According to string theory, spacetime as we know it isn't 4-dimensional, but 10-dimensional. The next question is, where are the extra 6 dimensions that we don't see? One answer is that they're 'compactified': roughly speaking, rolled up into such a small shape that they're unobservable by humans.
Calabi-Yau spaces may be that submicroscopic shape. There are many such spaces, but being 6-dimensional, they're not easy to draw! This model is a 3D cross-section through a likely space. Surprisingly it's beautiful – a wildly self-intersecting ride.
Too small? Mega Calabi-Yau Manifold is here.
Laser etched glass