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
+ t0 = tetrahedron cube 0
+ t3 = tetrahedron cube 3
-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
prop_c0120_identity2 cube =
c t1 0 1 2 0 ~= (c t1 0 0 2 1 + c t0 0 0 1 2) / 2
where
- t0 = tetrahedron0 cube
- t1 = tetrahedron1 cube
+ t0 = tetrahedron cube 0
+ t1 = tetrahedron cube 1
-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
-- 'prop_c0120_identity1' with tetrahedrons 1 and 2.
prop_c0120_identity3 cube =
c t2 0 1 2 0 ~= (c t2 0 0 2 1 + c t1 0 0 1 2) / 2
where
- t1 = tetrahedron1 cube
- t2 = tetrahedron2 cube
+ 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 =
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_identity5 cube =
c t5 0 1 2 0 ~= (c t5 0 0 2 1 + c t4 0 0 1 2) / 2
where
- t4 = tetrahedron4 cube
- t5 = tetrahedron5 cube
+ 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_identity6 cube =
c t6 0 1 2 0 ~= (c t6 0 0 2 1 + c t5 0 0 1 2) / 2
where
- t5 = tetrahedron5 cube
- t6 = tetrahedron6 cube
+ t5 = tetrahedron cube 5
+ t6 = tetrahedron cube 6
-- -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
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 = tetrahedron6 cube
- t7 = tetrahedron7 cube
+ t6 = tetrahedron cube 6
+ t7 = tetrahedron cube 7
-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
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
+ t0 = tetrahedron cube 0
+ t3 = tetrahedron cube 3
-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
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
+ t0 = tetrahedron cube 0
+ t3 = tetrahedron cube 3
-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
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
+ t0 = tetrahedron cube 0
+ t3 = tetrahedron cube 3
-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
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
+ t0 = tetrahedron cube 0
+ t3 = tetrahedron cube 3
-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
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
+ t0 = tetrahedron cube 0
+ t3 = tetrahedron cube 3
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
+ t0 = tetrahedron cube 0
+ t1 = tetrahedron cube 1
-- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
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
+ t0 = tetrahedron cube 0
+ t1 = tetrahedron cube 1
-- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
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
+ t0 = tetrahedron cube 0
+ t1 = tetrahedron cube 1
-- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
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
+ t0 = tetrahedron cube 0
+ t1 = tetrahedron cube 1
-- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
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
+ t0 = tetrahedron cube 0
+ t1 = tetrahedron cube 1
-- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
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
+ t0 = tetrahedron cube 0
+ t1 = tetrahedron cube 1
-- | Given in Sorokina and Zeilfelder, p. 79, (2.8). The third and
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
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
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
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
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
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
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.
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) $
prop_c_tilde_2100_correct cube =
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
expected = eval fvs $
(3/8)*I +
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
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