Combining Symmetries

Order matters

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Doing one symmetry after another gives another symmetry.
• Order matters: R then F differs from F then R.
• Every symmetry has an inverse, and the identity does nothing.

Steps

1. Moves in sequence
2. Does order matter?
3. Back to the start
4. Undoing a move
5. Counting flips
6. A familiar pattern