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'One Reflection Implies Another' printed from http://nrich.maths.org/
This problem builds on from 'A Roll of Patterned Paper'
For the unit shapes I've tried so far I noticed something
When a strip maps to itself with a mirror line somewhere across it,
there always seems to be a second place where a mirror line would
also map the pattern to itself.
An illustration may help :
The mirror could be at position 1 or at position 2, either way the
reflection will map the pattern onto itself.
Your challenge :
Can you find a design with only one mirror line across the
Or perhaps, if you thought that was impossible, can you explain how
you could be sure about that?
If you're ready for more, try the problem called 'Rotations Aren't
Single Round Here'.