src/Tests/Cube.hs

   1 module Tests.Cube
   2 where
   3
   4 import Prelude hiding (LT)
   5
   6 import Cardinal
   7 import Comparisons
   8 import Cube hiding (i, j, k)
   9 import FunctionValues
  10 import Misc (all_equal, disjoint)
  11 import Tests.FunctionValues ()
  12 import Tetrahedron (b0, b1, b2, b3, c, fv,
  13                     v0, v1, v2, v3, volume)
  14
  15
  16 -- Quickcheck tests.
  17
  18 -- | The 'front_half_tetrahedra' and 'back_half_tetrahedra' should
  19 --   have no tetrahedra in common.
  20 prop_front_back_tetrahedra_disjoint :: Cube -> Bool
  21 prop_front_back_tetrahedra_disjoint c =
  22     disjoint (front_half_tetrahedra c) (back_half_tetrahedra c)
  23
  24
  25 -- | The 'top_half_tetrahedra' and 'down_half_tetrahedra' should
  26 --   have no tetrahedra in common.
  27 prop_top_down_tetrahedra_disjoint :: Cube -> Bool
  28 prop_top_down_tetrahedra_disjoint c =
  29     disjoint (top_half_tetrahedra c) (down_half_tetrahedra c)
  30
  31
  32 -- | The 'left_half_tetrahedra' and 'right_half_tetrahedra' should
  33 --   have no tetrahedra in common.
  34 prop_left_right_tetrahedra_disjoint :: Cube -> Bool
  35 prop_left_right_tetrahedra_disjoint c =
  36     disjoint (left_half_tetrahedra c) (right_half_tetrahedra c)
  37
  38
  39 -- | Since the grid size is necessarily positive, all tetrahedra
  40 --   (which comprise cubes of positive volume) must have positive volume
  41 --   as well.
  42 prop_all_volumes_positive :: Cube -> Bool
  43 prop_all_volumes_positive cube =
  44     null nonpositive_volumes
  45     where
  46       ts = tetrahedra cube
  47       volumes = map volume ts
  48       nonpositive_volumes = filter (<= 0) volumes
  49
  50 -- | In fact, since all of the tetrahedra are identical, we should
  51 --   already know their volumes. There's 24 tetrahedra to a cube, so
  52 --   we'd expect the volume of each one to be (1/24)*h^3.
  53 prop_all_volumes_exact :: Cube -> Bool
  54 prop_all_volumes_exact cube =
  55     and [volume t ~~= (1/24)*(delta^(3::Int)) | t <- tetrahedra cube]
  56     where
  57       delta = h cube
  58
  59 -- | All tetrahedron should have their v0 located at the center of the cube.
  60 prop_v0_all_equal :: Cube -> Bool
  61 prop_v0_all_equal cube = (v0 t0) == (v0 t1)
  62     where
  63       t0 = head (tetrahedra cube) -- Doesn't matter which two we choose.
  64       t1 = head $ tail (tetrahedra cube)
  65
  66
  67 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Note that the
  68 --   third and fourth indices of c-t1 have been switched. This is
  69 --   because we store the triangles oriented such that their volume is
  70 --   positive. If T and T-tilde share \<v0,v1,v2\> and v3,v3-tilde point
  71 --   in opposite directions, one of them has to have negative volume!
  72 prop_c0120_identity1 :: Cube -> Bool
  73 prop_c0120_identity1 cube =
  74    c t0 0 1 2 0 ~= (c t0 0 0 2 1 + c t3 0 0 1 2) / 2
  75      where
  76        t0 = tetrahedron0 cube
  77        t3 = tetrahedron3 cube
  78
  79
  80 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
  81 --   'prop_c0120_identity1' with tetrahedrons 1 and 2.
  82 prop_c0120_identity2 :: Cube -> Bool
  83 prop_c0120_identity2 cube =
  84    c t1 0 1 2 0 ~= (c t1 0 0 2 1 + c t0 0 0 1 2) / 2
  85      where
  86        t0 = tetrahedron0 cube
  87        t1 = tetrahedron1 cube
  88
  89 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
  90 --   'prop_c0120_identity1' with tetrahedrons 1 and 2.
