Koehler-Lutz (arXiv:math/0506520), Table 4: neighborly 3-spheres with 10..14 vertices, rebuilt from orbits
  3_10^1_1   n=10 group Z          |generated group|=10  facets=35 (listed 35) closed pseudomanifold=True neighborly=True |Aut|=10 n-cycle in Aut=True  remarks: [3], [4, N^10_3574], [52, 1_10], non-polytopal
  3_10^3_1   n=10 group D          |generated group|=20  facets=35 (listed 35) closed pseudomanifold=True neighborly=True |Aut|=20 n-cycle in Aut=True  remarks: dC_4(10), [4, N^10_4], [52, I_10]
  3_10^4_2   n=10 group half[5:4]2 |generated group|=20  facets=35 (listed 35) closed pseudomanifold=True neighborly=True |Aut|=20 n-cycle in Aut=False  remarks: [4, N^10_425], [13], non-polytopal
  3_11^1_1   n=11 group Z          |generated group|=11  facets=44 (listed 44) closed pseudomanifold=True neighborly=True |Aut|=11 n-cycle in Aut=True  remarks: [52, 1_11]
  3_11^2_1   n=11 group D          |generated group|=22  facets=44 (listed 44) closed pseudomanifold=True neighborly=True |Aut|=22 n-cycle in Aut=True  remarks: dC_4(11), [52, I_11]
  3_12^12_1  n=12 group D          |generated group|=24  facets=54 (listed 54) closed pseudomanifold=True neighborly=True |Aut|=24 n-cycle in Aut=True  remarks: dC_4(12), [52, I_12]
  3_13^1_3   n=13 group Z          |generated group|=13  facets=65 (listed 65) closed pseudomanifold=True neighborly=True |Aut|=13 n-cycle in Aut=True  remarks: [52, 2_13]
  3_13^1_5   n=13 group Z          |generated group|=13  facets=65 (listed 65) closed pseudomanifold=True neighborly=True |Aut|=13 n-cycle in Aut=True  remarks: [52, 4_13]
  3_13^2_1   n=13 group D          |generated group|=26  facets=65 (listed 65) closed pseudomanifold=True neighborly=True |Aut|=26 n-cycle in Aut=True  remarks: dC_4(13), [52, I_13]
  3_14^1_4   n=14 group Z          |generated group|=14  facets=77 (listed 77) closed pseudomanifold=True neighborly=True |Aut|=14 n-cycle in Aut=True  remarks: [52, 1_14]
  3_14^1_7   n=14 group Z          |generated group|=14  facets=77 (listed 77) closed pseudomanifold=True neighborly=True |Aut|=14 n-cycle in Aut=True  remarks: [52, 7_14]
  3_14^1_8   n=14 group Z          |generated group|=14  facets=77 (listed 77) closed pseudomanifold=True neighborly=True |Aut|=14 n-cycle in Aut=True  remarks: [52, 4_14]
  3_14^1_11  n=14 group Z          |generated group|=14  facets=77 (listed 77) closed pseudomanifold=True neighborly=True |Aut|=14 n-cycle in Aut=True  remarks: [52, 8_14]
  3_14^1_14  n=14 group Z          |generated group|=14  facets=77 (listed 77) closed pseudomanifold=True neighborly=True |Aut|=14 n-cycle in Aut=True  remarks: [52, 9_14]
  3_14^1_17  n=14 group Z          |generated group|=14  facets=77 (listed 77) closed pseudomanifold=True neighborly=True |Aut|=14 n-cycle in Aut=True  remarks: [52, 10_14]
  3_14^1_18  n=14 group Z          |generated group|=14  facets=77 (listed 77) closed pseudomanifold=True neighborly=True |Aut|=14 n-cycle in Aut=True  remarks: [52, 11_14]
  3_14^1_26  n=14 group Z          |generated group|=14  facets=77 (listed 77) closed pseudomanifold=True neighborly=True |Aut|=14 n-cycle in Aut=True  remarks: [52, 16_14]
  3_14^1_27  n=14 group Z          |generated group|=14  facets=77 (listed 77) closed pseudomanifold=True neighborly=True |Aut|=14 n-cycle in Aut=True  remarks: [52, 17_14]
  3_14^3_1   n=14 group D          |generated group|=28  facets=77 (listed 77) closed pseudomanifold=True neighborly=True |Aut|=28 n-cycle in Aut=True  remarks: dC_4(14), [52, I_14]
(1) Table 1 of the paper
  A10    |Aut|=10  = ['3_10^1_1']
  A11    |Aut|=11  = ['3_11^1_1']
  Z13_0  |Aut|=13  = ['3_13^1_3']
  Z13_1  |Aut|=13  = ['3_13^1_5']
  Z14_0  |Aut|=14  = ['3_14^1_17']
  Z14_1  |Aut|=14  = ['3_14^1_14']
  Z14_2  |Aut|=14  = ['3_14^1_26']
  Z14_3  |Aut|=14  = ['3_14^1_18']
  Z14_4  |Aut|=14  = ['3_14^1_27']
  Z14_5  |Aut|=14  = ['3_14^1_4']
  Z14_6  |Aut|=14  = ['3_14^1_8']
  Z14_7  |Aut|=14  = ['3_14^1_7']
  Z14_8  |Aut|=14  = ['3_14^1_11']
(2) orbit search of Section 6.4 versus the entries with an n-cycle in their automorphism group
  n = 10: orbit search 2, Koehler-Lutz 2 ['3_10^1_1', '3_10^3_1'], identical sets: True
  n = 11: orbit search 2, Koehler-Lutz 2 ['3_11^1_1', '3_11^2_1'], identical sets: True
  n = 12: orbit search 1, Koehler-Lutz 1 ['3_12^12_1'], identical sets: True
  n = 13: orbit search 3, Koehler-Lutz 3 ['3_13^1_3', '3_13^1_5', '3_13^2_1'], identical sets: True
  n = 14: orbit search 10, Koehler-Lutz 10 ['3_14^1_11', '3_14^1_14', '3_14^1_17', '3_14^1_18', '3_14^1_26', '3_14^1_27', '3_14^1_4', '3_14^1_7', '3_14^1_8', '3_14^3_1'], identical sets: True
(3) vertex-transitive spheres among the neighborly ten-vertex spheres of data/spheres3_n10.txt.gz
  lines: 247882, neighborly: 3540, vertex-transitive: 3
  line 5415 (0-based): |Aut|=20 = ['3_10^3_1']
  line 29778 (0-based): |Aut|=20 = ['3_10^4_2']
  line 35806 (0-based): |Aut|=10 = ['3_10^1_1']
(4) cross-check of the matches with sphere_tools.canonical_form
  A10    = 3_10^1_1   True
  A11    = 3_11^1_1   True
  Z13_0  = 3_13^1_3   True
  Z13_1  = 3_13^1_5   True
  Z14_0  = 3_14^1_17  True
  Z14_1  = 3_14^1_14  True
  Z14_2  = 3_14^1_26  True
  Z14_3  = 3_14^1_18  True
  Z14_4  = 3_14^1_27  True
  Z14_5  = 3_14^1_4   True
  Z14_6  = 3_14^1_8   True
  Z14_7  = 3_14^1_7   True
  Z14_8  = 3_14^1_11  True
ALL CHECKS PASSED
