edge orbits: 19 (sizes [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6])
representatives: 001-101, 001-011, 001-002, 002-012, 002-003, 003-103, 003-013, 011-111, 011-012, 012-112, 012-013, 013-113, 021-121, 021-031, 021-022, 022-122, 022-023, 111-211, 112-212
square orbits: 9  (given by opposite corners min-max): [001,012]x6, [001,111]x6, [002,013]x6, [003,113]x6, [011,112]x6, [012,113]x6, [021,122]x6, [021,131]x6, [111,122]x6
cubes: [(1, 1, 1)]

non-corner certificate per vertex orbit:
  orbit of 001 (size 6): neighbours +x +y +z; neighbours in distinct directions, but the spanned 3-cube lacks edge(s) 002-102, 101-102
  orbit of 002 (size 6): neighbours +y +z -z; has two opposite neighbours
  orbit of 003 (size 6): neighbours +x +y -z; neighbours in distinct directions, but the spanned 3-cube lacks edge(s) 002-102
  orbit of 011 (size 6): neighbours +x -y +z -z; has two opposite neighbours
  orbit of 012 (size 6): neighbours +x -y +z -z; has two opposite neighbours
  orbit of 013 (size 6): neighbours +x -y -z; neighbours in distinct directions, but the spanned 3-cube lacks edge(s) 002-102
  orbit of 021 (size 6): neighbours +x +y +z; neighbours in distinct directions, but the spanned 3-cube lacks edge(s) 031-032, 131-132
  orbit of 022 (size 6): neighbours +x +y +z -z; has two opposite neighbours
  orbit of 023 (size 6): neighbours +x +y -z; neighbours in distinct directions, but the spanned 3-cube lacks edge(s) 123-133
  orbit of 111 (size 2): neighbours +x -x +y -y +z -z; has two opposite neighbours
  orbit of 112 (size 6): neighbours +x -x +y -y +z -z; has two opposite neighbours
