A design is repeated endlessly along a line - rather like a stream of paper coming off a roll. Make a strip that matches itself after rotation, or after reflection
When a strip has vertical symmetry there always seems to be a second place where a mirror line could go. Perhaps you can find a design that has only one mirror line across it. Or, if you thought that. . . .
I noticed this about streamers that have rotation symmetry : if there was one centre of rotation there always seems to be a second centre that also worked. Can you find a design that has only. . . .
Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.
Make a footprint pattern using only reflections.
Nick Lord says "This problem encapsulates for me the best features of the NRICH collection."