Bonds are flexible and can hold mechanical stress, so there is only a "preferred" length, not a guaranteed length.
Protein design and fold prediction was being held back by using fixed (equilibrium) bond angles in proteins, and if you have enough CPU time, you can optimize those values (they often end up centering around non-equilibrium angles for the particular atom types) to get better predictions.
And the web-based Polyhedronisme for a quick fix: http://levskaya.github.io/polyhedronisme/
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:
(Example output: https://photos.google.com/album/AF1QipM029IxQ5P5FacaGywBPlxS... )
One factor that unifies all three projects is conway operations discovered John "Game of Life" Conway: https://en.wikipedia.org/wiki/Conway_polyhedron_notation later investigated and expanded upon by George Hart - who is mentioned in the opening of the main article.