== cyclic polytope C(6,4) f-vector (6, 15, 18, 9) dropped points 0
   Petersen-family minors found (models verified): ['PF6[555555]']
   cycles: 197, pairs of disjoint cycles: 10
   Schlegel facet 0: |lk| histogram over all these pairs: {0: 9, 1: 1}
   Schlegel facet 8 gives the same values up to the global sign +
   projection method agrees on 11 pairs (all linked pairs + random sample); sign relation: lk_cone = +lk_proj
   reduction to fundamental cycles: 197 cycles, 20 (C, D) tests, 2 linked; agrees with direct enumeration
   the linked pair: [0, 2, 4] [1, 3, 5] lk = 1 | are they 2-faces? False False
== octahedral prism f-vector (12, 30, 28, 10) dropped points 0
   Petersen-family minors found (models verified): ['PF6[555555]', 'PF7[5554443]', 'PF7[6444444]', 'PF8[54444333]', 'PF8[44444433]', 'PF9[444333333]', 'PF10[3333333333]']
   cycles of length <= 6: 402, pairs of disjoint cycles: 5675
   Schlegel facet 0: |lk| histogram over all these pairs: {0: 5669, 1: 6}
   Schlegel facet 9 gives the same values up to the global sign -
   projection method agrees on 306 pairs (all linked pairs + random sample); sign relation: lk_cone = +lk_proj
   pair of the task: C = [9, 7, 11, 10, 4, 8] D = [1, 5, 3, 2, 6, 0] lk (cone) = -1 lk (projection: over, under) = (-1, -1)
   all cycles: 13100, (C, D) tests: 4122, linked (C, basis D) pairs: 12, max |lk| = 1
== 3-3 duoprism f-vector (9, 18, 15, 6) dropped points 0
   Petersen-family minors found (models verified): NONE (7 x UNSAT)
   cycles: 312, pairs of disjoint cycles: 78
   Schlegel facet 0: |lk| histogram over all these pairs: {0: 78}
   Schlegel facet 5 gives the same values up to the global sign n/a (all zero)
   projection method agrees on 78 pairs (all linked pairs + random sample); sign relation: n/a
   reduction to fundamental cycles: 312 cycles, 96 (C, D) tests, 0 linked; agrees with direct enumeration
   => no Petersen-family minor and no linked pair of disjoint cycles (all pairs enumerated)
== prism over the tetrahedron f-vector (8, 16, 14, 6) dropped points 0
   Petersen-family minors found (models verified): NONE (7 x UNSAT)
   cycles: 170, pairs of disjoint cycles: 52
   Schlegel facet 0: |lk| histogram over all these pairs: {0: 52}
   Schlegel facet 5 gives the same values up to the global sign n/a (all zero)
   projection method agrees on 52 pairs (all linked pairs + random sample); sign relation: n/a
   reduction to fundamental cycles: 170 cycles, 48 (C, D) tests, 0 linked; agrees with direct enumeration
   => no Petersen-family minor and no linked pair of disjoint cycles (all pairs enumerated)
== 4-simplex f-vector (5, 10, 10, 5) dropped points 0
   Petersen-family minors found (models verified): NONE (7 x UNSAT)
   cycles: 37, pairs of disjoint cycles: 0
   Schlegel facet 0: |lk| histogram over all these pairs: {}
   Schlegel facet 4 gives the same values up to the global sign n/a (all zero)
   projection method agrees on 0 pairs (all linked pairs + random sample); sign relation: n/a
   reduction to fundamental cycles: 37 cycles, 0 (C, D) tests, 0 linked; agrees with direct enumeration
   => no Petersen-family minor and no linked pair of disjoint cycles (all pairs enumerated)
== 3-4 duoprism f-vector (12, 24, 19, 7) dropped points 0
   Petersen-family minors found (models verified): NONE (7 x UNSAT)
   cycles: 1531, pairs of disjoint cycles: 723
   Schlegel facet 0: |lk| histogram over all these pairs: {0: 723}
   Schlegel facet 6 gives the same values up to the global sign n/a (all zero)
   projection method agrees on 300 pairs (all linked pairs + random sample); sign relation: n/a
   reduction to fundamental cycles: 1531 cycles, 553 (C, D) tests, 0 linked; agrees with direct enumeration
