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Did a little knot theory research in college too. But with Dowker notation.
It wasn't entirely clear from the wiki page, but can this notation be used to describe every type of tangled shape, including those such as the twisted proteins folding@home attempts to untangle?
My understanding of knot theory is pretty limited, but very few proteins are topologically different from a straight line—while there are lots of wiggles back and forth, if you pulled really hard on the ends, you would in most cases have no knots in it.
Got to love the number of fascinating things that carry Conways name.

I was searching for an interesting way to generate polyhedra and came across Conway Operators: https://en.wikipedia.org/wiki/Conway_polyhedron_notation

The results can be pretty awesome: http://elfnor.com/conway-polyhedron-operators-in-sverchok.ht... (not my code)

I've got a Unity based "toy" underway utilizing this. I'm currently struggling with adding a UI - mainly because that's the hardest and least interesting aspect of it to me :-(

https://github.com/Ixxy-Open-Source/wythoff-polyhedra

(The base contruction method is this: https://en.wikipedia.org/wiki/Wythoff_construction - the Conway operators are then used to further add complexity. I'm not sure if I can generate all the uniform polyhedra purely using Conway operators...)

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