point sets read from 1 file(s) (9 vertices: from the first file only): 1630; pairwise non-isomorphic:
  vertices 5: 1 types found (known number of types: 1)
  vertices 6: 4 types found (known number of types: 4)
  vertices 7: 31 types found (known number of types: 31)
  vertices 8: 1294 types found (known number of types: 1294)
  vertices 9: 300 types found (known number of types: 274148)

   5 vertices  f=(5, 10, 10, 5)   pairs=0    non-zero=0   odd=0   max|lk|=0  minor=None  vertex as in Lemma 6.1: True  (cyclic)
   6 vertices  f=(6, 13, 13, 6)   pairs=4    non-zero=0   odd=0   max|lk|=0  minor=None  vertex as in Lemma 6.1: True  (cube vertices)
   6 vertices  f=(6, 14, 15, 7)   pairs=6    non-zero=0   odd=0   max|lk|=0  minor=None  vertex as in Lemma 6.1: True  (pyramid over grid points)
   6 vertices  f=(6, 14, 16, 8)   pairs=6    non-zero=0   odd=0   max|lk|=0  minor=None  vertex as in Lemma 6.1: True  (grid {0,1,2}^4)
   6 vertices  f=(6, 15, 18, 9)   pairs=10   non-zero=1   odd=1   max|lk|=1  minor=K6    vertex as in Lemma 6.1: False  (cyclic)
   7 vertices  f=(7, 15, 14, 6)   pairs=16   non-zero=0   odd=0   max|lk|=0  minor=None  vertex as in Lemma 6.1: True  (cube vertices)
   7 vertices  f=(7, 16, 16, 7)   pairs=20   non-zero=0   odd=0   max|lk|=0  minor=None  vertex as in Lemma 6.1: True  (pyramid over grid points)
   7 vertices  f=(7, 16, 16, 7)   pairs=24   non-zero=0   odd=0   max|lk|=0  minor=None  vertex as in Lemma 6.1: True  (pyramid over grid points)
   7 vertices  f=(7, 17, 17, 7)   pairs=34   non-zero=0   odd=0   max|lk|=0  minor=None  vertex as in Lemma 6.1: True  (cube vertices)
   7 vertices  f=(7, 17, 18, 8)   pairs=39   non-zero=0   odd=0   max|lk|=0  minor=None  vertex as in Lemma 6.1: True  (grid {0,1,2}^4)
   7 vertices  f=(7, 17, 18, 8)   pairs=34   non-zero=0   odd=0   max|lk|=0  minor=None  vertex as in Lemma 6.1: True  (pyramid over grid points)
   7 vertices  f=(7, 17, 18, 8)   pairs=34   non-zero=0   odd=0   max|lk|=0  minor=None  vertex as in Lemma 6.1: True  (grid {0,1,2}^4)
   7 vertices  f=(7, 17, 18, 8)   pairs=44   non-zero=0   odd=0   max|lk|=0  minor=None  vertex as in Lemma 6.1: True  (grid {0,1,2}^4)
   7 vertices  f=(7, 17, 19, 9)   pairs=34   non-zero=0   odd=0   max|lk|=0  minor=None  vertex as in Lemma 6.1: True  (grid {0,1,2}^4)
   7 vertices  f=(7, 18, 19, 8)   pairs=51   non-zero=0   odd=0   max|lk|=0  minor=None  vertex as in Lemma 6.1: True  (grid {0,1,2}^4)
   7 vertices  f=(7, 18, 20, 9)   pairs=64   non-zero=0   odd=0   max|lk|=0  minor=None  vertex as in Lemma 6.1: True  (grid {0,1,2}^4)
   7 vertices  f=(7, 18, 20, 9)   pairs=51   non-zero=0   odd=0   max|lk|=0  minor=None  vertex as in Lemma 6.1: True  (pyramid over grid points)
   7 vertices  f=(7, 18, 20, 9)   pairs=51   non-zero=0   odd=0   max|lk|=0  minor=None  vertex as in Lemma 6.1: True  (grid {0,1,2}^4)
   7 vertices  f=(7, 18, 20, 9)   pairs=51   non-zero=0   odd=0   max|lk|=0  minor=None  vertex as in Lemma 6.1: True  (grid {0,1,2,3}^4)
   7 vertices  f=(7, 18, 20, 9)   pairs=64   non-zero=0   odd=0   max|lk|=0  minor=None  vertex as in Lemma 6.1: True  (grid {0,1,2}^4)
   7 vertices  f=(7, 18, 20, 9)   pairs=55   non-zero=1   odd=1   max|lk|=1  minor=K6    vertex as in Lemma 6.1: False  (cube vertices)
   7 vertices  f=(7, 18, 21, 10)  pairs=51   non-zero=0   odd=0   max|lk|=0  minor=None  vertex as in Lemma 6.1: True  (grid {0,1,2}^4)
   7 vertices  f=(7, 18, 21, 10)  pairs=51   non-zero=0   odd=0   max|lk|=0  minor=None  vertex as in Lemma 6.1: True  (grid {0,1,2}^4)
   7 vertices  f=(7, 18, 21, 10)  pairs=55   non-zero=1   odd=1   max|lk|=1  minor=K6    vertex as in Lemma 6.1: False  (grid {0,1,2}^4)
   7 vertices  f=(7, 18, 21, 10)  pairs=64   non-zero=0   odd=0   max|lk|=0  minor=None  vertex as in Lemma 6.1: True  (grid {0,1,2}^4)
   7 vertices  f=(7, 18, 22, 11)  pairs=51   non-zero=0   odd=0   max|lk|=0  minor=None  vertex as in Lemma 6.1: True  (box [-6,6]^4)
   7 vertices  f=(7, 19, 22, 10)  pairs=85   non-zero=1   odd=1   max|lk|=1  minor=K6    vertex as in Lemma 6.1: False  (grid {0,1,2}^4)
   7 vertices  f=(7, 19, 22, 10)  pairs=76   non-zero=3   odd=3   max|lk|=1  minor=K6    vertex as in Lemma 6.1: False  (grid {0,1,2}^4)
   7 vertices  f=(7, 19, 23, 11)  pairs=76   non-zero=3   odd=3   max|lk|=1  minor=K6    vertex as in Lemma 6.1: False  (grid {0,1,2}^4)
   7 vertices  f=(7, 19, 23, 11)  pairs=85   non-zero=1   odd=1   max|lk|=1  minor=K6    vertex as in Lemma 6.1: False  (grid {0,1,2,3}^4)
   7 vertices  f=(7, 19, 23, 11)  pairs=85   non-zero=6   odd=6   max|lk|=1  minor=K6    vertex as in Lemma 6.1: False  (grid {0,1,2}^4)
   7 vertices  f=(7, 19, 24, 12)  pairs=76   non-zero=3   odd=3   max|lk|=1  minor=K6    vertex as in Lemma 6.1: False  (box [-6,6]^4)
   7 vertices  f=(7, 19, 24, 12)  pairs=85   non-zero=1   odd=1   max|lk|=1  minor=K6    vertex as in Lemma 6.1: False  (grid {0,1,2}^4)
   7 vertices  f=(7, 20, 25, 12)  pairs=120  non-zero=9   odd=9   max|lk|=1  minor=K6    vertex as in Lemma 6.1: False  (grid {0,1,2}^4)
   7 vertices  f=(7, 20, 26, 13)  pairs=120  non-zero=9   odd=9   max|lk|=1  minor=K6    vertex as in Lemma 6.1: False  (grid {0,1,2}^4)
   7 vertices  f=(7, 21, 28, 14)  pairs=175  non-zero=21  odd=21  max|lk|=1  minor=K6    vertex as in Lemma 6.1: False  (cyclic)