  91 prop_c0120_identity3 :: Cube -> Bool
  92 prop_c0120_identity3 cube =
  93    c t2 0 1 2 0 ~= (c t2 0 0 2 1 + c t1 0 0 1 2) / 2
  94      where
  95        t1 = tetrahedron1 cube
  96        t2 = tetrahedron2 cube
  97
  98 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
  99 --   'prop_c0120_identity1' with tetrahedrons 2 and 3.
 100 prop_c0120_identity4 :: Cube -> Bool
 101 prop_c0120_identity4 cube =
 102    c t3 0 1 2 0 ~= (c t3 0 0 2 1 + c t2 0 0 1 2) / 2
 103      where
 104        t2 = tetrahedron2 cube
 105        t3 = tetrahedron3 cube
 106
 107
 108 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
 109 --   'prop_c0120_identity1' with tetrahedrons 4 and 5.
 110 prop_c0120_identity5 :: Cube -> Bool
 111 prop_c0120_identity5 cube =
 112     c t5 0 1 2 0 ~= (c t5 0 0 2 1 + c t4 0 0 1 2) / 2
 113     where
 114       t4 = tetrahedron4 cube
 115       t5 = tetrahedron5 cube
 116
 117 -- -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
 118 -- --   'prop_c0120_identity1' with tetrahedrons 5 and 6.
 119 prop_c0120_identity6 :: Cube -> Bool
 120 prop_c0120_identity6 cube =
 121    c t6 0 1 2 0 ~= (c t6 0 0 2 1 + c t5 0 0 1 2) / 2
 122      where
 123        t5 = tetrahedron5 cube
 124        t6 = tetrahedron6 cube
 125
 126
 127 -- -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
 128 -- --   'prop_c0120_identity1' with tetrahedrons 6 and 7.
 129 prop_c0120_identity7 :: Cube -> Bool
 130 prop_c0120_identity7 cube =
 131    c t7 0 1 2 0 ~= (c t7 0 0 2 1 + c t6 0 0 1 2) / 2
 132      where
 133        t6 = tetrahedron6 cube
 134        t7 = tetrahedron7 cube
 135
 136
 137 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
 138 --   'prop_c0120_identity1'.
 139 prop_c0210_identity1 :: Cube -> Bool
 140 prop_c0210_identity1 cube =
 141     c t0 0 2 1 0 ~= (c t0 0 1 1 1 + c t3 0 1 1 1) / 2
 142       where
 143         t0 = tetrahedron0 cube
 144         t3 = tetrahedron3 cube
 145
 146
 147 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
 148 --   'prop_c0120_identity1'.
 149 prop_c0300_identity1 :: Cube -> Bool
 150 prop_c0300_identity1 cube =
 151     c t0 0 3 0 0 ~= (c t0 0 2 0 1 + c t3 0 2 1 0) / 2
 152       where
 153         t0 = tetrahedron0 cube
 154         t3 = tetrahedron3 cube
 155
 156
 157 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
 158 --   'prop_c0120_identity1'.
 159 prop_c1110_identity :: Cube -> Bool
 160 prop_c1110_identity cube =
 161     c t0 1 1 1 0 ~= (c t0 1 0 1 1 + c t3 1 0 1 1) / 2
 162       where
 163         t0 = tetrahedron0 cube
 164         t3 = tetrahedron3 cube
 165
 166
 167 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
 168 --   'prop_c0120_identity1'.
 169 prop_c1200_identity1 :: Cube -> Bool
 170 prop_c1200_identity1 cube =
 171     c t0 1 2 0 0 ~= (c t0 1 1 0 1 + c t3 1 1 1 0) / 2
 172       where
 173         t0 = tetrahedron0 cube
 174         t3 = tetrahedron3 cube
 175
 176
 177 -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
 178 --   'prop_c0120_identity1'.
 179 prop_c2100_identity1 :: Cube -> Bool
 180 prop_c2100_identity1 cube =
 181     c t0 2 1 0 0 ~= (c t0 2 0 0 1 + c t3 2 0 1 0) / 2
 182       where
 183         t0 = tetrahedron0 cube
 184         t3 = tetrahedron3 cube
 185
 186
 187
 188 -- | Given in Sorokina and Zeilfelder, p. 79, (2.7). Note that the
 189 --   third and fourth indices of c-t3 have been switched. This is
 190 --   because we store the triangles oriented such that their volume is
 191 --   positive. If T and T-tilde share \<v0,v1,v2\> and v3,v3-tilde
 192 --   point in opposite directions, one of them has to have negative
 193 --   volume!
