Petersen family generated: 7 graphs; (vertices, edges) = [(6, 15), (7, 15), (7, 15), (8, 15), (8, 15), (9, 15), (10, 15)]

== 4-simplex
   f-vector (5, 10, 10, 5), graph: 5 vertices, 10 edges, degrees [4, 4, 4, 4, 4]
   (P5) pairs of 2-faces by intersection type: {'empty': 0, 'vertex': 15, 'edge': 30, 'BAD': 0}
   (P6) facets 5, failures 0;  (P7) failures 0
   cycles: 37; pairs (cycle, fundamental cycle of the complement) tested: 0; non-zero: no; odd values: 0; max |lk|: 0
   second apex pair gives the same values: True; symmetry lk(C,D)=lk(D,C): True
   direct enumeration: 0 unordered pairs of disjoint cycles, 0 with lk != 0, values []
   no Petersen-family minor (exhaustive search over all partitions into connected blocks; 0 partitions examined)
   RESULT: all linking numbers 0; Petersen-family minor: no; expected flat -> CONSISTENT   [0.0 s]

== cyclic C(6,4)
   f-vector (6, 15, 18, 9), graph: 6 vertices, 15 edges, degrees [5, 5, 5, 5, 5, 5]
   (P5) pairs of 2-faces by intersection type: {'empty': 9, 'vertex': 72, 'edge': 72, 'BAD': 0}
   (P6) facets 9, failures 0;  (P7) failures 0
   cycles: 197; pairs (cycle, fundamental cycle of the complement) tested: 20; non-zero: yes; odd values: 2; max |lk|: 1
   first linked pair: (0, 2, 4) and (3, 1, 5), lk = 1
   second apex pair gives the same values: True; symmetry lk(C,D)=lk(D,C): True
   direct enumeration: 10 unordered pairs of disjoint cycles, 1 with lk != 0, values [-1, 0]
   Petersen-family minors found (verified models): [('family[0]', '6 vertices')]
   model of family[0] (branch sets, vertices as indices into the sorted point list): [[0], [1], [2], [3], [4], [5]]
   RESULT: linked; Petersen-family minor: yes; expected linked -> CONSISTENT   [0.0 s]
   the 10 pairs of complementary triangles (T, T', lk, T is a 2-face, T' is a 2-face):
      ((0, 1, 2), (3, 4, 5), 0, True, True)
      ((0, 1, 3), (2, 4, 5), 0, True, True)
      ((0, 1, 4), (2, 3, 5), 0, True, True)
      ((0, 1, 5), (2, 3, 4), 0, True, True)
      ((0, 2, 3), (1, 4, 5), 0, True, True)
      ((0, 2, 4), (1, 3, 5), -1, False, False)
      ((0, 2, 5), (1, 3, 4), 0, True, True)
      ((0, 3, 4), (1, 2, 5), 0, True, True)
      ((0, 3, 5), (1, 2, 4), 0, True, True)
      ((0, 4, 5), (1, 2, 3), 0, True, True)

== prism over tetrahedron
   f-vector (8, 16, 14, 6), graph: 8 vertices, 16 edges, degrees [4, 4, 4, 4, 4, 4, 4, 4]
   (P5) pairs of 2-faces by intersection type: {'empty': 19, 'vertex': 24, 'edge': 48, 'BAD': 0}
   (P6) facets 6, failures 0;  (P7) failures 0
   cycles: 170; pairs (cycle, fundamental cycle of the complement) tested: 48; non-zero: no; odd values: 0; max |lk|: 0
   second apex pair gives the same values: True; symmetry lk(C,D)=lk(D,C): True
   direct enumeration: 52 unordered pairs of disjoint cycles, 0 with lk != 0, values [0]
   no Petersen-family minor (exhaustive search over all partitions into connected blocks; 138 partitions examined)
   RESULT: all linking numbers 0; Petersen-family minor: no; expected flat -> CONSISTENT   [0.0 s]

== 3-3 duoprism
   f-vector (9, 18, 15, 6), graph: 9 vertices, 18 edges, degrees [4, 4, 4, 4, 4, 4, 4, 4, 4]
   (P5) pairs of 2-faces by intersection type: {'empty': 24, 'vertex': 27, 'edge': 54, 'BAD': 0}
   (P6) facets 6, failures 0;  (P7) failures 0
   cycles: 312; pairs (cycle, fundamental cycle of the complement) tested: 96; non-zero: no; odd values: 0; max |lk|: 0
   second apex pair gives the same values: True; symmetry lk(C,D)=lk(D,C): True
   direct enumeration: 78 unordered pairs of disjoint cycles, 0 with lk != 0, values [0]
   no Petersen-family minor (exhaustive search over all partitions into connected blocks; 922 partitions examined)
   RESULT: all linking numbers 0; Petersen-family minor: no; expected flat -> CONSISTENT   [0.0 s]

