models of the 35 smallest fullerenes
I noticed that Shapeways had 13 models of the roundest of the fullerenes (one of the 1812 forms of C60), but none of the less regular forms; so I made some.
Each of the white pieces has mirror symmetry; the red pieces are chiral. Not shown (because it hasn’t been printed yet): the blue set, which is a reflection of the red set. The idea is that you buy both red and blue if and only if you count reflected chiral forms separately.
These figures have 12 pentagons and up to 8 hexagons. They include the two smallest forms with no nontrivial symmetries, and the two smallest with no ‘peaks’ where three pentagons meet.
When someone other than me tried to order a set in color, a Shapeways bot found that it may be too thin to survive the polishing process — though mine obviously did. Evidently they’re more liberal in what they’ll sell to the designer than in what they’ll sell to others.
It’s odd that they stopped selling unpolished colored plastic. Odd, too, that the available colors do not include yellow or green.
At least one of my pieces has a break. I’ve taken the fullerenes out of my catalog; I intend to replace them anyway, with thicker “pseudo-fullerenes” whose faces are planar and as nearly regular as can be. I think they’ll be prettier, anyway, and easier for the eye to understand.
Polished plastic takes the dyes better. They’ve added colors.
[This is spam, but not uninteresting, so I keep it but remove the link.]
I find this discussion of miakng sure we create friendly AI fascinating. My take is that the challenge of value misalignment goes far deeper than many seem to have articulated. Let us put aside AI for a moment. Individual humans’ values are not exactly aligned with others. Even within a marriage or close relationship value misalignment is a challenge we deal with constantly. How do we manage this when each of us has what amounts to a host of chaotic and ever-competing utility functions (designed by evolution) vying for exclusive control of our prefrontal cortex. What brings equilibrium/harmony/tranquility? I would argue that equality in standing/power/influence as individuals is what stabilizes the system.Would you trust your neighbor to be endowed with some arbitrary superhuman ability? How would we feel if there were a cohort of people who were so much more intelligent than us such that they could manipulate or use the masses to satisfy their every whim? These scenarios are not palatable to me much less the granting of a machine these powers.One might argue that we could create super-human AI that is perfectly human-like minus the mammalian aggression. I would argue that it is exactly that that motivates us all to work hard, achieve higher, and solve the unsolved (as a byproduct of the drive to defend ourselves and compete for sustenance and mates). If we were to create such a being with the raw intelligence to understand what mankind cannot, why would it want to? So we come back to miakng it human-like. I don’t care whether it’s a post-human or a machine, I don’t see how human society will trust any being with greatly augmented abilities. The only peaceful solution to this problem I see is an incremental elevation of all individuals together. But there will be the luddites .