Having trouble wrapping your presents? Paper always ends up in a mess? Well, whatever geometrical shape you've accidentally produced, we bet it's not as wonderful as these favourites:

Take an illustrated tour of an extraordinary geometric construction: the Klein bottle.

What do butterflies, ketchup, microcellular structures, and plastics have in common? It's a curious minimal surface called the gyroid.

Sometimes the best way to express a scientific idea is through an image that grabs the eye and invites viewers to wonder what they're seeing. Artist Luc Benard and mathematician Richard Palais have done exactly this with their winning illustration "Still Life: Five Glass Surfaces on a Tabletop".

That geometry should be relevant to physics is no surprise — after all, space is the arena in which physics happens. What is surprising, though, is the extent to which the geometry of space actually determines physics and just how exotic the geometric structure of our Universe appears to be. This article explores the famous Calabi-Yau manifold.