src/Tests/Face.hs

   1 module Tests.Face
   2 where
   3
   4 -- -- | Given in Sorokina and Zeilfelder, p. 79.
   5 -- prop_c0210_identity1 :: Cube -> Bool
   6 -- prop_c0210_identity1 cube =
   7 --     c t0' 0 2 1 0 ~= (c t0' 0 1 1 1 + c t1' 0 1 1 1) / 2
   8 --       where
   9 --         t0 = tetrahedron0 (face0 cube)
  10 --         t1 = tetrahedron1 (face0 cube)
  11 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  12 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
  13
  14
  15 -- -- | Given in Sorokina and Zeilfelder, p. 79.
  16 -- prop_c0300_identity1 :: Cube -> Bool
  17 -- prop_c0300_identity1 cube =
  18 --     c t0' 0 3 0 0 ~= (c t0' 0 2 0 1 + c t1' 0 2 0 1) / 2
  19 --       where
  20 --         t0 = tetrahedron0 (face0 cube)
  21 --         t1 = tetrahedron1 (face0 cube)
  22 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  23 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
  24
  25 -- -- | Given in Sorokina and Zeilfelder, p. 79.
  26 -- prop_c1110_identity :: Cube -> Bool
  27 -- prop_c1110_identity cube =
  28 --     c t0' 1 1 1 0 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
  29 --       where
  30 --         t0 = tetrahedron0 (face0 cube)
  31 --         t1 = tetrahedron1 (face0 cube)
  32 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  33 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
  34
  35
  36 -- -- | Given in Sorokina and Zeilfelder, p. 79.
  37 -- prop_c1200_identity1 :: Cube -> Bool
  38 -- prop_c1200_identity1 cube =
  39 --     c t0' 1 2 0 0 ~= (c t0' 1 1 0 1 + c t1' 1 1 0 1) / 2
  40 --       where
  41 --         t0 = tetrahedron0 (face0 cube)
  42 --         t1 = tetrahedron1 (face0 cube)
  43 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  44 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
  45
  46
  47 -- -- | Given in Sorokina and Zeilfelder, p. 79.
  48 -- prop_c2100_identity1 :: Cube -> Bool
  49 -- prop_c2100_identity1 cube =
  50 --     c t0' 2 1 0 0 ~= (c t0' 2 0 0 1 + c t1' 2 0 0 1) / 2
  51 --       where
  52 --         t0 = tetrahedron0 (face0 cube)
  53 --         t1 = tetrahedron1 (face0 cube)
  54 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  55 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
  56
  57
  58 -- -- | Given in Sorokina and Zeilfelder, p. 79.
  59 -- prop_c0102_identity1 :: Cube -> Bool
  60 -- prop_c0102_identity1 cube =
  61 --     c t0' 0 1 0 2 ~= (c t0' 0 0 1 2 + c t3' 0 0 1 2) / 2
  62 --       where
  63 --         t0 = tetrahedron0 (face0 cube)
  64 --         t3 = tetrahedron3 (face0 cube)
  65 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  66 --         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
  67
  68
  69 -- -- | Given in Sorokina and Zeilfelder, p. 79.
  70 -- prop_c0201_identity1 :: Cube -> Bool
  71 -- prop_c0201_identity1 cube =
  72 --     c t0' 0 2 0 1 ~= (c t0' 0 1 1 1 + c t3' 0 1 1 1) / 2
  73 --       where
  74 --         t0 = tetrahedron0 (face0 cube)
  75 --         t3 = tetrahedron3 (face0 cube)
  76 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  77 --         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
  78
  79
  80 -- -- | Given in Sorokina and Zeilfelder, p. 79.
  81 -- prop_c0300_identity2 :: Cube -> Bool
  82 -- prop_c0300_identity2 cube =
  83 --     c t0' 3 0 0 0 ~= (c t0' 0 2 1 0 + c t3' 0 2 1 0) / 2
  84 --       where
  85 --         t0 = tetrahedron0 (face0 cube)
  86 --         t3 = tetrahedron3 (face0 cube)
  87 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  88 --         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
  89
  90 -- -- | Given in Sorokina and Zeilfelder, p. 79.
