube =
+-- c t0 0 3 0 0 ~= (c t0 1 2 0 0 + c t1 1 2 0 0) / 2
+-- where
+-- t0 = tetrahedron0 (face0 cube)
+-- t1 = tetrahedron0 (face2 (top cube))
+-- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+-- t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
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