vertices  types    not linked, no minor   linked, K_6-minor      other      pairs        vertex as in Lemma 6.1 (among the not linked)
5         1        1                      0                      0          0            1 of 1
6         4        3                      1                      0          26           3 of 3
7         31       19                     12                     0          1921         19 of 19
8         1294     302                    992                    0          599709       298 of 302
9         300      117                    183                    0          484620       110 of 117

8 vertices by f-vector: (f-vector): types not linked / linked
   (8, 16, 14, 6)        1 /    0
   (8, 18, 17, 7)        4 /    0
   (8, 19, 18, 7)        1 /    0
   (8, 19, 19, 8)       13 /    0
   (8, 19, 20, 9)        1 /    0
   (8, 20, 20, 8)       12 /    0
   (8, 20, 21, 9)       28 /    3
   (8, 20, 22, 10)       7 /    0
   (8, 21, 21, 8)        2 /    0
   (8, 21, 22, 9)       28 /    9
   (8, 21, 23, 10)      52 /   19
   (8, 21, 24, 11)      19 /    7
   (8, 21, 25, 12)       4 /    0
   (8, 22, 23, 9)        6 /    1
   (8, 22, 24, 10)      29 /   27
   (8, 22, 25, 11)      50 /   78
   (8, 22, 26, 12)      32 /   43
   (8, 22, 27, 13)      10 /    6
   (8, 22, 28, 14)       3 /    0
   (8, 23, 25, 10)       0 /    3
   (8, 23, 26, 11)       0 /   51
   (8, 23, 27, 12)       0 /  129
   (8, 23, 28, 13)       0 /  112
   (8, 23, 29, 14)       0 /   30
   (8, 23, 30, 15)       0 /    5
   (8, 24, 28, 12)       0 /   17
   (8, 24, 29, 13)       0 /   90
   (8, 24, 30, 14)       0 /  103
   (8, 24, 31, 15)       0 /   39
   (8, 24, 32, 16)       0 /    8
   (8, 25, 31, 14)       0 /   30
   (8, 25, 32, 15)       0 /   73
   (8, 25, 33, 16)       0 /   32
   (8, 25, 34, 17)       0 /    8
   (8, 26, 34, 16)       0 /   25
   (8, 26, 35, 17)       0 /   23
   (8, 26, 36, 18)       0 /    6
   (8, 27, 37, 18)       0 /    8
   (8, 27, 38, 19)       0 /    4
   (8, 28, 40, 20)       0 /    3

polytopes analysed: 1630; pairs of disjoint cycles: 1086276; pairs with non-zero linking number: 42057; time 73 s
exceptions to "non-zero pair <=> odd pair <=> minor in the Petersen family <=> K_6-minor", to Lemmas 3.1 and 3.3, to Lemma 6.1, or disagreement of the Gauss integral: 0
rows for 5, 6, 7 vertices equal to Table 1 of the note (1/1/0, 4/3/1, 31/19/12): True
all 1294 types with 8 vertices were found; row of Table 1 (1294 / 302 / 992): True
ALL OK