== octahedral prism
   f-vector (12, 30, 28, 10), graph: 12 vertices, 30 edges, degrees [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]
   (P5) pairs of 2-faces by intersection type: {'empty': 150, 'vertex': 120, 'edge': 108, 'BAD': 0}
   (P6) facets 10, failures 0;  (P7) failures 0
   cycles of length <= 8: 2460; pairs (cycle, fundamental cycle of the complement) tested: 3738; non-zero: yes; odd values: 12; max |lk|: 1
   first linked pair: (0, 1, 3, 11, 10, 8) and (4, 2, 6, 7, 9, 5), lk = 1
   second apex pair gives the same values: True; symmetry lk(C,D)=lk(D,C): True
   Petersen-family minors found (verified models): [('family[0]', '6 vertices')]
   model of family[0] (branch sets, vertices as indices into the sorted point list): [[0, 1, 2], [4, 6, 8], [3, 5], [7], [9], [10, 11]]
   RESULT: linked; Petersen-family minor: yes; expected linked -> CONSISTENT   [0.1 s]

== bipyramid over tetrahedron (graph K6 - e)
   f-vector (6, 14, 16, 8), graph: 6 vertices, 14 edges, degrees [4, 4, 5, 5, 5, 5]
   (P5) pairs of 2-faces by intersection type: {'empty': 6, 'vertex': 54, 'edge': 60, 'BAD': 0}
   (P6) facets 8, failures 0;  (P7) failures 0
   cycles: 133; pairs (cycle, fundamental cycle of the complement) tested: 12; non-zero: no; odd values: 0; max |lk|: 0
   second apex pair gives the same values: True; symmetry lk(C,D)=lk(D,C): True
   direct enumeration: 6 unordered pairs of disjoint cycles, 0 with lk != 0, values [0]
   no Petersen-family minor (exhaustive search over all partitions into connected blocks; 0 partitions examined)
   RESULT: all linking numbers 0; Petersen-family minor: no; expected flat -> CONSISTENT   [0.0 s]

== pyramid over triangular bipyramid (graph K6 - e)
   f-vector (6, 14, 15, 7), graph: 6 vertices, 14 edges, degrees [4, 4, 5, 5, 5, 5]
   (P5) pairs of 2-faces by intersection type: {'empty': 6, 'vertex': 48, 'edge': 51, 'BAD': 0}
   (P6) facets 7, failures 0;  (P7) failures 0
   cycles: 133; pairs (cycle, fundamental cycle of the complement) tested: 12; non-zero: no; odd values: 0; max |lk|: 0
   second apex pair gives the same values: True; symmetry lk(C,D)=lk(D,C): True
   direct enumeration: 6 unordered pairs of disjoint cycles, 0 with lk != 0, values [0]
   no Petersen-family minor (exhaustive search over all partitions into connected blocks; 0 partitions examined)
   RESULT: all linking numbers 0; Petersen-family minor: no; expected flat -> CONSISTENT   [0.0 s]

== pyramid over octahedron
   f-vector (7, 18, 20, 9), graph: 7 vertices, 18 edges, degrees [5, 5, 5, 5, 5, 5, 6]
   (P5) pairs of 2-faces by intersection type: {'empty': 28, 'vertex': 90, 'edge': 72, 'BAD': 0}
   (P6) facets 9, failures 0;  (P7) failures 0
   cycles: 459; pairs (cycle, fundamental cycle of the complement) tested: 84; non-zero: no; odd values: 0; max |lk|: 0
   second apex pair gives the same values: True; symmetry lk(C,D)=lk(D,C): True
   direct enumeration: 64 unordered pairs of disjoint cycles, 0 with lk != 0, values [0]
   no Petersen-family minor (exhaustive search over all partitions into connected blocks; 20 partitions examined)
   RESULT: all linking numbers 0; Petersen-family minor: no; expected flat -> CONSISTENT   [0.0 s]

== 3-4 duoprism
   f-vector (12, 24, 19, 7), graph: 12 vertices, 24 edges, degrees [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]
   (P5) pairs of 2-faces by intersection type: {'empty': 63, 'vertex': 36, 'edge': 72, 'BAD': 0}
   (P6) facets 7, failures 0;  (P7) failures 0
   cycles: 1531; pairs (cycle, fundamental cycle of the complement) tested: 553; non-zero: no; odd values: 0; max |lk|: 0
   second apex pair gives the same values: True; symmetry lk(C,D)=lk(D,C): True
   no Petersen-family minor (exhaustive search over all partitions into connected blocks; 113058 partitions examined)
   RESULT: all linking numbers 0; Petersen-family minor: no; expected flat -> CONSISTENT   [9.4 s]

