Nice article. The expansion of Euclidean geometry into hyperbolic and elliptical space did change all this fundamentally, most popularly seen in MC Escher's work. Here for example is a hyperbolic dodecahedron (in which each pentagon has five right angles).

http://www.bulatov.org/math/1101/webtalk.html#(38)

That site also has a lot of other nice examples and analysis of MC Escher drawings.

What is mindlbowing to me is that all this work on geometry was initially done when there was absolutely no concept of atomic particles, and very little real representation in "visible" nature.

Then hundreds of years later we started to look at macromolecules and found their assembly states often are perfect, or near-perfect representations of platonic solids, such as icosahedral viruses, octohedral and tetrahedral iron storage proteins, etc.

Why is it mind-blowing?

You don't need atomic model to build polyhedra at macro scale (aka dice).

Atomic stuff was going to look like something once we could see or simulate it.