X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FTests%2FCube.hs;h=2fd8cb67187c601fb63b3811bb3e7ad5cb6341fe;hb=3f0b6b7faecc561af0b7312a11c73a44a1b416f6;hp=b5e771b2684c50df9658f49ce7d76c9258dc5084;hpb=7bfd79b7cc06dfd0b08cf14794d7659a940b8f08;p=spline3.git

diff --git a/src/Tests/Cube.hs b/src/Tests/Cube.hs
index b5e771b..2fd8cb6 100644
--- a/src/Tests/Cube.hs
+++ b/src/Tests/Cube.hs
@@ -2,257 +2,60 @@ module Tests.Cube
 where
 
 import Prelude hiding (LT)
-import Test.QuickCheck
 
 import Cardinal
 import Comparisons
 import Cube hiding (i, j, k)
 import FunctionValues
-import Misc (all_equal)
-import Tests.FunctionValues ()
+import Misc (all_equal, disjoint)
 import Tetrahedron (b0, b1, b2, b3, c, fv,
                     v0, v1, v2, v3, volume)
 
-instance Arbitrary Cube where
-    arbitrary = do
-      (Positive h') <- arbitrary :: Gen (Positive Double)
-      i' <- choose (coordmin, coordmax)
-      j' <- choose (coordmin, coordmax)
-      k' <- choose (coordmin, coordmax)
-      fv' <- arbitrary :: Gen FunctionValues
-      return (Cube h' i' j' k' fv')
-        where
-          coordmin = -268435456 -- -(2^29 / 2)
-          coordmax = 268435456  -- +(2^29 / 2)
-
 
 -- 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 -> Bool
-prop_all_volumes_positive cube =
-    null nonpositive_volumes
-    where
-      ts = tetrahedrons cube
-      volumes = map volume ts
-      nonpositive_volumes = filter (<= 0) volumes
+prop_opposite_octant_tetrahedra_disjoint1 :: Cube -> Bool
+prop_opposite_octant_tetrahedra_disjoint1 c =
+  disjoint (front_left_top_tetrahedra c) (front_right_down_tetrahedra c)
 
--- | 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_tetrahedron0_volumes_exact :: Cube -> Bool
-prop_tetrahedron0_volumes_exact cube =
-    volume (tetrahedron0 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
+prop_opposite_octant_tetrahedra_disjoint2 :: Cube -> Bool
+prop_opposite_octant_tetrahedra_disjoint2 c =
+  disjoint (back_left_top_tetrahedra c) (back_right_down_tetrahedra c)
 
+prop_opposite_octant_tetrahedra_disjoint3 :: Cube -> Bool
+prop_opposite_octant_tetrahedra_disjoint3 c =
+  disjoint (front_left_top_tetrahedra c) (back_right_top_tetrahedra c)
 
--- | 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 cube =
-    volume (tetrahedron1 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      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 cube =
-    volume (tetrahedron2 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
+prop_opposite_octant_tetrahedra_disjoint4 :: Cube -> Bool
+prop_opposite_octant_tetrahedra_disjoint4 c =
+  disjoint (front_left_down_tetrahedra c) (back_right_down_tetrahedra c)
 
--- | 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 cube =
-    volume (tetrahedron3 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
+prop_opposite_octant_tetrahedra_disjoint5 :: Cube -> Bool
+prop_opposite_octant_tetrahedra_disjoint5 c =
+  disjoint (front_left_top_tetrahedra c) (back_left_down_tetrahedra c)
 
--- | 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 cube =
-    volume (tetrahedron4 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      delta = h cube
+prop_opposite_octant_tetrahedra_disjoint6 :: Cube -> Bool
+prop_opposite_octant_tetrahedra_disjoint6 c =
+  disjoint (front_right_top_tetrahedra c) (back_right_down_tetrahedra c)
 