 194 prop_c0102_identity1 :: Cube -> Bool
 195 prop_c0102_identity1 cube =
 196     c t0 0 1 0 2 ~= (c t0 0 0 1 2 + c t1 0 0 2 1) / 2
 197       where
 198         t0 = tetrahedron0 cube
 199         t1 = tetrahedron1 cube
 200
 201
 202 -- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
 203 --   'prop_c0102_identity1'.
 204 prop_c0201_identity1 :: Cube -> Bool
 205 prop_c0201_identity1 cube =
 206     c t0 0 2 0 1 ~= (c t0 0 1 1 1 + c t1 0 1 1 1) / 2
 207       where
 208         t0 = tetrahedron0 cube
 209         t1 = tetrahedron1 cube
 210
 211
 212 -- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
 213 --   'prop_c0102_identity1'.
 214 prop_c0300_identity2 :: Cube -> Bool
 215 prop_c0300_identity2 cube =
 216     c t0 0 3 0 0 ~= (c t0 0 2 1 0 + c t1 0 2 0 1) / 2
 217       where
 218         t0 = tetrahedron0 cube
 219         t1 = tetrahedron1 cube
 220
 221
 222 -- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
 223 --   'prop_c0102_identity1'.
 224 prop_c1101_identity :: Cube -> Bool
 225 prop_c1101_identity cube =
 226     c t0 1 1 0 1 ~= (c t0 1 0 1 1 + c t1 1 0 1 1) / 2
 227       where
 228         t0 = tetrahedron0 cube
 229         t1 = tetrahedron1 cube
 230
 231
 232 -- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
 233 --   'prop_c0102_identity1'.
 234 prop_c1200_identity2 :: Cube -> Bool
 235 prop_c1200_identity2 cube =
 236     c t0 1 2 0 0 ~= (c t0 1 1 1 0 + c t1 1 1 0 1) / 2
 237       where
 238         t0 = tetrahedron0 cube
 239         t1 = tetrahedron1 cube
 240
 241
 242 -- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
 243 --   'prop_c0102_identity1'.
 244 prop_c2100_identity2 :: Cube -> Bool
 245 prop_c2100_identity2 cube =
 246     c t0 2 1 0 0 ~= (c t0 2 0 1 0 + c t1 2 0 0 1) / 2
 247       where
 248         t0 = tetrahedron0 cube
 249         t1 = tetrahedron1 cube
 250
 251
 252 -- | Given in Sorokina and Zeilfelder, p. 79, (2.8). The third and
 253 --   fourth indices of c-t6 have been switched. This is because we
 254 --   store the triangles oriented such that their volume is
 255 --   positive. If T and T-tilde share \<v0,v1,v2\> and v3,v3-tilde
 256 --   point in opposite directions, one of them has to have negative
 257 --   volume!
 258 prop_c3000_identity :: Cube -> Bool
 259 prop_c3000_identity cube =
 260     c t0 3 0 0 0 ~= c t0 2 1 0 0 + c t6 2 1 0 0
 261                     - ((c t0 2 0 1 0 + c t0 2 0 0 1)/ 2)
 262       where
 263         t0 = tetrahedron0 cube
 264         t6 = tetrahedron6 cube
 265
 266
 267 -- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
 268 --   'prop_c3000_identity'.
 269 prop_c2010_identity :: Cube -> Bool
 270 prop_c2010_identity cube =
 271     c t0 2 0 1 0 ~= c t0 1 1 1 0 + c t6 1 1 0 1
 272                     - ((c t0 1 0 2 0 + c t0 1 0 1 1)/ 2)
 273       where
 274         t0 = tetrahedron0 cube
 275         t6 = tetrahedron6 cube
 276
 277
 278 -- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
 279 --   'prop_c3000_identity'.
 280 prop_c2001_identity :: Cube -> Bool
 281 prop_c2001_identity cube =
 282     c t0 2 0 0 1 ~= c t0 1 1 0 1 + c t6 1 1 1 0
 283                     - ((c t0 1 0 0 2 + c t0 1 0 1 1)/ 2)
 284       where
 285         t0 = tetrahedron0 cube
 286         t6 = tetrahedron6 cube
 287
 288
 289 -- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
 290 --   'prop_c3000_identity'.
