Icositetrachoron

There are six convex regular 4-polytopes; five of these are the higher dimensional analogs of the Platonic solids, and one additional figure, the icositetrachoron, has no three-dimensional equivalent.

The icositetrachoron (hyperdiamond, octaplex or 24-cell) is the most unique polychoron, because it has no direct analog in any other dimension.

Shape of Nature comes from a unique, optimally symmetric geometric object: the sixth platonic element, the icositetrachoron (or 24-cell regular polytope), crystallized as a hyperdiamond network, mathematically and physically made of loops and connections.