--- | 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 cube =
-    volume (tetrahedron5 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      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 cube =
-    volume (tetrahedron6 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      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 cube =
-    volume (tetrahedron7 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      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_tetrahedron8_volumes_exact :: Cube -> Bool
-prop_tetrahedron8_volumes_exact cube =
-    volume (tetrahedron8 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      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_tetrahedron9_volumes_exact :: Cube -> Bool
-prop_tetrahedron9_volumes_exact cube =
-    volume (tetrahedron9 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      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_tetrahedron10_volumes_exact :: Cube -> Bool
-prop_tetrahedron10_volumes_exact cube =
-    volume (tetrahedron10 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      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_tetrahedron11_volumes_exact :: Cube -> Bool
-prop_tetrahedron11_volumes_exact cube =
-    volume (tetrahedron11 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      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_tetrahedron12_volumes_exact :: Cube -> Bool
-prop_tetrahedron12_volumes_exact cube =
-    volume (tetrahedron12 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      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_tetrahedron13_volumes_exact :: Cube -> Bool
-prop_tetrahedron13_volumes_exact cube =
-    volume (tetrahedron13 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      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_tetrahedron14_volumes_exact :: Cube -> Bool
-prop_tetrahedron14_volumes_exact cube =
-    volume (tetrahedron14 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      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_tetrahedron15_volumes_exact :: Cube -> Bool
-prop_tetrahedron15_volumes_exact cube =
-    volume (tetrahedron15 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      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_tetrahedron16_volumes_exact :: Cube -> Bool
-prop_tetrahedron16_volumes_exact cube =
-    volume (tetrahedron16 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      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_tetrahedron17_volumes_exact :: Cube -> Bool
-prop_tetrahedron17_volumes_exact cube =
-    volume (tetrahedron17 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      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_tetrahedron18_volumes_exact :: Cube -> Bool
-prop_tetrahedron18_volumes_exact cube =
-    volume (tetrahedron18 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      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_tetrahedron19_volumes_exact :: Cube -> Bool
-prop_tetrahedron19_volumes_exact cube =
-    volume (tetrahedron19 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      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_tetrahedron20_volumes_exact :: Cube -> Bool
-prop_tetrahedron20_volumes_exact cube =
-    volume (tetrahedron20 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      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_tetrahedron21_volumes_exact :: Cube -> Bool
-prop_tetrahedron21_volumes_exact cube =
-    volume (tetrahedron21 cube) ~~= (1/24)*(delta^(3::Int))
-    where
-      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_tetrahedron22_volumes_exact :: Cube -> Bool
-prop_tetrahedron22_volumes_exact cube =
-    volume (tetrahedron22 cube) ~~= (1/24)*(delta^(3::Int))
+-- | Since the grid size is necessarily positive, all tetrahedra
+--   (which comprise cubes of positive volume) must have positive volume
+--   as well.
+prop_all_volumes_positive :: Cube -> Bool
+prop_all_volumes_positive cube =
+    null nonpositive_volumes
     where
-      delta = h cube
+      ts = tetrahedra cube
+      volumes = map volume ts
+      nonpositive_volumes = filter (<= 0) volumes
 
 -- | 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_tetrahedron23_volumes_exact :: Cube -> Bool
-prop_tetrahedron23_volumes_exact cube =
-    volume (tetrahedron23 cube) ~~= (1/24)*(delta^(3::Int))
+prop_all_volumes_exact :: Cube -> Bool
+prop_all_volumes_exact cube =
+    and [volume t ~~= (1/24)*(delta^(3::Int)) | t <- tetrahedra cube]
     where
       delta = h cube
 
