[r-t] Symmetries

[Richard Smith]

Don Morrison wrote:

> What exactly are "glide" and "rotational" symmetry in a method?

Glide symmetry is when a method grid is unchanged by
reflection in a vertical plane, followed by a
half-lead translation.  It is the symmetry of Double Eastern
Bob Major, Double Cambridge Cyclic Bob Major and Double
Resurrection Cyclic Bob Royal.  It is sometimes also called
Double symmetry.

Rotational symmetry is when a method grid is unchanged by a
180-degree rotation.  It is symmetry of Purple Cyclic Bob
Major.

Depending on your point of view, mirror symmetry can either
be viewed as a distinct symmetry (and, assuming you have the
shortest choice of lead, it is mutually exclusive with glide
symmetry), or as a form of glide symmetry (but without the
translation phase).

Phil's webpage gives more examples of these:

  http://ringing.8bit.co.uk/sym.html

And for a more mathematical treatment, Martin has written a
short article on it:

  http://www.boojum.org.uk/ringing/symmetry.pdf

> Are they, together with the usual palindromic symmetry and
> the symmetry of a double method the only interesting
> symmetries a method can possess, or are there others?

Glide symmetry *is* the symmetry of a double method.

> Indeed, is the symmetry of a double method
> something different, or is it perhaps a combination of the usual
> palindromic symmetry with one of the others?

No; any two of glide, rotational and palindromic symmetry
implies the third.

RAS