Rubik's Cube Net: Permutation-Group Move Engine (2D)

Face Turns (real permutation generators)

Scramble

Scramble depth (random moves) 20

Live State

Moves made

Scramble length

State

SOLVED

Last move

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How it works

Every sticker is a point in 3D: (x, y, z) ∈ {−1, 0, 1}³, tagged with a colour. A face turn rotates all stickers whose coordinate along that face's axis equals the face's layer value (e.g. U turns every sticker with y = 1) by a real 90° rotation matrix about that axis — the same rigid transform a physical layer undergoes. The unfolded net below just re-projects each sticker's current (x, y, z) back onto its face's 3×3 grid cell, so what you see is a faithful readout of the permutation group state, not a decorative shuffle.

U (y=1):  x' = −z,  z' =  x
D (y=−1): x' =  z,  z' = −x
F (z=1):  x' =  y,  y' = −x
B (z=−1): x' = −y,  y' =  x
R (x=1):  y' =  z,  z' = −y
L (x=−1): y' = −z,  z' =  y
prime (') = same axis, opposite sign → inverse rotation

12 generators — U D L R F B and their inverses (U' D' L' R' F' B') — are the standard generating set of the Rubik's-cube group (order ≈4.3×10¹⁹).
Scramble applies N random generators in sequence; the move counter and scramble-length readout are independent so you can see exactly how many of your own turns it took relative to the scramble.
Solved detector checks all 54 stickers: solved iff every one of the 6 faces shows a single uniform colour across its 9 cells.

U (white) D (yellow) F (green) B (blue) L (orange) R (red)