@@ -260,364 +63,193 @@ prop_tetrahedron23_volumes_exact cube =
 prop_v0_all_equal :: Cube -> Bool
 prop_v0_all_equal cube = (v0 t0) == (v0 t1)
     where
-      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 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 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 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 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 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 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 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 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 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 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 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 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, (2.6). It appears that
---   the assumptions in sections (2.6) and (2.7) have been
---   switched. From the description, one would expect 'tetrahedron0'
---   and 'tetrahedron3' to share face \<v0,v1,v2\>; however, we have
---   to use 'tetrahedron0' and 'tetahedron1' for all of the tests in
---   section (2.6). Also 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,v2\> and v3,v3-tilde point in opposite directions,
---   one of them has to have negative volume!
+      t0 = head (tetrahedra cube) -- Doesn't matter which two we choose.
+      t1 = head $ tail (tetrahedra cube)
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). 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,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 t1 0 0 1 2) / 2
+   c t0 0 1 2 0 ~= (c t0 0 0 2 1 + c t3 0 0 1 2) / 2
      where
-       t0 = tetrahedron0 cube
-       t1 = tetrahedron1 cube
+       t0 = tetrahedron cube 0
+       t3 = tetrahedron cube 3
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
 --   'prop_c0120_identity1' with tetrahedrons 1 and 2.
 prop_c0120_identity2 :: Cube -> Bool
 prop_c0120_identity2 cube =
-   c t1 0 1 2 0 ~= (c t1 0 0 2 1 + c t2 0 0 1 2) / 2
+   c t1 0 1 2 0 ~= (c t1 0 0 2 1 + c t0 0 0 1 2) / 2
      where
-       t1 = tetrahedron1 cube
-       t2 = tetrahedron2 cube
-
+       t0 = tetrahedron cube 0
+       t1 = tetrahedron cube 1
+            
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
---   'prop_c0120_identity1' with tetrahedrons 2 and 3.
+--   'prop_c0120_identity1' with tetrahedrons 1 and 2.
 prop_c0120_identity3 :: Cube -> Bool
 prop_c0120_identity3 cube =
-   c t2 0 1 2 0 ~= (c t2 0 0 2 1 + c t3 0 0 1 2) / 2
+   c t2 0 1 2 0 ~= (c t2 0 0 2 1 + c t1 0 0 1 2) / 2
+     where
+       t1 = tetrahedron cube 1
+       t2 = tetrahedron cube 2
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
+--   'prop_c0120_identity1' with tetrahedrons 2 and 3.
+prop_c0120_identity4 :: Cube -> Bool
+prop_c0120_identity4 cube =
+   c t3 0 1 2 0 ~= (c t3 0 0 2 1 + c t2 0 0 1 2) / 2
      where
-       t2 = tetrahedron2 cube
-       t3 = tetrahedron3 cube
+       t2 = tetrahedron cube 2
+       t3 = tetrahedron cube 3
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
 --   'prop_c0120_identity1' with tetrahedrons 4 and 5.
--- prop_c0120_identity4 :: Cube -> Bool
--- prop_c0120_identity4 cube =
---     sum [trace ("c_t4_0120: " ++ (show tmp1)) tmp1,
---          trace ("c_t5_0012: " ++ (show tmp2)) tmp2,
---          trace ("c_t5_0102: " ++ (show tmp3)) tmp3,
---          trace ("c_t5_1002: " ++ (show tmp4)) tmp4,
---          trace ("c_t5_0120: " ++ (show tmp5)) tmp5,
---          trace ("c_t5_1020: " ++ (show tmp6)) tmp6,
---          trace ("c_t5_1200: " ++ (show tmp7)) tmp7,
---          trace ("c_t5_0021: " ++ (show tmp8)) tmp8,
---          trace ("c_t5_0201: " ++ (show tmp9)) tmp9,
---          trace ("c_t5_2001: " ++ (show tmp10)) tmp10,
---          trace ("c_t5_0210: " ++ (show tmp11)) tmp11,
---          trace ("c_t5_2010: " ++ (show tmp12)) tmp12,
---          trace ("c_t5_2100: " ++ (show tmp13)) tmp13] == 10
--- --   c t4 0 1 2 0 ~= (c t4 0 0 2 1 + c t5 0 0 1 2) / 2
---      where
---        t4 = tetrahedron4 cube
---        t5 = tetrahedron5 cube
---        tmp1 = c t4 0 1 2 0
---        tmp2 = (c t4 0 0 2 1 + c t5 0 0 1 2) / 2
---        tmp3 = (c t4 0 0 2 1 + c t5 0 1 0 2) / 2
---        tmp4 = (c t4 0 0 2 1 + c t5 1 0 0 2) / 2
---        tmp5 = (c t4 0 0 2 1 + c t5 0 1 2 0) / 2
---        tmp6 = (c t4 0 0 2 1 + c t5 1 0 2 0) / 2
---        tmp7 = (c t4 0 0 2 1 + c t5 1 2 0 0) / 2
---        tmp8 = (c t4 0 0 2 1 + c t5 0 0 2 1) / 2
---        tmp9 = (c t4 0 0 2 1 + c t5 0 2 0 1) / 2
---        tmp10 = (c t4 0 0 2 1 + c t5 2 0 0 1) / 2
---        tmp11 = (c t4 0 0 2 1 + c t5 0 2 1 0) / 2
---        tmp12 = (c t4 0 0 2 1 + c t5 2 0 1 0) / 2
---        tmp13 = (c t4 0 0 2 1 + c t5 2 1 0 0) / 2
+prop_c0120_identity5 :: Cube -> Bool
+prop_c0120_identity5 cube =
+    c t5 0 1 2 0 ~= (c t5 0 0 2 1 + c t4 0 0 1 2) / 2
+    where
+      t4 = tetrahedron cube 4
+      t5 = tetrahedron cube 5
 
