When it comes to 2D shapes, however, it gets a bit harder since none of them have the perfect beauty of an icosahedron. If I had to choose I guess it would be a hexagon - a regular one, naturally, purely for it's tessellatability. The fact that the hexagon tessellates so beautifully is a slight downfall as it means there can be no hexagon-based Platonic solids. Don't worry though, you can still have a largely hexagon-based solid - but it'll be an Archimedean solid instead of a Platonic one - like my second favourite 3D shape, the truncated icosahedron. It has some pentagons in it too, but we can just ignore them.
Icosahedra aren't the most easy shape to find, so let's go with some hexagonal pretties today:
And of course, here's a little reminder of everyone's favourite set of hexagons...
Any of you have a different favourite shape?