Rotations Are Not Single Round Here

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 one centre of rotation ? Or if you thought that was impossible, could you say why ?
Age
14 to 16
Challenge level
filled star filled star filled star
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



If you haven't seen the problem 'A Roll of Patterned Paper' you may want to try that first.

In that problem I'd been finding designs for streamers - this problem follows on from that.

I noticed this about the streamers that had rotation symmetry :

In the ones I tried, if there was one centre of rotation there always seems to be another centre that worked as well.

Rotations Are Not Single Round Here


Your challenge :

Can you find a design with only one centre of rotation?

Or if you thought that was in fact impossible, could you say why that's true ?

Taking it further :

I noticed that if there are mirror lines across the strip, and if there is also a horizontal mirror line, then the strip always seems to have rotation symmetry.

Can that be explained?