 -- -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
 -- --   'prop_c0120_identity1' with tetrahedrons 5 and 6.
--- prop_c0120_identity5 :: Cube -> Bool
--- prop_c0120_identity5 cube =
---    c t5 0 1 2 0 ~= (c t5 0 0 2 1 + c t6 0 0 1 2) / 2
---      where
---        t5 = tetrahedron5 cube
---        t6 = tetrahedron6 cube
+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
+       t5 = tetrahedron cube 5
+       t6 = tetrahedron cube 6
 
 
 -- -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
 -- --   'prop_c0120_identity1' with tetrahedrons 6 and 7.
--- prop_c0120_identity6 :: Cube -> Bool
--- prop_c0120_identity6 cube =
---    c t6 0 1 2 0 ~= (c t6 0 0 2 1 + c t7 0 0 1 2) / 2
---      where
---        t6 = tetrahedron6 cube
---        t7 = tetrahedron7 cube
+prop_c0120_identity7 :: Cube -> Bool
+prop_c0120_identity7 cube =
+   c t7 0 1 2 0 ~= (c t7 0 0 2 1 + c t6 0 0 1 2) / 2
+     where
+       t6 = tetrahedron cube 6
+       t7 = tetrahedron cube 7
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
 --   'prop_c0120_identity1'.
 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
+    c t0 0 2 1 0 ~= (c t0 0 1 1 1 + c t3 0 1 1 1) / 2
       where
-        t0 = tetrahedron0 cube
-        t1 = tetrahedron1 cube
+        t0 = tetrahedron cube 0
+        t3 = tetrahedron cube 3
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
 --   'prop_c0120_identity1'.
 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 1 0) / 2
+    c t0 0 3 0 0 ~= (c t0 0 2 0 1 + c t3 0 2 1 0) / 2
       where
-        t0 = tetrahedron0 cube
-        t1 = tetrahedron1 cube
+        t0 = tetrahedron cube 0
+        t3 = tetrahedron cube 3
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
 --   'prop_c0120_identity1'.
 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
+    c t0 1 1 1 0 ~= (c t0 1 0 1 1 + c t3 1 0 1 1) / 2
       where
-        t0 = tetrahedron0 cube
-        t1 = tetrahedron1 cube
+        t0 = tetrahedron cube 0
+        t3 = tetrahedron cube 3
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
 --   'prop_c0120_identity1'.
 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 1 0) / 2
+    c t0 1 2 0 0 ~= (c t0 1 1 0 1 + c t3 1 1 1 0) / 2
       where
-        t0 = tetrahedron0 cube
-        t1 = tetrahedron1 cube
+        t0 = tetrahedron cube 0
+        t3 = tetrahedron cube 3
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
 --   'prop_c0120_identity1'.
 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 1 0) / 2
+    c t0 2 1 0 0 ~= (c t0 2 0 0 1 + c t3 2 0 1 0) / 2
       where
-        t0 = tetrahedron0 cube
-        t1 = tetrahedron1 cube
+        t0 = tetrahedron cube 0
+        t3 = tetrahedron cube 3
 
 
 
