src/Tests/Face.hs

   1 module Tests.Face
   2 where
   3
   4
   5
   6
   7
   8 -- -- | Given in Sorokina and Zeilfelder, p. 79.
   9 -- prop_c0102_identity1 :: Cube -> Bool
  10 -- prop_c0102_identity1 cube =
  11 --     c t0' 0 1 0 2 ~= (c t0' 0 0 1 2 + c t3' 0 0 1 2) / 2
  12 --       where
  13 --         t0 = tetrahedron0 (face0 cube)
  14 --         t3 = tetrahedron3 (face0 cube)
  15 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  16 --         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
  17
  18
  19 -- -- | Given in Sorokina and Zeilfelder, p. 79.
  20 -- prop_c0201_identity1 :: Cube -> Bool
  21 -- prop_c0201_identity1 cube =
  22 --     c t0' 0 2 0 1 ~= (c t0' 0 1 1 1 + c t3' 0 1 1 1) / 2
  23 --       where
  24 --         t0 = tetrahedron0 (face0 cube)
  25 --         t3 = tetrahedron3 (face0 cube)
  26 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  27 --         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
  28
  29
  30 -- -- | Given in Sorokina and Zeilfelder, p. 79.
  31 -- prop_c0300_identity2 :: Cube -> Bool
  32 -- prop_c0300_identity2 cube =
  33 --     c t0' 3 0 0 0 ~= (c t0' 0 2 1 0 + c t3' 0 2 1 0) / 2
  34 --       where
  35 --         t0 = tetrahedron0 (face0 cube)
  36 --         t3 = tetrahedron3 (face0 cube)
  37 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  38 --         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
  39
  40 -- -- | Given in Sorokina and Zeilfelder, p. 79.
  41 -- prop_c1101_identity :: Cube -> Bool
  42 -- prop_c1101_identity cube =
  43 --     c t0' 1 1 0 1 ~= (c t0' 1 1 0 1 + c t3' 1 1 0 1) / 2
  44 --       where
  45 --         t0 = tetrahedron0 (face0 cube)
  46 --         t3 = tetrahedron3 (face0 cube)
  47 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  48 --         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
  49
  50
  51 -- -- | Given in Sorokina and Zeilfelder, p. 79.
  52 -- prop_c1200_identity2 :: Cube -> Bool
  53 -- prop_c1200_identity2 cube =
  54 --     c t0' 1 1 1 0 ~= (c t0' 1 1 1 0 + c t3' 1 1 1 0) / 2
  55 --       where
  56 --         t0 = tetrahedron0 (face0 cube)
  57 --         t3 = tetrahedron3 (face0 cube)
  58 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  59 --         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
  60
  61
  62 -- -- | Given in Sorokina and Zeilfelder, p. 79.
  63 -- prop_c2100_identity2 :: Cube -> Bool
  64 -- prop_c2100_identity2 cube =
  65 --     c t0' 2 1 0 0 ~= (c t0' 2 0 1 0 + c t3' 2 0 1 0) / 2
  66 --       where
  67 --         t0 = tetrahedron0 (face0 cube)
  68 --         t3 = tetrahedron3 (face0 cube)
  69 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  70 --         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
  71
  72
  73 -- -- | Given in Sorokina and Zeilfelder, p. 79.
  74 -- prop_c3000_identity :: Cube -> Bool
  75 -- prop_c3000_identity cube =
  76 --     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)
  77 --       where
  78 --         t0 = tetrahedron0 (face0 cube)
  79 --         t2 = tetrahedron2 (face5 cube)
  80 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  81 --         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
  82
  83
  84 -- -- | Given in Sorokina and Zeilfelder, p. 79.
  85 -- prop_c2010_identity :: Cube -> Bool
  86 -- prop_c2010_identity cube =
  87 --     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)
  88 --       where
  89 --         t0 = tetrahedron0 (face0 cube)
  90 --         t2 = tetrahedron2 (face5 cube)
  91 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  92 --         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
  93
  94
  95 -- -- | Given in Sorokina and Zeilfelder, p. 79.
