The same thing can happen on some Rubik's cuboids - it seems unsolvable with a parity problem, then the answer is to swap two seemingly identical elements. I k

The same thing can happen on some Rubik's cuboids - it seems unsolvable with a parity problem, then the answer is to swap two seemingly identical elements. I know it happens on the 3x3x4 cuboid - each of the 3x4 faces has two centers that appear identical, but if you have exactly two such unsolved pieces, it's unsolvable because it's impossible to exchange exactly two of them - what you need to do is cycle 3 of them where 2 appear identical. I remember this happening on some other shapes and sizes as well. (Pic for reference: https://www.grubiks.com/images/puzzles/30/small.png https://www.grubiks.com/images/puzzles/30/small.png . This puzzle exists as do many other NxMxH cuboids. Rectangular but non-square faces can only make 180º turns.)