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?
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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?