><i>Going further, I note that the ideal bond length was given to me with just two significant digits, suggesting that an error of one part in a billion is much smaller than our uncertainty in measuring the “true” bond length in the first place.</i><p>Bonds are flexible and can hold mechanical stress, so there is only a "preferred" length, not a guaranteed length.
This touches on something I find fascinating: that in the pure world of perfect maths there's a lot of near misses, things that nearly work out but don't quite, but that if we have a world where a bit of error is allowed (our bendy molecular world, with our limited consciousness) then an enormous host of possibilities opens up. My personal theory is that this is exactly why we find ourselves in a reality that is slightly fuzzy with an awareness that's alright but not perfect.
For anyone interested in polyhedra I'd like to highlight the wonderful antiprism project:<p><a href="http://www.antiprism.com/" rel="nofollow">http://www.antiprism.com/</a><p>And the web-based Polyhedronisme for a quick fix: <a href="http://levskaya.github.io/polyhedronisme/" rel="nofollow">http://levskaya.github.io/polyhedronisme/</a><p>Finally (personal plug) I've been scratching my own polyhedral itch with a project that aims to cover similar ground but in a more interactive, visual way:<p><a href="https://github.com/IxxyXR/Polyhydra" rel="nofollow">https://github.com/IxxyXR/Polyhydra</a><p>(Example output: <a href="https://photos.google.com/album/AF1QipM029IxQ5P5FacaGywBPlxSLFFCtyCAXiWXX9p8" rel="nofollow">https://photos.google.com/album/AF1QipM029IxQ5P5FacaGywBPlxS...</a> )<p>One factor that unifies all three projects is conway operations discovered John "Game of Life" Conway: <a href="https://en.wikipedia.org/wiki/Conway_polyhedron_notation" rel="nofollow">https://en.wikipedia.org/wiki/Conway_polyhedron_notation</a> later investigated and expanded upon by George Hart - who is mentioned in the opening of the main article.
A graphic illustration of the molecule is here <a href="https://www.nature.com/articles/s41586-019-1185-4/figures/8" rel="nofollow">https://www.nature.com/articles/s41586-019-1185-4/figures/8</a>