counterexample_G62.json edge set invariant under <sigma,iota>: True
edge orbit sizes: [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6] count 19
vertex orbit sizes: [2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6] count 11
square orbit sizes: [6, 6, 6, 6, 6, 6, 6, 6, 6] count 9
the 11 listed reps hit every vertex orbit exactly once: True
  001  nbrs +x +y +z       spanned cube lacks 002-102, 101-102
  002  nbrs +y +z -z       opposite neighbours
  003  nbrs +x +y -z       spanned cube lacks 002-102
  011  nbrs +x -y +z -z    opposite neighbours
  012  nbrs +x -y +z -z    opposite neighbours
  013  nbrs +x -y -z       spanned cube lacks 002-102
  021  nbrs +x +y +z       spanned cube lacks 031-032, 131-132
  022  nbrs +x +y +z -z    opposite neighbours
  023  nbrs +x +y -z       spanned cube lacks 123-133
  111  nbrs +x -x +y -y +z -z opposite neighbours
  112  nbrs +x -x +y -y +z -z opposite neighbours
x=0          x=1/2        x=1          x=3/2        x=2          x=5/2        x=3          
  o-o-o        o   o      o-o o-o      o-o o        o-o o-o      o-o o-o      o-o o-o      
  |#|#|        |   |      |#| |#|        | |          | |#|        | | |      |#| | |      
o-o-o-o      o-o-o-o      o-o-o-o        o-o        o-o-o-o      o-o-o o      o-o-o o      
|            |            |#|#|#|        |#|        |#|#|#|            |            |      
o o-o-o      o o-o-o      o-o-o-o        o-o        o-o-o-o      o-o-o-o      o-o-o-o      
| | |#|      | | |        |#| |          | |        |#| |#|      |   |        |#|#|        
o-o o-o      o-o o-o      o-o o-o        o o-o      o-o o-o      o   o        o-o-o        
induced closure of G62: |E| = 138  squares = 102  cubes = 25  corners = 12
counterexample_G62.json condition (3) [graph metric]:
  dir x alpha=1/2 : VIOLATED  [('N-', False, ('003', '001', 2, 4, 2)), ('N+', False, ('113', '123', 8, 9, 1))]
  dir x alpha=3/2 : SATISFIED  [('N-', True, None), ('N+', True, None)]
  dir x alpha=5/2 : VIOLATED  [('N-', False, ('210', '220', 8, 9, 1)), ('N+', False, ('300', '310', 2, 3, 1))]
  dir y alpha=1/2 : VIOLATED  [('N-', False, ('303', '302', 2, 3, 1)), ('N+', False, ('310', '312', 8, 10, 2))]
  dir y alpha=3/2 : SATISFIED  [('N-', True, None), ('N+', True, None)]
  dir y alpha=5/2 : VIOLATED  [('N-', False, ('021', '023', 8, 10, 2)), ('N+', False, ('233', '033', 2, 4, 2))]
  dir z alpha=1/2 : VIOLATED  [('N-', False, ('010', '030', 2, 4, 2)), ('N+', False, ('031', '231', 8, 10, 2))]
  dir z alpha=3/2 : SATISFIED  [('N-', True, None), ('N+', True, None)]
  dir z alpha=5/2 : VIOLATED  [('N-', False, ('202', '102', 8, 9, 1)), ('N+', False, ('323', '303', 2, 4, 2))]
  direction(s) in which (3) holds for all half-integer pieces: none

min62_c3inv.json edge set invariant under <sigma,iota>: True
edge orbit sizes: [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6] count 19
vertex orbit sizes: [2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6] count 11
square orbit sizes: [6, 6, 6, 6, 6, 6, 6, 6, 6] count 9
the 11 listed reps hit every vertex orbit exactly once: True
  001  nbrs +x +y +z       spanned cube lacks 002-012, 011-012
  002  nbrs +x +z -z       opposite neighbours
  003  nbrs +x +y -z       spanned cube lacks 002-012
  011  nbrs +x +y -y -z    opposite neighbours
  012  nbrs +x +y +z       spanned cube lacks 013-023, 113-123
  013  nbrs +x -y -z       spanned cube lacks 002-012
  021  nbrs +x +y -y -z    opposite neighbours
  022  nbrs +x +y -y +z    opposite neighbours
  023  nbrs +x +y -z       spanned cube lacks 132-133
  111  nbrs +x -x +y -y +z -z opposite neighbours
  112  nbrs +x -x +y -y +z -z opposite neighbours
min62_c3inv.json condition (3) [graph metric]:
  dir x alpha=1/2 : VIOLATED  [('N-', False, ('010', '030', 2, 4, 2)), ('N+', False, ('132', '131', 8, 9, 1))]
  dir x alpha=3/2 : SATISFIED  [('N-', True, None), ('N+', True, None)]
  dir x alpha=5/2 : VIOLATED  [('N-', False, ('202', '201', 8, 9, 1)), ('N+', False, ('323', '303', 2, 4, 2))]
  dir y alpha=1/2 : VIOLATED  [('N-', False, ('303', '203', 2, 3, 1)), ('N+', False, ('113', '213', 8, 9, 1))]
  dir y alpha=3/2 : SATISFIED  [('N-', True, None), ('N+', True, None)]
  dir y alpha=5/2 : VIOLATED  [('N-', False, ('120', '220', 8, 9, 1)), ('N+', False, ('030', '130', 2, 3, 1))]
  dir z alpha=1/2 : VIOLATED  [('N-', False, ('320', '330', 2, 3, 1)), ('N+', False, ('311', '321', 8, 9, 1))]
  dir z alpha=3/2 : SATISFIED  [('N-', True, None), ('N+', True, None)]
  dir z alpha=5/2 : VIOLATED  [('N-', False, ('012', '022', 8, 9, 1)), ('N+', False, ('233', '033', 2, 4, 2))]
  direction(s) in which (3) holds for all half-integer pieces: none