== cyclic C(7,4)
   f-vector (7, 21, 28, 14), graph: 7 vertices, 21 edges, degrees [6, 6, 6, 6, 6, 6, 6]
   (P5) pairs of 2-faces by intersection type: {'empty': 49, 'vertex': 196, 'edge': 133, 'BAD': 0}
   (P6) facets 14, failures 0;  (P7) failures 0
   cycles: 1172; pairs (cycle, fundamental cycle of the complement) tested: 210; non-zero: yes; odd values: 25; max |lk|: 1
   first linked pair: (0, 1, 3, 5) and (4, 2, 6), lk = 1
   second apex pair gives the same values: True; symmetry lk(C,D)=lk(D,C): True
   direct enumeration: 175 unordered pairs of disjoint cycles, 21 with lk != 0, values [-1, 0, 1]
   Petersen-family minors found (verified models): [('family[0]', '6 vertices'), ('family[1]', '7 vertices'), ('family[2]', '7 vertices')]
   model of family[0] (branch sets, vertices as indices into the sorted point list): [[0, 1], [2], [3], [4], [5], [6]]
   RESULT: linked; Petersen-family minor: yes; expected linked -> CONSISTENT   [0.1 s]

== 4-cross-polytope
   f-vector (8, 24, 32, 16), graph: 8 vertices, 24 edges, degrees [6, 6, 6, 6, 6, 6, 6, 6]
   (P5) pairs of 2-faces by intersection type: {'empty': 112, 'vertex': 240, 'edge': 144, 'BAD': 0}
   (P6) facets 16, failures 0;  (P7) failures 0
   cycles: 2766; pairs (cycle, fundamental cycle of the complement) tested: 598; non-zero: yes; odd values: 6; max |lk|: 1
   first linked pair: (0, 1, 7, 6) and (3, 2, 4, 5), lk = -1
   second apex pair gives the same values: True; symmetry lk(C,D)=lk(D,C): True
   direct enumeration: 691 unordered pairs of disjoint cycles, 3 with lk != 0, values [-1, 0, 1]
   Petersen-family minors found (verified models): [('family[0]', '6 vertices'), ('family[1]', '7 vertices'), ('family[2]', '7 vertices'), ('family[3]', '8 vertices'), ('family[4]', '8 vertices')]
   model of family[0] (branch sets, vertices as indices into the sorted point list): [[0, 1], [2, 3], [4], [5], [6], [7]]
   RESULT: linked; Petersen-family minor: yes; expected linked -> CONSISTENT   [0.5 s]

== hypersimplex Delta(2,5)
   f-vector (10, 30, 30, 10), graph: 10 vertices, 30 edges, degrees [6, 6, 6, 6, 6, 6, 6, 6, 6, 6]
   (P5) pairs of 2-faces by intersection type: {'empty': 165, 'vertex': 180, 'edge': 90, 'BAD': 0}
   (P6) facets 10, failures 0;  (P7) failures 0
   cycles: 15703; pairs (cycle, fundamental cycle of the complement) tested: 3942; non-zero: yes; odd values: 12; max |lk|: 1
   first linked pair: (0, 1, 5, 9, 7) and (3, 6, 8, 2, 4), lk = -1
   second apex pair gives the same values: True; symmetry lk(C,D)=lk(D,C): True
   Petersen-family minors found (verified models): [('family[0]', '6 vertices')]
   model of family[0] (branch sets, vertices as indices into the sorted point list): [[0, 1, 4], [2, 3, 5], [6], [7], [8], [9]]
   RESULT: linked; Petersen-family minor: yes; expected linked -> CONSISTENT   [0.2 s]

== 4-cube
   f-vector (16, 32, 24, 8), graph: 16 vertices, 32 edges, degrees [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]
   (P5) pairs of 2-faces by intersection type: {'empty': 132, 'vertex': 48, 'edge': 96, 'BAD': 0}
   (P6) facets 8, failures 0;  (P7) failures 0
   cycles of length <= 8: 848; pairs (cycle, fundamental cycle of the complement) tested: 2656; non-zero: yes; odd values: 24; max |lk|: 1
   first linked pair: (0, 1, 9, 11, 15, 14, 6, 4) and (3, 2, 10, 8, 12, 13, 5, 7), lk = -1
   second apex pair gives the same values: True; symmetry lk(C,D)=lk(D,C): True
   Petersen-family minors found (verified models): [('family[0]', '6 vertices')]
   model of family[0] (branch sets, vertices as indices into the sorted point list): [[0, 1, 2, 5], [4, 8, 9, 12], [3, 11], [6, 7], [10, 14], [13, 15]]
   RESULT: linked; Petersen-family minor: yes; expected linked -> CONSISTENT   [27.5 s]

ALL EXAMPLES CONSISTENT WITH COROLLARY 2: True
