Square Torus

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Square Torus

Postby kingmaz » Tue Dec 23, 2008 10:26 pm

Hi, it might be a daft question but bear with me, I'm new.

In the HDDB rotope list I note that there are the following realmic figures:

10 - ETQ - triangular torus
13 - ELQ - (circular) torus

Presumably EEQ would generate a square (sectional) torus, but is there a reason that there is no mention of this?
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Re: Square Torus

Postby Keiji » Wed Dec 24, 2008 12:26 am

Those codes are CSG notation, which is obsolete. I guess I should really edit the list page because CSG has been obsolete for way over a year or two now. :oops:

To answer your question though, yes, EEQ would produce a square torus. However, you can't represent a square torus in group notation. An ordinary torus is ((II)I) and a triangular torus is (I'I). The closest you can get to a square torus would be (III), but that is a sphere.
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Re: Square Torus

Postby kingmaz » Fri Dec 26, 2008 7:29 pm

Thanks for the reply.

It's a pity, as I quite like CSG notation because it's easy for duffers to understand, though the (II)' notation isn't too bad.

Does this all mean that this area of study is rather overly geared towards group theory then?
I'm sure there are many advantages to this for mathematicians and geometers, but are there many disadvantages?

I suppose, that a square torus might be represented by 'big cylinder minus small cylinder' (don't know if that works in group notation though).
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Re: Square Torus

Postby Keiji » Sat Dec 27, 2008 2:36 am

Group notation has nothing to do with group theory, and I know nothing about group theory anyway. :P

I suppose, that a square torus might be represented by 'big cylinder minus small cylinder' (don't know if that works in group notation though).


Well the only way you could do that would be to use CSG notation or SSC1. It is not a rotope. Put simply:
Shape X being a rotope <=> shape X being representable in group notation <=> shape X being representable in digit notation.
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Re: Square Torus

Postby kingmaz » Sat Dec 27, 2008 9:35 pm

Hayate wrote:Group notation has nothing to do with group theory


Gawd, it's no wonder I'm confused. :\
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Re: Square Torus

Postby wendy » Sun Dec 28, 2008 8:09 am

A square-torus is indeed permitted. One only has to look at a washer to see something that has a rectangular section and a circular locus. (locus here is the path of the shape, when the section is reduced to a point). A square torus might be given by (r, theta, z) (where r, theta replace x, y), as max(abs r-c, z) =1, where c is the radius of the locus, r, z are coordinates. Points less than 1 lie in the centre.
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Re: Square Torus

Postby Keiji » Sun Dec 28, 2008 12:59 pm

Yes you can have a square torus, it just doesn't exist within the set of rotopes.

Sadly it also does not exist within the set of objects representable by SSC2.
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