Rotational symmetry

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 brianvds (February 19, 2015, 04:52:47 AM):
Short and to the point: can a 2D shape have an order of rational symmetry of 1? What kind of shape would that be?
 Rigil Kent (February 19, 2015, 06:35:42 AM):
Apparently not, as explained here.
 brianvds (February 19, 2015, 15:06:40 PM):
And I assume then that an asymmetrical shape would have a symmetry order of zero?

I just wanted to make sure the stuff in the grade 6 textbook is correct. :-)
 Mefiante (February 19, 2015, 16:01:13 PM):
Actually, it would have a rotational symmetry of order 1 because there is only one orientation in which its outline matchesâ€¦ >:D

'Luthon64
 brianvds (February 20, 2015, 04:14:03 AM):
Actually, it would have a rotational symmetry of order 1 because there is only one orientation in which its outline matchesâ€¦ >:D

'Luthon64

Well, that is my whole problem. In the textbook's "teacher's guide," which contains answers to the exercises, such a shape is claimed to have a symmetry order of zero. Now I still can't work out whether that is correct or not, because your smiley face indicates that your reply above may or may not be entirely serious.

If something like a propeller has an order of 2, i.e. we count the original position (or the 360 degree rotation, which comes to the same thing), then logic would suggest that in a shape lacking rotational symmetry, we should still count the original position as 1. I can't work out whether this is what is in fact done because of conflicting reports from various authorities. :-)