# Unsolving a Rubik's Cube so each face has a P pentomimo and L tetromino

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.

A simple way of getting this pattern. I've never cared for the traditional move notation. It doesn't reflect how I've ever handled a cube, and I find it hard to follow. Instead I'll give a mechanical description:

Hold a solved cube by the upper left edge (thumb of left hand on the front corner, finger on the rear corner).

1. With your right hand, turn the middle and right columns up a quarter turn.
2. Continue with the right column only an additional quarter turn up.
3. Turn the middle and bottom rows right a quarter turn.
4. Continue with the bottom row only an additional quarter turn right.
5. (Reverse of steps 1-4, but in the same order) Turn the middle and right columns down a quarter turn.
6. Continue with the right column only an additional quarter turn down.
7. Turn the middle and bottom rows left a quarter turn.
8. Continue with the bottom row only an additional quarter turn left.

This gives you a pattern consisting of two L-tetrominos of opposing colors on each face, but around a center of a different color, which in my opinion is a nicer pattern than the one asked for. But to get the requested P-L combo, simply do a 6-dots operation to move appropriate color centers into each face:

The front face will have two opposing colors. Turn the cube so that the center for one of those colors is on the top.

1. Turn the middle column down (I do this as middle + right down, then right back up.)
2. Turn the middle row right.
3. Turn the middle column up.
4. Turn the middle row left.