  96 -- prop_c2001_identity :: Cube -> Bool
  97 -- prop_c2001_identity cube =
  98 --     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)
  99 --       where
 100 --         t0 = tetrahedron0 (face0 cube)
 101 --         t2 = tetrahedron2 (face5 cube)
 102 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 103 --         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 104
 105 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 106 -- prop_c1020_identity :: Cube -> Bool
 107 -- prop_c1020_identity cube =
 108 --     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)
 109 --       where
 110 --         t0 = tetrahedron0 (face0 cube)
 111 --         t2 = tetrahedron2 (face5 cube)
 112 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 113 --         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 114
 115
 116 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 117 -- prop_c1002_identity :: Cube -> Bool
 118 -- prop_c1002_identity cube =
 119 --     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)
 120 --       where
 121 --         t0 = tetrahedron0 (face0 cube)
 122 --         t2 = tetrahedron2 (face5 cube)
 123 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 124 --         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 125
 126
 127 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 128 -- prop_c1011_identity :: Cube -> Bool
 129 -- prop_c1011_identity cube =
 130 --     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)
 131 --       where
 132 --         t0 = tetrahedron0 (face0 cube)
 133 --         t2 = tetrahedron2 (face5 cube)
 134 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 135 --         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 136
 137
 138 -- -- | Given in Sorokina and Zeilfelder, p. 80.
 139 -- prop_c0120_identity2 :: Cube -> Bool
 140 -- prop_c0120_identity2 cube =
 141 --         c t0' 0 1 2 0 ~= (c t0' 1 0 2 0 + c t1' 1 0 2 0) / 2
 142 --       where
 143 --         t0 = tetrahedron0 (face0 cube)
 144 --         t1 = tetrahedron0 (face2 (top cube))
 145 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 146 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 147
 148
 149 -- -- | Given in Sorokina and Zeilfelder, p. 80.
 150 -- prop_c0102_identity2 :: Cube -> Bool
 151 -- prop_c0102_identity2 cube =
 152 --     c t0' 0 1 0 2 ~= (c t0' 1 0 0 2 + c t1' 1 0 0 2) / 2
 153 --       where
 154 --         t0 = tetrahedron0 (face0 cube)
 155 --         t1 = tetrahedron0 (face2 (top cube))
 156 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 157 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 158
 159
 160 -- -- | Given in Sorokina and Zeilfelder, p. 80.
 161 -- prop_c0111_identity :: Cube -> Bool
 162 -- prop_c0111_identity cube =
 163 --     c t0' 0 1 1 1 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
 164 --       where
 165 --         t0 = tetrahedron0 (face0 cube)
 166 --         t1 = tetrahedron0 (face2 (top cube))
 167 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 168 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 169
 170
 171 -- -- | Given in Sorokina and Zeilfelder, p. 80.
 172 -- prop_c0210_identity2 :: Cube -> Bool
 173 -- prop_c0210_identity2 cube =
 174 --     c t0 0 2 1 0 ~= (c t0 1 1 1 0 + c t1 1 1 1 0) / 2
 175 --       where
 176 --         t0 = tetrahedron0 (face0 cube)
 177 --         t1 = tetrahedron0 (face2 (top cube))
 178 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 179 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 180
 181
 182 -- -- | Given in Sorokina and Zeilfelder, p. 80.
 183 -- prop_c0201_identity2 :: Cube -> Bool
 184 -- prop_c0201_identity2 cube =
 185 --     c t0 0 2 0 1 ~= (c t0 1 1 0 1 + c t1 1 1 0 1) / 2
 186 --       where
 187 --         t0 = tetrahedron0 (face0 cube)
 188 --         t1 = tetrahedron0 (face2 (top cube))
 189 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 190 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 191
 192
 193 -- -- | Given in Sorokina and Zeilfelder, p. 80.
 194 -- prop_c0300_identity3 :: Cube -> Bool
 195 -- prop_c0300_identity3 cube =
 196 --     c t0 0 3 0 0 ~= (c t0 1 2 0 0 + c t1 1 2 0 0) / 2
 197 --       where
 198 --         t0 = tetrahedron0 (face0 cube)
 199 --         t1 = tetrahedron0 (face2 (top cube))
 200 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 201 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)