 291 prop_c1020_identity :: Cube -> Bool
 292 prop_c1020_identity cube =
 293     c t0 1 0 2 0 ~= c t0 0 1 2 0 + c t6 0 1 0 2
 294                     - ((c t0 0 0 3 0 + c t0 0 0 2 1)/ 2)
 295       where
 296         t0 = tetrahedron0 cube
 297         t6 = tetrahedron6 cube
 298
 299
 300 -- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
 301 --   'prop_c3000_identity'.
 302 prop_c1002_identity :: Cube -> Bool
 303 prop_c1002_identity cube =
 304     c t0 1 0 0 2 ~= c t0 0 1 0 2 + c t6 0 1 2 0
 305                     - ((c t0 0 0 0 3 + c t0 0 0 1 2)/ 2)
 306       where
 307         t0 = tetrahedron0 cube
 308         t6 = tetrahedron6 cube
 309
 310
 311 -- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
 312 --   'prop_c3000_identity'.
 313 prop_c1011_identity :: Cube -> Bool
 314 prop_c1011_identity cube =
 315     c t0 1 0 1 1 ~= c t0 0 1 1 1 + c t6 0 1 1 1 -
 316                     ((c t0 0 0 1 2 + c t0 0 0 2 1)/ 2)
 317       where
 318         t0 = tetrahedron0 cube
 319         t6 = tetrahedron6 cube
 320
 321
 322
 323 -- | Given in Sorokina and Zeilfelder, p. 78.
 324 prop_cijk1_identity :: Cube -> Bool
 325 prop_cijk1_identity cube =
 326      and [ c t0 i j k 1 ~=
 327                  (c t1 (i+1) j k 0) * ((b0 t0) (v3 t1)) +
 328                  (c t1 i (j+1) k 0) * ((b1 t0) (v3 t1)) +
 329                  (c t1 i j (k+1) 0) * ((b2 t0) (v3 t1)) +
 330                  (c t1 i j k 1) * ((b3 t0) (v3 t1)) | i <- [0..2],
 331                                                       j <- [0..2],
 332                                                       k <- [0..2],
 333                                                       i + j + k == 2]
 334       where
 335         t0 = tetrahedron0 cube
 336         t1 = tetrahedron1 cube
 337
 338
 339 -- | The function values at the interior should be the same for all tetrahedra.
 340 prop_interior_values_all_identical :: Cube -> Bool
 341 prop_interior_values_all_identical cube =
 342     all_equal [i0, i1, i2, i3, i4, i5, i6, i7, i8,
 343                i9, i10, i11, i12, i13, i14, i15, i16,
 344                i17, i18, i19, i20, i21, i22, i23]
 345     where
 346       i0 = eval (Tetrahedron.fv (tetrahedron0 cube)) I
 347       i1 = eval (Tetrahedron.fv (tetrahedron1 cube)) I
 348       i2 = eval (Tetrahedron.fv (tetrahedron2 cube)) I
 349       i3 = eval (Tetrahedron.fv (tetrahedron3 cube)) I
 350       i4 = eval (Tetrahedron.fv (tetrahedron4 cube)) I
 351       i5 = eval (Tetrahedron.fv (tetrahedron5 cube)) I
 352       i6 = eval (Tetrahedron.fv (tetrahedron6 cube)) I
 353       i7 = eval (Tetrahedron.fv (tetrahedron7 cube)) I
 354       i8 = eval (Tetrahedron.fv (tetrahedron8 cube)) I
 355       i9 = eval (Tetrahedron.fv (tetrahedron9 cube)) I
 356       i10 = eval (Tetrahedron.fv (tetrahedron10 cube)) I
 357       i11 = eval (Tetrahedron.fv (tetrahedron11 cube)) I
 358       i12 = eval (Tetrahedron.fv (tetrahedron12 cube)) I
 359       i13 = eval (Tetrahedron.fv (tetrahedron13 cube)) I
 360       i14 = eval (Tetrahedron.fv (tetrahedron14 cube)) I
 361       i15 = eval (Tetrahedron.fv (tetrahedron15 cube)) I
 362       i16 = eval (Tetrahedron.fv (tetrahedron16 cube)) I
 363       i17 = eval (Tetrahedron.fv (tetrahedron17 cube)) I
 364       i18 = eval (Tetrahedron.fv (tetrahedron18 cube)) I
 365       i19 = eval (Tetrahedron.fv (tetrahedron19 cube)) I
 366       i20 = eval (Tetrahedron.fv (tetrahedron20 cube)) I
 367       i21 = eval (Tetrahedron.fv (tetrahedron21 cube)) I
 368       i22 = eval (Tetrahedron.fv (tetrahedron22 cube)) I
 369       i23 = eval (Tetrahedron.fv (tetrahedron23 cube)) I
 370
 371
 372 -- | We know what (c t6 2 1 0 0) should be from Sorokina and Zeilfelder, p. 87.
