Re: terminology for symmetry of cylinders

[Joel Rauber <Joel_Rauber@SDSTATE.EDU>]

> At 02:07 PM 1/22/01 -0500, Carl E. Mungan wrote:
> > *What, if anything, is the distinction between cylindrical, axial,
> > and azimuthal symmetry?
>
> I don't use those terms, and I don't recommend them.  For constructive
> counterproposals, see below.

I'm not a strict adherent to John's statement as the words above are nice
and short and descriptive and don't involve arcane crystallographic
nomenclature. OTOH they have their own elements of arcanity? about them and
are somewhat ambigous as John has pointed out.

A question to John:


> > In your reply, consider the following three
> > shapes for instance:
> >
> > (a) an infinitely long, straight, constant-diameter piece of
> spaghetti
> > (b) a finite-length, straight, constant-diameter piece of spaghetti
> > (c) an infinitely long, straight piece of spaghetti whose diameter
> > varies sinusoidally with distance along its axis
>
>
> a) This can be constructed as the product of three symmetries:
>     a1) rotational symmetry around the z-axis
>     a2) reflection symmetry in any plane perpendicular to the z axis
>     a3) translational invariance along the z-axis

Doesn't a2 (particularly with the word *any* in it) imply a3?