Talk:Conway notation (knot theory)

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I made this page in my user space, then moved it here. Unfortunately, I don't understand this subject too well, so it would be nice if someone could clarify some issues like: I'm also working on some pictures to explain the operations on the tangles.  J kasd  00:33, 23 April 2008 (UTC)
 * When forming into a knot, how are all the loose ends connected?
 * What does the * mean and how is it used?
 * Check all statements for factual accuracy.
 * Clean-up, add subsections, etc...


 * Since each tangle has four ends and every vertex has four edges, connect the tangles using the edges.
 * The "*" is just used to separate the polyhedron number from the other numbers. Additional "*"s are used to distinguish when there are several basic polyhedron types with the same number of vertices.
 * I'm afraid the additions to the copy of the section from knot theory (any copying by the way needs to be noted in the edit summary or talkpage for GFDL purposes) are not good.
 * The sectioning is rather bizarre. I don't know why one thing is called a "basic concept" but another is called "advanced".  The advanced concepts seem to be limited to just how to write down the tangles, which I would consider "basic".

It's probably better to expand and improve Tangle (mathematics) than to put too much of that here. For example, explanations and pictures of the Conway operations could go there. --C S (talk) 18:34, 5 May 2008 (UTC)


 * Basically, I was hoping someone else would clarify the article; after all, I mainly wrote it in hopes that I could learn more about it. I have Colin Adam's book, but that doesn't explain the polyhedra stuff, and I couldn't find any websites that really explained anything very well, so I made this article so that someone who knew about it could explain this stuff for me, and for everyone who wishes to learn more about it.  J kasd  04:27, 8 May 2008 (UTC)

I've added the picture, hopefully its correct and clear. If not, it's easily fixable.  J kasd  05:40, 8 May 2008 (UTC)

Can every knot be represented through these tangles?
-Question: Can every knot be represented through these tangles? Seems like this is the hope, but it is not clearly stated whether all knots can be expressed this way - Dragonflare82


 * Is there an algorithm to transform a knot projection into its Conway notation ? And does it only produce one notation from any knot projection ? Are distinct notations sure to produce different knots (rather than just different knot projections) ? - Rod57 (talk) 00:10, 9 June 2023 (UTC)

stars, periods and colons
In List of prime knots I see stars, periods and colons, e.g. [8*] and [.2.20.2]. What the what? This is so confusing, I feel like my brain's tangled up in knots.2001:558:6033:154:5800:776D:FCC3:B67B (talk) 20:49, 16 January 2015 (UTC)

Suggestions - start by adding examples
Please add examples for some of the simpler knots eg trefoil, figure-8, (as in list of prime knots) and show how the notation and knot are derived from each other. Perhaps later add the full syntax of the notation. and enough examples to show all parts of the syntax. - Rod57 (talk) 22:58, 8 June 2023 (UTC)

- Looking at the tangles article didn't help much; Where does it say how to relate a knot to its tangles or vice versa ? eg do you connect adjacent or opposite ends of the tangle arcs to form the knot, or do you just pick the one that gives a knot rather than 2 links ? - Rod57 (talk) 23:50, 8 June 2023 (UTC)