Remarkably, some of it is actually related to the Hodge Theory!

*Animation of the square in the plane.*

The configuration space of planar realizations of the "square" linkage

(polygon which has four equal sides), is not a circle but the union
of

three circles; each two of these circles share a common point.

The above animation illustrates three different irreducible components

of the configuration space. The realizations which look like parallelograms

correspond to one of these circles. The "folded" realizations correspond

to the two other circles.

Look here for a beautiful animation of the Peaucellier linkage.

Animation of a buckyball (carbon nanostructure).

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