Rubik s cube
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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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Rubik s cube

Rubik’s Cube

Rory Begin


The rubik s cube

The Rubik’s Cube

  • Faces

    • F - front

    • B - back

    • L - left

    • R - right

    • U - up

    • D - down


Construction

Construction

  • 27 small cubes

    • 26 are “real” and visible from the outside

  • “cubies”

  • “cubicles”

  • Center cubies stay in cubicles (don’t move”


Construction1

Construction


Naming

Naming

  • Cubies & Cubicles:

    • Corner ufr

    • Edge fr

    • Center f


Moves

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


Legal moves

Legal Moves

  • Basic moves: rotate each face 90º “clockwise”

    • f

    • b

    • l

    • r

    • u

    • d

Move shown: f


Legal moves group

Legal Moves Group

  • <G,*>

    • Elements: moves

    • * means sequential moves

  • Generated by {f, b, l, r, u, d}


Is g a group

Is <G,*> a group?

  • Closed

  • Identity - “empty move”

  • Inverses - can undo any move

  • Associative - think about doing 3 moves


Properties

Properties

  • Not abelian


  • Login