--- | Given in Sorokina and Zeilfelder, p. 79, (2.7). It appears that
---   the assumptions in sections (2.6) and (2.7) have been
---   switched. From the description, one would expect 'tetrahedron0'
---   and 'tetrahedron1' to share face \<v0,v1,v3\>; however, we have
---   to use 'tetrahedron0' and 'tetahedron3' for all of the tests in
---   section (2.7). Also 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!
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.7). 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_c0102_identity1 :: Cube -> Bool
 prop_c0102_identity1 cube =
-    c t0 0 1 0 2 ~= (c t0 0 0 1 2 + c t3 0 0 2 1) / 2
+    c t0 0 1 0 2 ~= (c t0 0 0 1 2 + c t1 0 0 2 1) / 2
       where
-        t0 = tetrahedron0 cube
-        t3 = tetrahedron3 cube
+        t0 = tetrahedron cube 0
+        t1 = tetrahedron cube 1
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
 --   'prop_c0102_identity1'.
 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
+    c t0 0 2 0 1 ~= (c t0 0 1 1 1 + c t1 0 1 1 1) / 2
       where
-        t0 = tetrahedron0 cube
-        t3 = tetrahedron3 cube
+        t0 = tetrahedron cube 0
+        t1 = tetrahedron cube 1
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
 --   'prop_c0102_identity1'.
 prop_c0300_identity2 :: Cube -> Bool
 prop_c0300_identity2 cube =
-    c t0 0 3 0 0 ~= (c t0 0 2 1 0 + c t3 0 2 0 1) / 2
+    c t0 0 3 0 0 ~= (c t0 0 2 1 0 + c t1 0 2 0 1) / 2
       where
-        t0 = tetrahedron0 cube
-        t3 = tetrahedron3 cube
+        t0 = tetrahedron cube 0
+        t1 = tetrahedron cube 1
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
 --   'prop_c0102_identity1'.
 prop_c1101_identity :: Cube -> Bool
 prop_c1101_identity cube =
-    c t0 1 1 0 1 ~= (c t0 1 0 1 1 + c t3 1 0 1 1) / 2
+    c t0 1 1 0 1 ~= (c t0 1 0 1 1 + c t1 1 0 1 1) / 2
       where
-        t0 = tetrahedron0 cube
-        t3 = tetrahedron3 cube
+        t0 = tetrahedron cube 0
+        t1 = tetrahedron cube 1
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
 --   'prop_c0102_identity1'.
 prop_c1200_identity2 :: Cube -> Bool
 prop_c1200_identity2 cube =
-    c t0 1 2 0 0 ~= (c t0 1 1 1 0 + c t3 1 1 0 1) / 2
+    c t0 1 2 0 0 ~= (c t0 1 1 1 0 + c t1 1 1 0 1) / 2
       where
-        t0 = tetrahedron0 cube
-        t3 = tetrahedron3 cube
+        t0 = tetrahedron cube 0
+        t1 = tetrahedron cube 1
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
 --   'prop_c0102_identity1'.
 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 0 1) / 2
+    c t0 2 1 0 0 ~= (c t0 2 0 1 0 + c t1 2 0 0 1) / 2
       where
-        t0 = tetrahedron0 cube
-        t3 = tetrahedron3 cube
+        t0 = tetrahedron cube 0
+        t1 = tetrahedron cube 1
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.8). The third and
@@ -631,8 +263,8 @@ 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
+        t0 = tetrahedron cube 0
+        t6 = tetrahedron cube 6
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
@@ -642,8 +274,8 @@ prop_c2010_identity cube =
     c t0 2 0 1 0 ~= c t0 1 1 1 0 + c t6 1 1 0 1
                     - ((c t0 1 0 2 0 + c t0 1 0 1 1)/ 2)
       where
-        t0 = tetrahedron0 cube
-        t6 = tetrahedron6 cube
+        t0 = tetrahedron cube 0
+        t6 = tetrahedron cube 6
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
@@ -653,8 +285,8 @@ prop_c2001_identity cube =
     c t0 2 0 0 1 ~= c t0 1 1 0 1 + c t6 1 1 1 0
                     - ((c t0 1 0 0 2 + c t0 1 0 1 1)/ 2)
       where
-        t0 = tetrahedron0 cube
-        t6 = tetrahedron6 cube
+        t0 = tetrahedron cube 0
+        t6 = tetrahedron cube 6
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
@@ -664,8 +296,8 @@ prop_c1020_identity cube =
     c t0 1 0 2 0 ~= c t0 0 1 2 0 + c t6 0 1 0 2
                     - ((c t0 0 0 3 0 + c t0 0 0 2 1)/ 2)
       where
-        t0 = tetrahedron0 cube
-        t6 = tetrahedron6 cube
+        t0 = tetrahedron cube 0
+        t6 = tetrahedron cube 6
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
@@ -675,8 +307,8 @@ prop_c1002_identity cube =
     c t0 1 0 0 2 ~= c t0 0 1 0 2 + c t6 0 1 2 0
                     - ((c t0 0 0 0 3 + c t0 0 0 1 2)/ 2)
       where
-        t0 = tetrahedron0 cube
-        t6 = tetrahedron6 cube
+        t0 = tetrahedron cube 0
+        t6 = tetrahedron cube 6
 