   => no Petersen-family minor and no linked pair of disjoint cycles (all pairs enumerated)
== 4-cube f-vector (16, 32, 24, 8) dropped points 0
   Petersen-family minors found (models verified): ['PF6[555555]', 'PF7[5554443]', 'PF7[6444444]', 'PF8[54444333]', 'PF8[44444433]', 'PF9[444333333]', 'PF10[3333333333]']
   cycles of length <= 8: 848, pairs of disjoint cycles: 5680
   Schlegel facet 0: |lk| histogram over all these pairs: {0: 5668, 1: 12}
   Schlegel facet 7 gives the same values up to the global sign -
   projection method agrees on 312 pairs (all linked pairs + random sample); sign relation: lk_cone = +lk_proj
   first pair with odd linking number (search by increasing length of C): C = [0, 1, 3, 7, 15, 14, 12, 8] D = [9, 11, 10, 2, 6, 4, 5, 13] lk = 1 (confirmed by the projection method)
== cross-polytope f-vector (8, 24, 32, 16) dropped points 0
   Petersen-family minors found (models verified): ['PF6[555555]', 'PF7[5554443]', 'PF7[6444444]', 'PF8[54444333]', 'PF8[44444433]']
   cycles of length <= 5: 422, pairs of disjoint cycles: 691
   Schlegel facet 0: |lk| histogram over all these pairs: {0: 688, 1: 3}
   Schlegel facet 15 gives the same values up to the global sign -
   projection method agrees on 303 pairs (all linked pairs + random sample); sign relation: lk_cone = +lk_proj
   first pair with odd linking number (search by increasing length of C): C = [0, 2, 1, 3] D = [5, 6, 4, 7] lk = 1 (confirmed by the projection method)
== cyclic polytope C(7,4) f-vector (7, 21, 28, 14) dropped points 0
   Petersen-family minors found (models verified): ['PF6[555555]', 'PF7[5554443]', 'PF7[6444444]']
   cycles of length <= 5: 392, pairs of disjoint cycles: 175
   Schlegel facet 0: |lk| histogram over all these pairs: {0: 154, 1: 21}
   Schlegel facet 13 gives the same values up to the global sign +
   projection method agrees on 196 pairs (all linked pairs + random sample); sign relation: lk_cone = +lk_proj
   first pair with odd linking number (search by increasing length of C): C = [0, 2, 4] D = [3, 1, 5] lk = -1 (confirmed by the projection method)
== hypersimplex Delta(2,5) f-vector (10, 30, 30, 10) dropped points 0
   Petersen-family minors found (models verified): ['PF6[555555]', 'PF7[5554443]', 'PF7[6444444]', 'PF8[54444333]', 'PF8[44444433]', 'PF9[444333333]', 'PF10[3333333333]']
   cycles of length <= 5: 432, pairs of disjoint cycles: 3756
   Schlegel facet 0: |lk| histogram over all these pairs: {0: 3750, 1: 6}
   Schlegel facet 9 gives the same values up to the global sign -
   projection method agrees on 306 pairs (all linked pairs + random sample); sign relation: lk_cone = +lk_proj
   first pair with odd linking number (search by increasing length of C): C = [0, 1, 7, 9, 6] D = [4, 5, 2, 3, 8] lk = 1 (confirmed by the projection method)
== prism over the cube = 4-cube, other coordinates f-vector (16, 32, 24, 8) dropped points 0
   Petersen-family minors found (models verified): ['PF6[555555]', 'PF7[5554443]', 'PF7[6444444]', 'PF8[54444333]', 'PF8[44444433]', 'PF9[444333333]', 'PF10[3333333333]']
   cycles of length <= 4: 24, pairs of disjoint cycles: 132
   Schlegel facet 0: |lk| histogram over all these pairs: {0: 132}
   Schlegel facet 7 gives the same values up to the global sign n/a (all zero)
   projection method agrees on 132 pairs (all linked pairs + random sample); sign relation: n/a
   first pair with odd linking number (search by increasing length of C): C = [0, 1, 3, 7, 15, 14, 12, 8] D = [9, 11, 10, 2, 6, 4, 5, 13] lk = 1 (confirmed by the projection method)
ALL VALIDATION CHECKS PASSED; universal sign relation between the two linking programs: lk_cone = +lk_proj