 373 --   This test checks the rotation works as expected.
 374 prop_c_tilde_2100_rotation_correct :: Cube -> Bool
 375 prop_c_tilde_2100_rotation_correct cube =
 376     expr1 == expr2
 377     where
 378       t0 = tetrahedron0 cube
 379       t6 = tetrahedron6 cube
 380
 381       -- What gets computed for c2100 of t6.
 382       expr1 = eval (Tetrahedron.fv t6) $
 383           (3/8)*I +
 384           (1/12)*(T + R + L + D) +
 385           (1/64)*(FT + FR + FL + FD) +
 386           (7/48)*F +
 387           (1/48)*B +
 388           (1/96)*(RT + LD + LT + RD) +
 389           (1/192)*(BT + BR + BL + BD)
 390
 391       -- What should be computed for c2100 of t6.
 392       expr2 = eval (Tetrahedron.fv t0) $
 393               (3/8)*I +
 394               (1/12)*(F + R + L + B) +
 395               (1/64)*(FT + RT + LT + BT) +
 396               (7/48)*T +
 397               (1/48)*D +
 398               (1/96)*(FR + FL + BR + BL) +
 399               (1/192)*(FD + RD + LD + BD)
 400
 401
 402 -- | We know what (c t6 2 1 0 0) should be from Sorokina and Zeilfelder, p. 87.
 403 --   This test checks the actual value based on the FunctionValues of the cube.
 404 prop_c_tilde_2100_correct :: Cube -> Bool
 405 prop_c_tilde_2100_correct cube =
 406     c t6 2 1 0 0 == (3/8)*int
 407                     + (1/12)*(f + r + l + b)
 408                     + (1/64)*(ft + rt + lt + bt)
 409                     + (7/48)*t + (1/48)*d + (1/96)*(fr + fl + br + bl)
 410                     + (1/192)*(fd + rd + ld + bd)
 411     where
 412       t0 = tetrahedron0 cube
 413       t6 = tetrahedron6 cube
 414       fvs = Tetrahedron.fv t0
 415       int = interior fvs
 416       f = front fvs
 417       r = right fvs
 418       l = left fvs
 419       b = back fvs
 420       ft = front_top fvs
 421       rt = right_top fvs
 422       lt = left_top fvs
 423       bt = back_top fvs
 424       t = top fvs
 425       d = down fvs
 426       fr = front_right fvs
 427       fl = front_left fvs
 428       br = back_right fvs
 429       bl = back_left fvs
 430       fd = front_down fvs
 431       rd = right_down fvs
 432       ld = left_down fvs
 433       bd = back_down fvs
 434
 435 -- Tests to check that the correct edges are incidental.
