# Unsolving a Rubik's Cube

A few days ago I picked up a solved Rubik's Cube that I had abandoned due to forgetting how to solve it, and started turning the faces to make nice patterns. A few minutes later, I'd made one - each face contained a P-pentomino in one colour and an L-tetromino in another: i.e. it looked like a rotation of one of these two (in different colours, obviously):

Since I couldn't solve it, I thought it'd be a nice challenge Rubik's Cube enthusiasts to try something different:

Can you find a sequence of moves from a solved cube to recreate my position (or anything fitting the description)?

Note: I am sure no corners got turned (since my cube can't do that) and no centres got swapped (since nothing fell out of the cube). Please don't just try positions on an online solver, I have included the tag.

For example, a valid final configuration (if it were attainable, which it isn't) would be this:

Here is one method for attaining such a pattern.

Swap the top layer edges in opposite pairs:
M2 U2 M2 U M2 U2 M2 U'
where M is a move of the vertical middle slice between the R and L faces. Then do R2 F2 to reach the pattern.

I found this pattern as follows:

First I decided to only mix opposite colours, like you get when only doing half turns.

Then I looked only at corners, to find a sequence that mixed them correctly, giving every face two adjacent corners of the opposite colour. The move sequence R2 F2 did this. The U and D faces already have the complete pattern, only the side faces need fixing.

Finally, I looked at what edges needed to be swapped to finish the pattern. A simple double swap worked (of the top edges before the R2F2 moves).

EDIT:
A shorter method is:

U M2 U2 M2 U, R2 F2
It works the same way, just swapping slightly different edge pairs.