Is it possible to achieve a Rubiks Cube with Complementary colors as center piece?

Question

Info

Achieving a Rubik's Cube with different center pieces (like a dot) is fairly simple when you have a correctly solved Cube. From the top of my head, you can get something like orange edges with a blue dot, blue edges with a white dot, yellow with red, etc.

However, it seems impossible to have a Cube where the dots are Complementary Colors.

This means having an Orange face with a blue dot, a Blue face with an Orange dot, Green - Red, Red - Green, and for the sake of the Cube's colors, Yellow - White and White - Yellow.

Question

Is it possible to solve a Rubik's Cube where the center pieces of each face is a Complementary color?

After trying it myself

I have tried to achieve this through two strategies; The first one using a solved cube to get the 'normal' dots (in non Complementary Colors) then try to achieve Complementary Colors. I got stuck quite quickly here.

The second by trying to solve the Rubik's Cube in the 'default' way (using the basic algorithms) but then by imagining the center to be the same color as the others, while I was actually using the Complementary ones. For example, get the white face with yellow in center complete, then do the other algorithms but imagine blue being part of the orange edges, etc... This strategy seems to be working up untill the final algorithm to rotate corners and finish the cube. I can complete maybe up to 4 faces (top, bottom and 2 in the middle) with their Complementary Colors but it seems impossible to swap the final 2 corners.

Feedback

I would love to hear if this is indeed not possible (I ask if it is possible but my own conclusion is that it is not dues to the way the cube is build). I would also like to hear or get references to the answer as to why this is impossible.

Final note: Should this question have been answered somewhere else, or if you have some feedback on the information, please let me know so I can edit it.

Answer 1

One of the things that is impossible to change is the order of the colors around a corner.

For example, on my Rubik's cube, around one of the corners, the colors of the adjacent faces are red, white, and blue in counter-clockwise order.

No matter how I twist the cube, this will always be preserved:

• The centers cannot move with respect to one another, so they will always be red, white, and blue in counter-clockwise order.
• The corner cube itself will always be red, white, and blue in counter-clockwise order.

However, if you swap all three opposite pairs of colors, you reverse the orientation, since that amounts to three reflections. Thus, the new configuration is impossible.

Explicitly, the face pairs on my cube are

• red-orange
• white-yellow
• blue-green

But the opposite colors go orange-green-yellow in counter-clockwise order, not the orange-yellow-green you're asking for.

Swapping only two pairs of opposite colors preserves the ordering of the colors around each corner, so the obstacle of this answer is no longer present. (and as you've observed, can actually be achieved on the cube)