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
-- (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
-- 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 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 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 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 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. Repeats
+-- prop_c0120_identity2 with tetrahedrons 3 and 2.
+prop_c0120_identity2 :: Cube -> Bool
+prop_c0120_identity2 cube =
+ c t3 0 1 2 0 ~= (c t3 0 0 2 1 + c t2 0 0 1 2) / 2
+ where
+ t3 = tetrahedron3 cube
+ t2 = tetrahedron2 cube
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Repeats
+-- prop_c0120_identity1 with tetrahedrons 2 and 1.
+prop_c0120_identity3 :: Cube -> Bool
+prop_c0120_identity3 cube =
+ c t2 0 1 2 0 ~= (c t2 0 0 2 1 + c t1 0 0 1 2) / 2
+ where
+ t2 = tetrahedron2 cube
+ t1 = tetrahedron1 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Repeats
+-- prop_c0120_identity1 with tetrahedrons 4 and 7.
+prop_c0120_identity4 :: Cube -> Bool
+prop_c0120_identity4 cube =
+ c t4 0 1 2 0 ~= (c t4 0 0 2 1 + c t7 0 0 1 2) / 2
+ where
+ t4 = tetrahedron4 cube
+ t7 = tetrahedron7 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Repeats
+-- prop_c0120_identity1 with tetrahedrons 7 and 6.
+prop_c0120_identity5 :: Cube -> Bool
+prop_c0120_identity5 cube =
+ c t7 0 1 2 0 ~= (c t7 0 0 2 1 + c t6 0 0 1 2) / 2
+ where
+ t7 = tetrahedron7 cube
+ t6 = tetrahedron6 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Repeats
+-- prop_c0120_identity1 with tetrahedrons 6 and 5.
+prop_c0120_identity6 :: Cube -> Bool
+prop_c0120_identity6 cube =
+ c t6 0 1 2 0 ~= (c t6 0 0 2 1 + c t5 0 0 1 2) / 2
+ where
+ t6 = tetrahedron6 cube
+ t5 = tetrahedron5 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
+
+
+-- | 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
+
+
+-- Tests to check that the correct edges are incidental.
+prop_t0_shares_edge_with_t1 :: Cube -> Bool
+prop_t0_shares_edge_with_t1 cube =
+ (v1 t0) == (v1 t1) && (v3 t0) == (v2 t1)
+ where
+ t0 = tetrahedron0 cube
+ t1 = tetrahedron1 cube
+
+prop_t0_shares_edge_with_t3 :: Cube -> Bool
+prop_t0_shares_edge_with_t3 cube =
+ (v1 t0) == (v1 t3) && (v2 t0) == (v3 t3)
+ where
+ t0 = tetrahedron0 cube
+ t3 = tetrahedron3 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
+
+prop_t1_shares_edge_with_t2 :: Cube -> Bool
+prop_t1_shares_edge_with_t2 cube =
+ (v1 t1) == (v1 t2) && (v3 t1) == (v2 t2)
+ where
+ t1 = tetrahedron1 cube
+ t2 = tetrahedron2 cube
+
+prop_t1_shares_edge_with_t19 :: Cube -> Bool
+prop_t1_shares_edge_with_t19 cube =
+ (v2 t1) == (v3 t19) && (v3 t1) == (v2 t19)
+ where
+ t1 = tetrahedron1 cube
+ t19 = tetrahedron19 cube
+
+prop_t2_shares_edge_with_t3 :: Cube -> Bool
+prop_t2_shares_edge_with_t3 cube =
+ (v1 t1) == (v1 t2) && (v3 t1) == (v2 t2)
+ where
+ t1 = tetrahedron1 cube
+ t2 = tetrahedron2 cube
+
+prop_t2_shares_edge_with_t12 :: Cube -> Bool
+prop_t2_shares_edge_with_t12 cube =
+ (v2 t2) == (v3 t12) && (v3 t2) == (v2 t12)
+ where
+ t2 = tetrahedron2 cube
+ t12 = tetrahedron12 cube
+
+prop_t3_shares_edge_with_t21 :: Cube -> Bool
+prop_t3_shares_edge_with_t21 cube =
+ (v2 t3) == (v3 t21) && (v3 t3) == (v2 t21)
+ where
+ t3 = tetrahedron3 cube
+ t21 = tetrahedron21 cube
+
+prop_t4_shares_edge_with_t5 :: Cube -> Bool
+prop_t4_shares_edge_with_t5 cube =
+ (v1 t4) == (v1 t5) && (v3 t4) == (v2 t5)
+ where
+ t4 = tetrahedron4 cube
+ t5 = tetrahedron5 cube
+
+prop_t4_shares_edge_with_t7 :: Cube -> Bool
+prop_t4_shares_edge_with_t7 cube =
+ (v1 t4) == (v1 t7) && (v2 t4) == (v3 t7)
+ where
+ t4 = tetrahedron4 cube
+ t7 = tetrahedron7 cube
+
+prop_t4_shares_edge_with_t10 :: Cube -> Bool
+prop_t4_shares_edge_with_t10 cube =
+ (v2 t4) == (v3 t10) && (v3 t4) == (v2 t10)
+ where
+ t4 = tetrahedron4 cube
+ t10 = tetrahedron10 cube
+
+prop_t5_shares_edge_with_t6 :: Cube -> Bool
+prop_t5_shares_edge_with_t6 cube =
+ (v1 t5) == (v1 t6) && (v3 t5) == (v2 t6)
+ where
+ t5 = tetrahedron5 cube
+ t6 = tetrahedron6 cube
+
+prop_t5_shares_edge_with_t16 :: Cube -> Bool
+prop_t5_shares_edge_with_t16 cube =
+ (v2 t5) == (v3 t16) && (v3 t5) == (v2 t16)
+ where
+ t5 = tetrahedron5 cube
+ t16 = tetrahedron16 cube
+
+prop_t6_shares_edge_with_t7 :: Cube -> Bool
+prop_t6_shares_edge_with_t7 cube =
+ (v1 t6) == (v1 t7) && (v3 t6) == (v2 t7)
+ where
+ t6 = tetrahedron6 cube
+ t7 = tetrahedron7 cube
+
+prop_t7_shares_edge_with_t20 :: Cube -> Bool
+prop_t7_shares_edge_with_t20 cube =
+ (v2 t7) == (v3 t20) && (v2 t7) == (v3 t20)
+ where
+ t7 = tetrahedron7 cube
+ t20 = tetrahedron20 cube