> I was wondering what the next simplest shape similar to a moebius trefoil
> would be. It's fairly easy to make a 5-lobed knot similar to the 3-lobed
> trefoil, but my attempts to produce something with four lobes tended to
> produce structures that consisted of two loops with various degrees of
> linking between them. Then I happened to create this thing. I'm not sure if
> it's a knot or not.

Knot Theory - the theroy of knots and their properties - is a complex 
but (IMHO) fascinating theory.

One of the topics it deals with is whether to seemingly different 
arrangements of string are actually the same knot, arranged into a 
different position, or whether they actually *are* different.

In this theory, the simplest knot is the "unknot" or "trivial knot" - 
which is simply a closed loop of string. (Not necessarily a circle - you 
can actually rearrange it into constructions which *look* like a 
different knot. But if you made the thing out of physical string, you 
could quickly untangle it.)

Anyway, to determine whether your knot is the unknot or whether it's a 
"real knot", you could try computing one of the knot invariants on it... 
(Er... or you could wait a few minutes while *I* compute some 
invariants! :-S)

The idea of a knot invariant is that no matter how you rearrange the 
knot, you can still (fairly) easily compute the invariant from it, and 
you will still get the same answer. _However_, that doesn't mean two 
totally different knots can't just happen to have the same invariant.

Long story short: if two knots have a different invariant, they are NOT 
the same knot. If they have the same invariant, they MIGHT be the same knot.

Now, if you give me a moment, I'll just go Google the Jones polynomial...

Andrew.

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