 
 -- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
@@ -686,8 +318,8 @@ 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
+        t0 = tetrahedron cube 0
+        t6 = tetrahedron cube 6
 
 
 
@@ -703,41 +335,15 @@ prop_cijk1_identity cube =
                                                       k <- [0..2],
                                                       i + j + k == 2]
       where
-        t0 = tetrahedron0 cube
-        t1 = tetrahedron1 cube
+        t0 = tetrahedron cube 0
+        t1 = tetrahedron cube 1
 
 
--- | The function values at the interior should be the same for all tetrahedra.
+-- | The function values at the interior should be the same for all
+--   tetrahedra.
 prop_interior_values_all_identical :: Cube -> Bool
 prop_interior_values_all_identical cube =
-    all_equal [i0, i1, i2, i3, i4, i5, i6, i7, i8,
-               i9, i10, i11, i12, i13, i14, i15, i16,
-               i17, i18, i19, i20, i21, i22, i23]
-    where
-      i0 = eval (Tetrahedron.fv (tetrahedron0 cube)) I
-      i1 = eval (Tetrahedron.fv (tetrahedron1 cube)) I
-      i2 = eval (Tetrahedron.fv (tetrahedron2 cube)) I
-      i3 = eval (Tetrahedron.fv (tetrahedron3 cube)) I
-      i4 = eval (Tetrahedron.fv (tetrahedron4 cube)) I
-      i5 = eval (Tetrahedron.fv (tetrahedron5 cube)) I
-      i6 = eval (Tetrahedron.fv (tetrahedron6 cube)) I
-      i7 = eval (Tetrahedron.fv (tetrahedron7 cube)) I
-      i8 = eval (Tetrahedron.fv (tetrahedron8 cube)) I
-      i9 = eval (Tetrahedron.fv (tetrahedron9 cube)) I
-      i10 = eval (Tetrahedron.fv (tetrahedron10 cube)) I
-      i11 = eval (Tetrahedron.fv (tetrahedron11 cube)) I
-      i12 = eval (Tetrahedron.fv (tetrahedron12 cube)) I
-      i13 = eval (Tetrahedron.fv (tetrahedron13 cube)) I
-      i14 = eval (Tetrahedron.fv (tetrahedron14 cube)) I
-      i15 = eval (Tetrahedron.fv (tetrahedron15 cube)) I
-      i16 = eval (Tetrahedron.fv (tetrahedron16 cube)) I
-      i17 = eval (Tetrahedron.fv (tetrahedron17 cube)) I
-      i18 = eval (Tetrahedron.fv (tetrahedron18 cube)) I
-      i19 = eval (Tetrahedron.fv (tetrahedron19 cube)) I
-      i20 = eval (Tetrahedron.fv (tetrahedron20 cube)) I
-      i21 = eval (Tetrahedron.fv (tetrahedron21 cube)) I
-      i22 = eval (Tetrahedron.fv (tetrahedron22 cube)) I
-      i23 = eval (Tetrahedron.fv (tetrahedron23 cube)) I
+    all_equal [ eval (Tetrahedron.fv tet) I | tet <- tetrahedra cube ]
 
