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Looks like you have a single flipped edge piece. This renders your cube unsolvable: If you ignore everything except the corners, centers, and edge middle pieces, you get a 3x3x3 cube, and on that cube, a single piece flip is definitely unsolvable. Here's how to get from a solved cube to a situation that is one edge piece flip away from your cube's pattern. ...


If the three edge pieces you want to rotate are on the top layer at front, left and right, then the move $F^2UM^{-1}U^2MUF^2$ will permute them cyclically where $F$ means rotating the front face $90^{\circ}$ clockwise (so $F^2$ means rotating it $180^{\circ}$), $U$ means rotating the top (upper) face $90^{\circ}$ clockwise, and $M$ means rotating the ...

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