  91 -- prop_c1101_identity :: Cube -> Bool
  92 -- prop_c1101_identity cube =
  93 --     c t0' 1 1 0 1 ~= (c t0' 1 1 0 1 + c t3' 1 1 0 1) / 2
  94 --       where
  95 --         t0 = tetrahedron0 (face0 cube)
  96 --         t3 = tetrahedron3 (face0 cube)
  97 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  98 --         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
  99
 100
 101 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 102 -- prop_c1200_identity2 :: Cube -> Bool
 103 -- prop_c1200_identity2 cube =
 104 --     c t0' 1 1 1 0 ~= (c t0' 1 1 1 0 + c t3' 1 1 1 0) / 2
 105 --       where
 106 --         t0 = tetrahedron0 (face0 cube)
 107 --         t3 = tetrahedron3 (face0 cube)
 108 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 109 --         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 110
 111
 112 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 113 -- prop_c2100_identity2 :: Cube -> Bool
 114 -- prop_c2100_identity2 cube =
 115 --     c t0' 2 1 0 0 ~= (c t0' 2 0 1 0 + c t3' 2 0 1 0) / 2
 116 --       where
 117 --         t0 = tetrahedron0 (face0 cube)
 118 --         t3 = tetrahedron3 (face0 cube)
 119 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 120 --         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 121
 122
 123 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 124 -- prop_c3000_identity :: Cube -> Bool
 125 -- prop_c3000_identity cube =
 126 --     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)
 127 --       where
 128 --         t0 = tetrahedron0 (face0 cube)
 129 --         t2 = tetrahedron2 (face5 cube)
 130 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 131 --         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 132
 133
 134 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 135 -- prop_c2010_identity :: Cube -> Bool
 136 -- prop_c2010_identity cube =
 137 --     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)
 138 --       where
 139 --         t0 = tetrahedron0 (face0 cube)
 140 --         t2 = tetrahedron2 (face5 cube)
 141 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 142 --         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 143
 144
 145 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 146 -- prop_c2001_identity :: Cube -> Bool
 147 -- prop_c2001_identity cube =
 148 --     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)
 149 --       where
 150 --         t0 = tetrahedron0 (face0 cube)
 151 --         t2 = tetrahedron2 (face5 cube)
 152 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 153 --         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 154
 155 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 156 -- prop_c1020_identity :: Cube -> Bool
 157 -- prop_c1020_identity cube =
 158 --     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)
 159 --       where
 160 --         t0 = tetrahedron0 (face0 cube)
 161 --         t2 = tetrahedron2 (face5 cube)
 162 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 163 --         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 164
 165
 166 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 167 -- prop_c1002_identity :: Cube -> Bool
 168 -- prop_c1002_identity cube =
 169 --     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)
 170 --       where
 171 --         t0 = tetrahedron0 (face0 cube)
 172 --         t2 = tetrahedron2 (face5 cube)
 173 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 174 --         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 175
 176
 177 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 178 -- prop_c1011_identity :: Cube -> Bool
 179 -- prop_c1011_identity cube =
 180 --     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)
 181 --       where
 182 --         t0 = tetrahedron0 (face0 cube)
 183 --         t2 = tetrahedron2 (face5 cube)
 184 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 185 --         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 186
 187
 188 -- -- | Given in Sorokina and Zeilfelder, p. 80.
 189 -- prop_c0120_identity2 :: Cube -> Bool
 190 -- prop_c0120_identity2 cube =
 191 --         c t0' 0 1 2 0 ~= (c t0' 1 0 2 0 + c t1' 1 0 2 0) / 2
 192 --       where
 193 --         t0 = tetrahedron0 (face0 cube)
 194 --         t1 = tetrahedron0 (face2 (top cube))
 195 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 196 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 197
 198
 199 -- -- | Given in Sorokina and Zeilfelder, p. 80.
 200 -- prop_c0102_identity2 :: Cube -> Bool
 201 -- prop_c0102_identity2 cube =
 202 --     c t0' 0 1 0 2 ~= (c t0' 1 0 0 2 + c t1' 1 0 0 2) / 2
 203 --       where
 204 --         t0 = tetrahedron0 (face0 cube)
 205 --         t1 = tetrahedron0 (face2 (top cube))
 206 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 207 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 208
 209
 210 -- -- | Given in Sorokina and Zeilfelder, p. 80.
 211 -- prop_c0111_identity :: Cube -> Bool
 212 -- prop_c0111_identity cube =
 213 --     c t0' 0 1 1 1 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
 214 --       where
 215 --         t0 = tetrahedron0 (face0 cube)
 216 --         t1 = tetrahedron0 (face2 (top cube))
 217 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 218 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 219
 220
 221 -- -- | Given in Sorokina and Zeilfelder, p. 80.
 222 -- prop_c0210_identity2 :: Cube -> Bool
 223 -- prop_c0210_identity2 cube =
 224 --     c t0 0 2 1 0 ~= (c t0 1 1 1 0 + c t1 1 1 1 0) / 2
 225 --       where
 226 --         t0 = tetrahedron0 (face0 cube)
 227 --         t1 = tetrahedron0 (face2 (top cube))
 228 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 229 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 230
 231
 232 -- -- | Given in Sorokina and Zeilfelder, p. 80.
 233 -- prop_c0201_identity2 :: Cube -> Bool
 234 -- prop_c0201_identity2 cube =
 235 --     c t0 0 2 0 1 ~= (c t0 1 1 0 1 + c t1 1 1 0 1) / 2
 236 --       where
 237 --         t0 = tetrahedron0 (face0 cube)
 238 --         t1 = tetrahedron0 (face2 (top cube))
 239 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 240 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 241
 242
 243 -- -- | Given in Sorokina and Zeilfelder, p. 80.
 244 -- prop_c0300_identity3 :: Cube -> Bool
 245 -- prop_c0300_identity3 cube =
 246 --     c t0 0 3 0 0 ~= (c t0 1 2 0 0 + c t1 1 2 0 0) / 2
 247 --       where
 248 --         t0 = tetrahedron0 (face0 cube)
 249 --         t1 = tetrahedron0 (face2 (top cube))
 250 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 251 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)