 
 -- | We know what (c t6 2 1 0 0) should be from Sorokina and Zeilfelder, p. 87.
@@ -746,8 +352,8 @@ prop_c_tilde_2100_rotation_correct :: Cube -> Bool
 prop_c_tilde_2100_rotation_correct cube =
     expr1 == expr2
     where
-      t0 = tetrahedron0 cube
-      t6 = tetrahedron6 cube
+      t0 = tetrahedron cube 0
+      t6 = tetrahedron cube 6
 
       -- What gets computed for c2100 of t6.
       expr1 = eval (Tetrahedron.fv t6) $
@@ -770,141 +376,131 @@ prop_c_tilde_2100_rotation_correct cube =
               (1/192)*(FD + RD + LD + BD)
 
 
--- | We know what (c t6 2 1 0 0) should be from Sorokina and Zeilfelder, p. 87.
---   This test checks the actual value based on the FunctionValues of the cube.
+-- | We know what (c t6 2 1 0 0) should be from Sorokina and
+--   Zeilfelder, p. 87.  This test checks the actual value based on
+--   the FunctionValues of the cube.
+--
+--   If 'prop_c_tilde_2100_rotation_correct' passes, then this test is
+--   even meaningful!
 prop_c_tilde_2100_correct :: Cube -> Bool
 prop_c_tilde_2100_correct cube =
-    c t6 2 1 0 0 == (3/8)*int
-                    + (1/12)*(f + r + l + b)
-                    + (1/64)*(ft + rt + lt + bt)
-                    + (7/48)*t + (1/48)*d + (1/96)*(fr + fl + br + bl)
-                    + (1/192)*(fd + rd + ld + bd)
+    c t6 2 1 0 0 == expected
     where
-      t0 = tetrahedron0 cube
-      t6 = tetrahedron6 cube
+      t0 = tetrahedron cube 0
+      t6 = tetrahedron cube 6
       fvs = Tetrahedron.fv t0
-      int = interior fvs
-      f = front fvs
-      r = right fvs
-      l = left fvs
-      b = back fvs
-      ft = front_top fvs
-      rt = right_top fvs
-      lt = left_top fvs
-      bt = back_top fvs
-      t = top fvs
-      d = down fvs
-      fr = front_right fvs
-      fl = front_left fvs
-      br = back_right fvs
-      bl = back_left fvs
-      fd = front_down fvs
-      rd = right_down fvs
-      ld = left_down fvs
-      bd = back_down fvs
+      expected = eval fvs $
+                  (3/8)*I +
+                  (1/12)*(F + R + L + B) +
+                  (1/64)*(FT + RT + LT + BT) +
+                  (7/48)*T +
+                  (1/48)*D +
+                  (1/96)*(FR + FL + BR + BL) +
+                  (1/192)*(FD + RD + LD + BD)
+
 
 -- 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
+        t0 = tetrahedron cube 0
+        t1 = tetrahedron cube 1
 
 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
+        t0 = tetrahedron cube 0
+        t3 = tetrahedron cube 3
 
 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
+        t0 = tetrahedron cube 0
+        t6 = tetrahedron cube 6
 
 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
+        t1 = tetrahedron cube 1
+        t2 = tetrahedron cube 2
 
 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
+        t1 = tetrahedron cube 1
+        t19 = tetrahedron cube 19
 
 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
+        t1 = tetrahedron cube 1
+        t2 = tetrahedron cube 2
 
 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
+        t2 = tetrahedron cube 2
+        t12 = tetrahedron cube 12
 
 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
+        t3 = tetrahedron cube 3
+        t21 = tetrahedron cube 21
 
 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
+        t4 = tetrahedron cube 4
+        t5 = tetrahedron cube 5
 
 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
+        t4 = tetrahedron cube 4
+        t7 = tetrahedron cube 7
 
 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
+        t4 = tetrahedron cube 4
+        t10 = tetrahedron cube 10
 
 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
+        t5 = tetrahedron cube 5
+        t6 = tetrahedron cube 6
 
 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
+        t5 = tetrahedron cube 5
+        t16 = tetrahedron cube 16
 
 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
+        t6 = tetrahedron cube 6
+        t7 = tetrahedron cube 7
 
 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
+        t7 = tetrahedron cube 7
+        t20 = tetrahedron cube 20