I want to make a symmetric odd/even sudoku, where not only the clues but also the colored grid is symmetric. (i. e. if R1C2 is an odd number then also R9C8 should be odd, and if R1C3 is even then also R9C7 should be. R5C5 must be odd of course. Or saying it in other way I look for a way to color a sudoku grid so that in every row, column and box are 4 green and 5 yellow cells.

Any other symmetry or a jigsaw variant would also be nice. But I can't find a possible grid. Any idea?