Some solutions for 4X4X4 with equal 0-0 and 0-1 adjacencies
.....0........1........1........0........1........0........0........0
....0.0......1.0......0.1......1.0......1.0......0.0......0.0......0.0
...1.1.0....0.0.0....0.0.0....1.0.0....0.1.0....1.0.0....0.1.1....0.1.0
..1.0.0.0..0.0.1.1..0.0.1.1..0.1.0.0..0.0.0.0..0.1.1.0..0.0.0.1..0.0.1.1
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