 436 prop_t0_shares_edge_with_t1 :: Cube -> Bool
 437 prop_t0_shares_edge_with_t1 cube =
 438     (v1 t0) == (v1 t1) && (v3 t0) == (v2 t1)
 439       where
 440         t0 = tetrahedron0 cube
 441         t1 = tetrahedron1 cube
 442
 443 prop_t0_shares_edge_with_t3 :: Cube -> Bool
 444 prop_t0_shares_edge_with_t3 cube =
 445     (v1 t0) == (v1 t3) && (v2 t0) == (v3 t3)
 446       where
 447         t0 = tetrahedron0 cube
 448         t3 = tetrahedron3 cube
 449
 450 prop_t0_shares_edge_with_t6 :: Cube -> Bool
 451 prop_t0_shares_edge_with_t6 cube =
 452     (v2 t0) == (v3 t6) && (v3 t0) == (v2 t6)
 453       where
 454         t0 = tetrahedron0 cube
 455         t6 = tetrahedron6 cube
 456
 457 prop_t1_shares_edge_with_t2 :: Cube -> Bool
 458 prop_t1_shares_edge_with_t2 cube =
 459     (v1 t1) == (v1 t2) && (v3 t1) == (v2 t2)
 460       where
 461         t1 = tetrahedron1 cube
 462         t2 = tetrahedron2 cube
 463
 464 prop_t1_shares_edge_with_t19 :: Cube -> Bool
 465 prop_t1_shares_edge_with_t19 cube =
 466     (v2 t1) == (v3 t19) && (v3 t1) == (v2 t19)
 467       where
 468         t1 = tetrahedron1 cube
 469         t19 = tetrahedron19 cube
 470
 471 prop_t2_shares_edge_with_t3 :: Cube -> Bool
 472 prop_t2_shares_edge_with_t3 cube =
 473     (v1 t1) == (v1 t2) && (v3 t1) == (v2 t2)
 474       where
 475         t1 = tetrahedron1 cube
 476         t2 = tetrahedron2 cube
 477
 478 prop_t2_shares_edge_with_t12 :: Cube -> Bool
 479 prop_t2_shares_edge_with_t12 cube =
 480     (v2 t2) == (v3 t12) && (v3 t2) == (v2 t12)
 481       where
 482         t2 = tetrahedron2 cube
 483         t12 = tetrahedron12 cube
 484
 485 prop_t3_shares_edge_with_t21 :: Cube -> Bool
 486 prop_t3_shares_edge_with_t21 cube =
 487     (v2 t3) == (v3 t21) && (v3 t3) == (v2 t21)
 488       where
 489         t3 = tetrahedron3 cube
 490         t21 = tetrahedron21 cube
 491
 492 prop_t4_shares_edge_with_t5 :: Cube -> Bool
 493 prop_t4_shares_edge_with_t5 cube =
 494     (v1 t4) == (v1 t5) && (v3 t4) == (v2 t5)
 495       where
 496         t4 = tetrahedron4 cube
 497         t5 = tetrahedron5 cube
 498
 499 prop_t4_shares_edge_with_t7 :: Cube -> Bool
 500 prop_t4_shares_edge_with_t7 cube =
 501     (v1 t4) == (v1 t7) && (v2 t4) == (v3 t7)
 502       where
 503         t4 = tetrahedron4 cube
 504         t7 = tetrahedron7 cube
 505
 506 prop_t4_shares_edge_with_t10 :: Cube -> Bool
 507 prop_t4_shares_edge_with_t10 cube =
 508     (v2 t4) == (v3 t10) && (v3 t4) == (v2 t10)
 509       where
 510         t4 = tetrahedron4 cube
 511         t10 = tetrahedron10 cube
 512
 513 prop_t5_shares_edge_with_t6 :: Cube -> Bool
 514 prop_t5_shares_edge_with_t6 cube =
 515     (v1 t5) == (v1 t6) && (v3 t5) == (v2 t6)
 516       where
 517         t5 = tetrahedron5 cube
 518         t6 = tetrahedron6 cube
 519
 520 prop_t5_shares_edge_with_t16 :: Cube -> Bool
 521 prop_t5_shares_edge_with_t16 cube =
 522     (v2 t5) == (v3 t16) && (v3 t5) == (v2 t16)
 523       where
 524         t5 = tetrahedron5 cube
 525         t16 = tetrahedron16 cube
 526
 527 prop_t6_shares_edge_with_t7 :: Cube -> Bool
 528 prop_t6_shares_edge_with_t7 cube =
 529     (v1 t6) == (v1 t7) && (v3 t6) == (v2 t7)
 530       where
 531         t6 = tetrahedron6 cube
 532         t7 = tetrahedron7 cube
 533
 534 prop_t7_shares_edge_with_t20 :: Cube -> Bool
 535 prop_t7_shares_edge_with_t20 cube =
 536     (v2 t7) == (v3 t20) && (v2 t7) == (v3 t20)
 537       where
 538         t7 = tetrahedron7 cube
 539         t20 = tetrahedron20 cube