Cube Playground

Free experimentation space! Apply moves, test formulas, explore sequences, and share your discoveries. Your cube state and move history are saved in the URL - bookmark interesting patterns!

Your Cube

✓ Cube is solved!

Quick Moves

Formula Input

Examples:

- Sexy Move
- OLL algorithm

Move History

No moves yet. Apply some moves to see history!

How to Use the Playground

Quick Moves: Click any button to apply that move to the cube
Formula Input: Enter sequences like "R U R' U'" or commutators like "[R, U]"
History: Undo/redo moves or jump to any point in your sequence
Share: Copy a URL with your current cube state and move sequence to share with others
Reset: Return to solved state while keeping your move history
Clear: Start fresh with an empty history

Suggested Experiments

1. Find Non-Commuting Moves

Try applying R U, then reset and try U R. Do they give the same result?

Hint: Most moves don't commute! This is a fundamental property of the cube group.

2. Test the Sexy Move

Apply [R, U] (which expands to R U R' U'). Repeat it 6 times. What happens?

Hint: You should return to the solved state! The order of [R, U] is 6.

3. Create Your Own Pattern

Experiment with sequences and find interesting patterns. When you find something cool, click Share to save it!

Hint: Try combining conjugates and commutators for complex patterns.

4. Test Inverses

Apply any sequence of moves, then apply the reverse with all moves inverted. Does it return to solved?

Hint: Every sequence has an inverse that undoes it completely!

Pro Tips

Notation: R, U, F, L, D, B for clockwise turns. Add ' for counter-clockwise (R'), or 2 for 180° (R2)
Commutators: Use [A, B] notation to automatically expand to A B A' B'
History: Click any move in the history to jump to that point
Sharing: The URL updates with your cube state - bookmark patterns you discover!
Analysis: The formula input shows pattern analysis and identifies known algorithms

Back to Group Theory Demos