simont | (no subject)

(no subject)

Oh yes, and I've just added some more Stuff to my website. It's now getting to the point where I might have to fiddle with the front page so that it has a usable index; all this chatty text introducing each of my subpages is fine if you're reading it because you want to know about me, but even I'm increasingly finding it a pain when I actually want to find a specific page.

Still. For anyone with any interest in polyhedra, or even simply with a desire to look at some pretty pictures or see what weird mathematical things I've been up to recently when I should have been lying on my sofa watching DVDs, you can now go and look at http://www.chiark.greenend.org.uk/~sgtatham/polyhedra/.

Now, with any luck, I ought to be able to actually relax for a bit. These momentary obsessions tend to take me over totally for a week or so, but then leave me in peace after that…

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I don't believe that your 60-vertex solid really *is* that different from buckminsterfullerene. I can clearly see hexagons and pentagons in there, you just have an extra vertex in the centre of each face connected to all the corners. I wonder what happens if you start from an an example pentagon, pretend it's a flat face and remove the internal lines crossing the face, then move outwards to the hexagons and pentagons surrounding that, etc. Do you get anything that makes any sense?

I think one of the reasons you always get triangles with the vertex construction is that you've given yourself no maximum limit on how many edges can meet at any given vertex - thus of course as the number of points goes up, the face size will decompose down to a triangle.

When you're talking atoms, you can't approximate them as points, you'd have to approximate them as points *which must have a specific number of connections* - do you get anything interesting if try to build this kind of restriction into your models?

This all reminds me about some inorganic chemistry lectures I once went to. IIRC small clusters of metal atoms like to form constrained-to-sphere shapes, with a strong preference for lots of triangles.

I wonder about the other good way of arranging 8 points: an octahedron with two opposing faces being 'capped' by an extra vertex. Does your algorithm always get the global minimum?

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