What's the name of this kind of symmetry in roundish objects?

[Napier]

In finite element modeling it is common to identify symmetries and reduce the region modeled to the smallest possible repeat cell. One kind of symmetry occurs in round objects that have circular arrays of features, like an automobile wheel with 5 holes for the mounting studs. Obviously one could take 1/5 of this object to model, but even that would be symmetrical through one plane if chosen properly, so such a wheel could be reduced to 1/10 of a circle, a 36 degree wedge.

What is the name of this kind of symmetry? Is it a periodic rotational symmetry? an alternating tenfold angular symmetry? What?

Thanks!!

[naita]

LMWTFY

Generally speaking, an object with rotational symmetry, also known in biological contexts as radial symmetry, is an object that looks the same after a certain amount of rotation. An object may have more than one rotational symmetry; for instance, if reflections or turning it over are not counted. The degree of rotational symmetry is how many degrees the shape has to be turned to look the same on a different side or vertex. It can not be the same side or vertex.

Rotational symmetry of order n, also called n-fold rotational symmetry, or discrete rotational symmetry of the nth order, with respect to a particular point (in 2D) or axis (in 3D) means that rotation by an angle of 360°/n (180°, 120°, 90°, 72°, 60°, 51°, etc.) does not change the object. Note that “1-fold” symmetry is no symmetry, and “2-fold” is the simplest symmetry, so it does not mean “more than basic”.

Rotational symmetry

[naita]

I see on a second read-through that you specifically mean rotational symmetries where the subunits are also symmetric around a radius, but I expect that doesn’t have a single ubiquitous name.

[Chronos]

That’s not the whole question, though. A swastika, for instance, has rotational symmetry, but not the sort of symmetry the OP is talking about, which is a combination of rotational and reflectional symmetry. Which I don’t think has any better name than “a combination of rotational and reflectional symmetry”.

[Ronald_Raygun]

I’d call your example of a wheel with five spokes D5h. A printed swastika would be C4.

These designations are called point groups: http://en.wikipedia.org/wiki/Point_group

Since I assume you’re only dealing with 3D objects, this next link may be more helpful. There are plenty of examples as well:

http://en.wikipedia.org/wiki/Molecular_symmetry

Edit: It seems that objects like your wheel have an English name as well: prismatic symmetry.