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Rubik’s Cube

Rubik’s Cube. Rory Begin. The Rubik’s Cube. Faces F - front B - back L - left R - right U - up D - down. Construction. 27 small cubes 26 are “real” and visible from the outside “cubies” “cubicles” Center cubies stay in cubicles (don’t move”. Construction. Naming.

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Rubik’s Cube

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  1. Rubik’s Cube Rory Begin

  2. The Rubik’s Cube • Faces • F - front • B - back • L - left • R - right • U - up • D - down

  3. Construction • 27 small cubes • 26 are “real” and visible from the outside • “cubies” • “cubicles” • Center cubies stay in cubicles (don’t move”

  4. Construction

  5. Naming • Cubies & Cubicles: • Corner ufr • Edge fr • Center f

  6. Moves • Legal Moves - generated by {f,b,l,r,u,d} • Illegal Moves - legal moves and all other reconfigurations of cube - no pulling off stickers

  7. Legal Moves • Basic moves: rotate each face 90º “clockwise” • f • b • l • r • u • d Move shown: f

  8. Legal Moves Group • <G,*> • Elements: moves • * means sequential moves • Generated by {f, b, l, r, u, d}

  9. Is <G,*> a group? • Closed • Identity - “empty move” • Inverses - can undo any move • Associative - think about doing 3 moves

  10. Properties • Not abelian

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