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The representation we use here is a (1, 54) vector, each value representing the color of a sticker.
The 6 are listed in this order: Front Top Back Bottom Right Left
Each face contains 9 values (6 * 9 = 54)
Each value is an integer between 0 and 5 representing the color of the sticker:
COLORS = {
0: 'Green',
1: 'White',
2: 'Blue',
3: 'Yellow',
4: 'Red',
5: 'Orange'
}

The 'standard' position of the solved cube will be represented with the white face on top\

Actions are represented with (54, 54) permutation matrices.
state * action -> new_state
(1, 54) * (54, 54) -> (1, 54)\

The permutation matrices for all actions are obtained from the 3 basic permutation matrices representing the actions [r], [u], and R.
Notation of actions

online solver
original subject

WydD for his Cube knowledge
dennybritz for examples that helped me build my estimators