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

This 2D companion trades the 3D version's orbiting cube for the standard unfolded cross-net view and puts the real mechanics on screen: every one of the 54 stickers lives at an integer (x, y, z) coordinate, and each of the 12 face-turn generators (U D L R F B, and their primes) applies an actual 90° rotation matrix to every sticker in that layer — the exact rigid transform a physical Rubik's Cube layer undergoes, not a repainted grid. A scramble button fires N random generators from that same move set, a move counter tracks your own turns separately from the scramble length, and a solved-state detector checks all 54 stickers on every move so you always know exactly how close the permutation is to identity.